From 2c3752ae77103daec44ef3aef54c27f3457bfea4 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 13 Jul 2024 14:44:23 +0000 Subject: [PATCH] build based on 7f25a55 --- dev/.documenter-siteinfo.json | 2 +- dev/api/index.html | 18 +++++++++--------- dev/devdocs/index.html | 2 +- dev/examples/do-events/index.html | 2 +- dev/examples/ks_paleojump/6095c805.png | Bin 116196 -> 0 bytes dev/examples/ks_paleojump/7f9aca8d.png | Bin 0 -> 111314 bytes dev/examples/ks_paleojump/index.html | 4 ++-- dev/examples/logistic/27b70793.png | Bin 420431 -> 0 bytes dev/examples/logistic/ca9a6665.png | Bin 0 -> 408872 bytes dev/examples/logistic/dbc91bc3.png | Bin 0 -> 289274 bytes dev/examples/logistic/ff089469.png | Bin 300115 -> 0 bytes dev/examples/logistic/index.html | 6 +++--- dev/index.html | 2 +- dev/refs/index.html | 2 +- dev/tutorial/54ebd095.png | Bin 518263 -> 0 bytes dev/tutorial/8c762359.png | Bin 0 -> 521070 bytes dev/tutorial/a3381ef2.png | Bin 289739 -> 0 bytes dev/tutorial/d9311396.png | Bin 0 -> 297885 bytes dev/tutorial/index.html | 4 ++-- 19 files changed, 21 insertions(+), 21 deletions(-) delete mode 100644 dev/examples/ks_paleojump/6095c805.png create mode 100644 dev/examples/ks_paleojump/7f9aca8d.png delete mode 100644 dev/examples/logistic/27b70793.png create mode 100644 dev/examples/logistic/ca9a6665.png create mode 100644 dev/examples/logistic/dbc91bc3.png delete mode 100644 dev/examples/logistic/ff089469.png delete mode 100644 dev/tutorial/54ebd095.png create mode 100644 dev/tutorial/8c762359.png delete mode 100644 dev/tutorial/a3381ef2.png create mode 100644 dev/tutorial/d9311396.png diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 8d7c744..5e62ca9 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-13T13:54:19","documenter_version":"1.5.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-07-13T14:44:16","documenter_version":"1.5.0"}} \ No newline at end of file diff --git a/dev/api/index.html b/dev/api/index.html index 259a237..5506200 100644 --- a/dev/api/index.html +++ b/dev/api/index.html @@ -1,18 +1,18 @@ -API · TransitionsInTimeseries.jl

API

Main analysis functions

TransitionsInTimeseries.estimate_changesFunction
estimate_changes(config::ChangesConfig, x [,t]) → result

Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see ChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

Return the output as subtype of ChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

source

Sliding window

TransitionsInTimeseries.SlidingWindowConfigType
SlidingWindowConfig <: ChangesConfig
+API · TransitionsInTimeseries.jl

API

Main analysis functions

TransitionsInTimeseries.estimate_changesFunction
estimate_changes(config::ChangesConfig, x [,t]) → result

Estimate possible transitions for input timeseries x using the approach specified in the configuration type config, see ChangesConfig for possibilities. t is the time vector corresponding to x, which defaults to eachindex(x).

Return the output as subtype of ChangesResults. The particular form of the output depends on the config and is described in its docstring. Regardless of type, result can always be given to significant_transitions to deduce which possible transitions are statistically significant using a variety of significance tests.

source

Sliding window

TransitionsInTimeseries.SlidingWindowConfigType
SlidingWindowConfig <: ChangesConfig
 SlidingWindowConfig(indicators, change_metrics; kwargs...)

A configuration that can be given to estimate_changes. It estimates transitions by a sliding window approach:

  1. Estimate the timeseries of an indicator by sliding a window over the input timeseries.
  2. Estimate changes of an indicator by sliding a window of the change metric over the indicator timeseries.

Both indicators and change metrics are generic Julia functions that input an x::AbstractVector and output an s::Real. Any function may be given and see making custom indicators/change metrics in the documentation for more information on possible optimizations.

indicators can be a single function or a tuple of indicators. Similarly, change_metrics can be a tuple or a single function. If tuples, the length of indicators and change_metrics must match. This way the analysis can be efficiently repeated for many indicators and/or change metrics.

The results output corresponding to SlidingWindowConfig is SlidingWindowResults.

Step 1. is skipped if nothing is provided as indicators, in which case the change metrics are estimated directly from input data.

Keyword arguments

  • width_ind::Int=100, stride_ind::Int=1: width and stride given to WindowViewer to compute the indicator from the input timeseries.
  • width_cha::Int=50, stride_cha::Int=1: width and stride given to WindowViewer to compute the change metric timeseries from the indicator timeseries.
  • whichtime = midpoint: The time vector corresponding to the indicators / change metric timeseries is obtained from t in estimate_changes using the keyword whichtime. Options include:
    • last: use the last timepoint of each window
    • midpoint: use the mid timepoint of each time window
    • first: use first timepoint of each window
    In fact, the indicators time vector is computed simply via
    t_indicator = windowmap(whichtime, t; width_ind, stride_ind)
    -t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
    so any other function of the time window may be given to extract the time point itself, such as mean or median.
  • T = Float64: Element type of input timeseries to initialize some computations.
source
TransitionsInTimeseries.SlidingWindowResultsType
SlidingWindowResults <: ChangesResults

A struct containing the output of estimate_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

It has the following fields that the user may access

  • x: the input timeseries.

  • t: the time vector of the input timeseries.

  • x_indicator, the indicator timeseries (matrix with each column one indicator).

  • t_indicator, the time vector of the indicator timeseries.

  • x_change, the change metric timeseries (matrix with each column one change metric).

  • t_change, the time vector of the change metric timeseries.

  • config::SlidingWindowConfig, what was used for the analysis.

source

Segmented window

TransitionsInTimeseries.SegmentedWindowConfigType
SegmentedWindowConfig <: IndicatorsChangeConfig
-SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

A configuration that can be given to estimate_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

  1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
  2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

Keyword arguments

  • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
  • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
source
TransitionsInTimeseries.SegmentedWindowResultsType
SegmentedWindowResults <: ChangesResults

A struct containing the output of estimate_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

It has the following fields that the user may access

  • x: the input timeseries.

  • t: the time vector of the input timeseries.

  • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

  • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

  • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

  • t_change, the time vector of the change metric.

  • config::SegmentedWindowConfig, what was used for the analysis.

  • i1::Vector{Int} indices corresponding to start time of each segment.

  • i2::Vector{Int} indices corresponding to end time of each segment.

  • precomp_change_metrics vector containing the precomputed change metrics of each segment.

source

Slope change

TransitionsInTimeseries.SlopeChangeConfigType
SlopeChangeConfig <: ChangesConfig
-SlopeChangeConfig(; indicator = nothing, kw...)

A configuration that can be given to estimate_changes. It estimates a change of slope in the timeseries by fitting two connected linear segments to the timeseries, returning the results (i.e., the two-linear fits) as SlopeChangeResults.

Keyword arguments

  • indicator = nothing: if not nothing. Otherwise it should be a function f(x) -> Real. The slope fitting is then done over an indicator of the timeseries, which itself is estimated via a sliding window exactly as in SlidingWindowConfig.
  • width_ind, stride_ind, whichtime: exactly as in SlidingWindowConfig if indicator is not nothing.
source
TransitionsInTimeseries.SlopeChangeResultsType
SlopeChangeResults <: ChangesResults

A struct containing the output of estimate_changes used with SlopeChangeConfig. It can be used for further analysis, visualization, or given to significant_transitions. The only significance type that you can use this with significant_transitions is SlopeChangeSignificance.

It has the following fields that the user may access:

  • x: the input timeseries.
  • t: the time vector of the input timeseries.
  • x_indicator, the indicator timeseries.
  • t_indicator, the time vector of the indicator timeseries.
  • t_change, the time the slope changes.
  • fitparams = a, b, c, d, the fitted linear coefficients, a + b*t before. t_change and c + d*t after t_change.
source

Significance testing

TransitionsInTimeseries.significant_transitionsFunction
significant_transitions(res::ChangesResults, signif::Significance)

Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as the changes stored in res (which typically is stored in the field res.x_change). flags is true wherever a change metric of res is deemed significant.

source
TransitionsInTimeseries.SurrogatesSignificanceType
SurrogatesSignificance <: Significance
-SurrogatesSignificance(; kwargs...)

A configuration struct for significance testing significant_transitions using timeseries surrogates.

Keyword arguments

  • surromethod = RandomFourier(): method to generate surrogates
  • n = 1000: how many surrogates to generate
  • rng = Random.default_rng(): random number generator for the surrogates
  • p = 0.05: threshold for significance of the p-value
  • tail = :both: tail type used, see below

Description

When used with ChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in ChangesResults.

Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

source
TransitionsInTimeseries.ThresholdSignificanceType
ThresholdSignificance(threshold::Real; tail = :right) <: Significance

A configuration struct for significance testing in significant_transitions. Significance is estimated by comparing the value of each change metric with the given threshold. Values that exceed the threshold (if tail = :right) or subseed the threshold (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

source
TransitionsInTimeseries.SigmaSignificanceType
SigmaSignificance(; factor = 3.0, tail = :both) <: Significance

A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing how many standard deviations (σ) the value exceeds the mean value (μ). Values that exceed (if tail = :right) μ + factor*σ, or subseed (if tail = :left) μ - factor*σ are deemed significant. If tail = :both then either condition is checked.

factor can also be a vector of values, in which case a different value is used for each change metric.

See also QuantileSignificance.

source
TransitionsInTimeseries.QuantileSignificanceType
QuantileSignificance(; p = 0.95, tail = :both) <: Significance

A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

source
TransitionsInTimeseries.SlopeChangeSignificanceType
SlopeChangeSignificance(; moe_slope, moe_offset, slope_diff = moe_slope, pvalue = 0.05)

Test whether the result of SlopeChangeResults is statistically significant.

Two tests are done:

  1. Check whether the margin of error of the fitted parameters a, b, c, d of the two linear segments a + b*t, c + d*t is less than the specified margins of error, for a chosen pvalue.
  2. Test that the two slopes b, d have difference greater than slope_diff.

The Boolean & of the above two is the final test.

The margin of error is simply half the size of the confidence interval, also known as radius of the confidence interval.

source

Indicators

Note that any Julia function can be an indicator or change metric, so the list here is only just a couple of indicators directly implemented in this package.

Value distribution

Statistics.meanFunction
mean(A::AbstractArray, w::AbstractWeights[, dims::Int])

Compute the weighted mean of array A with weight vector w (of type AbstractWeights). If dim is provided, compute the weighted mean along dimension dims.

Examples

n = 20
+t_change = windowmap(whichtime, t_indicator; width_cha, stride_cha)
so any other function of the time window may be given to extract the time point itself, such as mean or median.
  • T = Float64: Element type of input timeseries to initialize some computations.
  • source
    TransitionsInTimeseries.SlidingWindowResultsType
    SlidingWindowResults <: ChangesResults

    A struct containing the output of estimate_changes used with SlidingWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

    It has the following fields that the user may access

    • x: the input timeseries.

    • t: the time vector of the input timeseries.

    • x_indicator, the indicator timeseries (matrix with each column one indicator).

    • t_indicator, the time vector of the indicator timeseries.

    • x_change, the change metric timeseries (matrix with each column one change metric).

    • t_change, the time vector of the change metric timeseries.

    • config::SlidingWindowConfig, what was used for the analysis.

    source

    Segmented window

    TransitionsInTimeseries.SegmentedWindowConfigType
    SegmentedWindowConfig <: IndicatorsChangeConfig
    +SegmentedWindowConfig(indicators, change_metrics, tseg_start, tseg_end; kwargs...)

    A configuration that can be given to estimate_changes. It estimates transitions by estimating indicators and changes in user-defined window segments as follows:

    1. For each segment specified, estimate the corresponding indicator timeseries by sliding a window over the input timeseries (within the window segment).
    2. For each segment of the indicator timeseries, estimate a scalar change metric by applying the change metric over the full segment of the indicator timeseries.d

    tseg_start, tseg_end are the starts and ends of the window segments (the window segments may overlap, that's okay). indicators, change_metrics are identical as in SlidingWindowConfig.

    The results output corresponding to SlidingWindowConfig is SegmentedWindowResults.

    Keyword arguments

    • width_ind::Int=100, stride_ind::Int=1, whichtime = midpoint, T = Float64: keywords identical as in SlidingWindowConfig.
    • min_width_cha::Int=typemax(Int): minimal width required to perform the change metric estimation. If a segment is not sufficiently long, the change metric is NaN.
    source
    TransitionsInTimeseries.SegmentedWindowResultsType
    SegmentedWindowResults <: ChangesResults

    A struct containing the output of estimate_changes used with SegmentedWindowConfig. It can be used for further analysis, visualization, or given to significant_transitions.

    It has the following fields that the user may access

    • x: the input timeseries.

    • t: the time vector of the input timeseries.

    • x_indicator::Vector{Matrix}, with x_indicator[k] the indicator timeseries (matrix with each column one indicator) of the k-th segment.

    • t_indicator::Vector{Vector}, with t_indicator[k] the time vector of the indicator timeseries for the k-th segment.

    • x_change::Matrix, the change metric values with x[k, i] the change metric of the i-th indicator for the k-th segment.

    • t_change, the time vector of the change metric.

    • config::SegmentedWindowConfig, what was used for the analysis.

    • i1::Vector{Int} indices corresponding to start time of each segment.

    • i2::Vector{Int} indices corresponding to end time of each segment.

    • precomp_change_metrics vector containing the precomputed change metrics of each segment.

    source

    Slope change

    TransitionsInTimeseries.SlopeChangeConfigType
    SlopeChangeConfig <: ChangesConfig
    +SlopeChangeConfig(; indicator = nothing, kw...)

    A configuration that can be given to estimate_changes. It estimates a change of slope in the timeseries by fitting two connected linear segments to the timeseries, returning the results (i.e., the two-linear fits) as SlopeChangeResults.

    Keyword arguments

    • indicator = nothing: if not nothing. Otherwise it should be a function f(x) -> Real. The slope fitting is then done over an indicator of the timeseries, which itself is estimated via a sliding window exactly as in SlidingWindowConfig.
    • width_ind, stride_ind, whichtime: exactly as in SlidingWindowConfig if indicator is not nothing.
    source
    TransitionsInTimeseries.SlopeChangeResultsType
    SlopeChangeResults <: ChangesResults

    A struct containing the output of estimate_changes used with SlopeChangeConfig. It can be used for further analysis, visualization, or given to significant_transitions. The only significance type that you can use this with significant_transitions is SlopeChangeSignificance.

    It has the following fields that the user may access:

    • x: the input timeseries.
    • t: the time vector of the input timeseries.
    • x_indicator, the indicator timeseries.
    • t_indicator, the time vector of the indicator timeseries.
    • t_change, the time the slope changes.
    • fitparams = a, b, c, d, the fitted linear coefficients, a + b*t before. t_change and c + d*t after t_change.
    source

    Significance testing

    TransitionsInTimeseries.significant_transitionsFunction
    significant_transitions(res::ChangesResults, signif::Significance)

    Estimate significant transtions in res using the method described by signif. Return flags, a Boolean matrix with identical size as the changes stored in res (which typically is stored in the field res.x_change). flags is true wherever a change metric of res is deemed significant.

    source
    TransitionsInTimeseries.SurrogatesSignificanceType
    SurrogatesSignificance <: Significance
    +SurrogatesSignificance(; kwargs...)

    A configuration struct for significance testing significant_transitions using timeseries surrogates.

    Keyword arguments

    • surromethod = RandomFourier(): method to generate surrogates
    • n = 1000: how many surrogates to generate
    • rng = Random.default_rng(): random number generator for the surrogates
    • p = 0.05: threshold for significance of the p-value
    • tail = :both: tail type used, see below

    Description

    When used with ChangesResults, significance is estimated as follows: n surrogates from the input timeseries are generated using surromethod, which is any Surrogate subtype provided by TimeseriesSurrogates.jl. For each surrogate, the indicator and then change metric timeseries is extracted. The values of the surrogate change metrics form a distribution of values (one at each time point). The value of the original change metric is compared to that of the surrogate distribution and a p-value is extracted according to the specified tail. The p-value is compared with p to claim significance. After using SurrogatesSignificance, you may access the full p-values before thresholding in the field .pvalues (to e.g., threshold with different p).

    The p-value is simply the proportion of surrogate change metric values that exceed (for tail = :right) or subseed (tail = :left) the original change metric at each given time point. Use tail = :left if the surrogate data are expected to have higher change metric values. This is the case for statistics that quantify entropy. For statistics that quantify autocorrelation, use tail = :right instead. For anything else, use the default tail = :both. An iterable of tail values can also be given, in which case a specific tail is used for each change metric in ChangesResults.

    Note that the raw p-values can be accessed in the field .pvalues, after calling the significant_transitions function with SurrogatesSignificance, in case you wish to obtain a different threshold of the p-values.

    source
    TransitionsInTimeseries.ThresholdSignificanceType
    ThresholdSignificance(threshold::Real; tail = :right) <: Significance

    A configuration struct for significance testing in significant_transitions. Significance is estimated by comparing the value of each change metric with the given threshold. Values that exceed the threshold (if tail = :right) or subseed the threshold (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

    source
    TransitionsInTimeseries.SigmaSignificanceType
    SigmaSignificance(; factor = 3.0, tail = :both) <: Significance

    A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing how many standard deviations (σ) the value exceeds the mean value (μ). Values that exceed (if tail = :right) μ + factor*σ, or subseed (if tail = :left) μ - factor*σ are deemed significant. If tail = :both then either condition is checked.

    factor can also be a vector of values, in which case a different value is used for each change metric.

    See also QuantileSignificance.

    source
    TransitionsInTimeseries.QuantileSignificanceType
    QuantileSignificance(; p = 0.95, tail = :both) <: Significance

    A configuration struct for significance testing significant_transitions. When used with ChangesResults, significance is estimated by comparing the value of each change metric with its p-quantile. Values that exceed the p-quantile (if tail = :right) or subseed the 1-p-quantile (if tail = :left) are deemed significant. If tail = :both then either condition is checked.

    QuantileSignficance guarantees that some values will be significant by the very definition of what a quantile is. See also SigmaSignificance that is similar but does not have this guarantee.

    source
    TransitionsInTimeseries.SlopeChangeSignificanceType
    SlopeChangeSignificance(; moe_slope, moe_offset, slope_diff = moe_slope, pvalue = 0.05)

    Test whether the result of SlopeChangeResults is statistically significant.

    Two tests are done:

    1. Check whether the margin of error of the fitted parameters a, b, c, d of the two linear segments a + b*t, c + d*t is less than the specified margins of error, for a chosen pvalue.
    2. Test that the two slopes b, d have difference greater than slope_diff.

    The Boolean & of the above two is the final test.

    The margin of error is simply half the size of the confidence interval, also known as radius of the confidence interval.

    source

    Indicators

    Note that any Julia function can be an indicator or change metric, so the list here is only just a couple of indicators directly implemented in this package.

    Value distribution

    Statistics.meanFunction
    mean(A::AbstractArray, w::AbstractWeights[, dims::Int])

    Compute the weighted mean of array A with weight vector w (of type AbstractWeights). If dim is provided, compute the weighted mean along dimension dims.

    Examples

    n = 20
     x = rand(n)
     w = rand(n)
    -mean(x, weights(w))
    source
    StatsBase.skewnessFunction
    skewness(v, [wv::AbstractWeights], m=mean(v))

    Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

    source
    StatsBase.kurtosisFunction
    kurtosis(v, [wv::AbstractWeights], m=mean(v))

    Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

    source

    Critical Slowing Down

    Statistics.varFunction
    var(x::AbstractArray, w::AbstractWeights, [dim]; mean=nothing, corrected=false)

    Compute the variance of a real-valued array x, optionally over a dimension dim. Observations in x are weighted using weight vector w. The uncorrected (when corrected=false) sample variance is defined as:

    \[\frac{1}{\sum{w}} \sum_{i=1}^n {w_i\left({x_i - μ}\right)^2 }\]

    where $n$ is the length of the input and $μ$ is the mean. The unbiased estimate (when corrected=true) of the population variance is computed by replacing $\frac{1}{\sum{w}}$ with a factor dependent on the type of weights used:

    • AnalyticWeights: $\frac{1}{\sum w - \sum {w^2} / \sum w}$
    • FrequencyWeights: $\frac{1}{\sum{w} - 1}$
    • ProbabilityWeights: $\frac{n}{(n - 1) \sum w}$ where $n$ equals count(!iszero, w)
    • Weights: ArgumentError (bias correction not supported)
    source
    var(ce::CovarianceEstimator, x::AbstractVector; mean=nothing)

    Compute the variance of the vector x using the estimator ce.

    source
    TransitionsInTimeseries.ar1_whitenoiseFunction
    ar1_whitenoise(x::AbstractVector)

    Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

    \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

    source

    Spectrum

    TransitionsInTimeseries.LowfreqPowerSpectrumType
    LowfreqPowerSpectrum(; q_lofreq = 0.1)

    Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

    lfps = precompute( LowfreqPowerSpectrum() )

    Keyword arguments:

    • q_lofreq: a number between 0 and 1 that characterises which portion of the

    frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

    source
    TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrumType
    PrecomputedLowfreqPowerSpectrum

    A struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:

    lfps(x)
    source

    Nonlinear dynamics

    Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

    For example, using the permutation entropy as an indicator is as simple as doing

    using ComplexityMeasures
    +mean(x, weights(w))
    source
    StatsBase.skewnessFunction
    skewness(v, [wv::AbstractWeights], m=mean(v))

    Compute the standardized skewness of a real-valued array v, optionally specifying a weighting vector wv and a center m.

    source
    StatsBase.kurtosisFunction
    kurtosis(v, [wv::AbstractWeights], m=mean(v))

    Compute the excess kurtosis of a real-valued array v, optionally specifying a weighting vector wv and a center m.

    source

    Critical Slowing Down

    Statistics.varFunction
    var(x::AbstractArray, w::AbstractWeights, [dim]; mean=nothing, corrected=false)

    Compute the variance of a real-valued array x, optionally over a dimension dim. Observations in x are weighted using weight vector w. The uncorrected (when corrected=false) sample variance is defined as:

    \[\frac{1}{\sum{w}} \sum_{i=1}^n {w_i\left({x_i - μ}\right)^2 }\]

    where $n$ is the length of the input and $μ$ is the mean. The unbiased estimate (when corrected=true) of the population variance is computed by replacing $\frac{1}{\sum{w}}$ with a factor dependent on the type of weights used:

    • AnalyticWeights: $\frac{1}{\sum w - \sum {w^2} / \sum w}$
    • FrequencyWeights: $\frac{1}{\sum{w} - 1}$
    • ProbabilityWeights: $\frac{n}{(n - 1) \sum w}$ where $n$ equals count(!iszero, w)
    • Weights: ArgumentError (bias correction not supported)
    source
    var(ce::CovarianceEstimator, x::AbstractVector; mean=nothing)

    Compute the variance of the vector x using the estimator ce.

    source
    TransitionsInTimeseries.ar1_whitenoiseFunction
    ar1_whitenoise(x::AbstractVector)

    Return the AR1 regression coefficient of a time series x by computing the analytic solution of the least-square parameter estimation under white-noise assumption for the data-generating process:

    \[\theta = \sum_{i=2}^{n} x_i x_{i-1} / \sum_{i=2}^{n} x_{i-1}^2\]

    source

    Spectrum

    TransitionsInTimeseries.LowfreqPowerSpectrumType
    LowfreqPowerSpectrum(; q_lofreq = 0.1)

    Return a PrecomputableFunction containing all the necessary fields to generate a PrecomputedLowfreqPowerSpectrum. The latter can be initialized by precompute:

    lfps = precompute( LowfreqPowerSpectrum() )

    Keyword arguments:

    • q_lofreq: a number between 0 and 1 that characterises which portion of the

    frequency spectrum is considered to be low. For instance, q_lofreq = 0.1 implies that the lowest 10% of frequencies are considered to be the low ones.

    source
    TransitionsInTimeseries.PrecomputedLowfreqPowerSpectrumType
    PrecomputedLowfreqPowerSpectrum

    A struct containing all the precomputed fields to efficiently perform repetitive computation of the low-frequency power spectrum (LFPS), a number between 0 and 1 that characterizes the amount of power contained in the low frequencies of the power density spectrum of x. Once lfps::PrecomputedLowfreqPowerSpectrum is initialized, it can be used as a function to obtain the LFPS of x::AbstractVector by:

    lfps(x)
    source

    Nonlinear dynamics

    Indicators that come from nonlinear timeseries analysis typically quantify some entropy-like or complexity measure from the timeseries. Thousands (literally) such measures are provided out of the box by the ComplexityMeasures.jl package. Given that any of these may be used as an indicator or change metric, we made the decision to not copy-paste any measure here, as it is easy for the user to use any of them.

    For example, using the permutation entropy as an indicator is as simple as doing

    using ComplexityMeasures
     est = OrdinalPatterns(; m = 3) # order 3
     # create a function that given timeseries returns permutation entropy
    -indicator = x -> entropy_normalized(est, x)

    and giving the created indicator to e.g., SlidingWindowConfig.

    Change metrics

    Slope

    TransitionsInTimeseries.kendalltauFunction
    kendalltau(x::AbstractVector)

    Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

    source
    TransitionsInTimeseries.spearmanFunction
    spearman(x::AbstractVector)

    Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

    source

    Value distribution differences

    TransitionsInTimeseries.difference_of_meansFunction
    difference_of_means(x::AbstractArray)

    Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

    # assumes 1-based indexing
    +indicator = x -> entropy_normalized(est, x)

    and giving the created indicator to e.g., SlidingWindowConfig.

    Change metrics

    Slope

    TransitionsInTimeseries.kendalltauFunction
    kendalltau(x::AbstractVector)

    Compute the kendall-τ correlation coefficient of the time series x. kendalltau can be used as a change metric focused on trend.

    source
    TransitionsInTimeseries.spearmanFunction
    spearman(x::AbstractVector)

    Compute the spearman correlation coefficient of the time series x. spearman can be used as a change metric focused on trend.

    source

    Value distribution differences

    TransitionsInTimeseries.difference_of_meansFunction
    difference_of_means(x::AbstractArray)

    Return the absolute difference of the means of the first and second halfs of x. difference_of_means can be used as a change metric focused on value differences. Creating similar statistical differences using other moments instead of mean is trivial. In fact, the source of difference_of_means is just:

    # assumes 1-based indexing
     n = length(x)
     x1 = view(x, 1:n÷2)
     x2 = view(x, (n÷2 + 1):n)
    -return abs(mean(x1) - mean(x2))

    difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

    source

    Make your own indicator/metric!

    The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

    There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

    Surrogates

    For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

    Sliding windows

    TransitionsInTimeseries.WindowViewerType
    WindowViewer(x; width, stride)

    Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

    If not given, the keywords width, stride are respectively taken as default_window_width(x) and 1.

    source
    TransitionsInTimeseries.windowmapFunction
    windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

    A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

    source

    Load data

    Visualization

    TransitionsInTimeseries.plot_indicator_changesFunction
    plot_indicator_changes(res) → (fig, axs)

    Return fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults has been visualised.

    Keyword arguments:

    • colors = default_colors sets the colors of the line plots that are to

    be cycled through. The default correspond to the color scheme of Julia Dynamics.

    • `indicatornames = defaultindicatorlabel(res), chametricnames =

    defaultchametriclabel(res)sets the labels for the indicators and the change metrics, with the default inferring them from the names ofres.config.indicatorsandres.config.change_metrics`.

    • accent_linewidth = 3 sets the line width for the original signals (the

    surrogates have linewidth = 1)

    source
    TransitionsInTimeseries.plot_significance!Function
    plot_significance!(axs, res, signif)

    Update the axs::Matrix{Axis} of a figure obtained with plot_indicator_changes(res) with the signif::SurrogatesSignificance.

    Keyword arguments:

    • flags = nothing provides the significance flags, for instance obtained by

    thresholding the pvalues.

    • nsurro = 20 sets the number of surrogates to plot.
    source

    Utils

    default_window_width
    +return abs(mean(x1) - mean(x2))

    difference_of_means can also sensibly be used for windows of size 2, in which case the change metric timeseries is the same as the abs.(diff(...)) of the indicator timeseries.

    source

    Make your own indicator/metric!

    The only difference between what is an "indicator" and what is a "change metric" is purely conceptual. As far as the code base of TransitionsInTimeseries.jl is concerned, they are both functions f: x::AbstractVector{Real} -> f(x)::Real. As a user you may give any such function for an indicator or change metric.

    There are situations where you may optimize such a function based on knowledge of input x type and length, in which case you may use PrecomputableFunction:

    TransitionsInTimeseries.PrecomputableFunctionType
    PrecomputableFunction

    Supertype of structs containing the necessary field to precompute a ::Function by:

    precompute(f::PrecomputableFunction, t)
    source
    TransitionsInTimeseries.precomputeFunction
    precompute(f, t)

    Precompute the function f given a time vector t.

    source

    Surrogates

    For the surrogate generation, you can use any subtype of Surrogate defined in Timeseriessurrogates.jl.

    Sliding windows

    TransitionsInTimeseries.WindowViewerType
    WindowViewer(x; width, stride)

    Initialize an iterator that generates views over the given timeseries x based on a window with a given width, incrementing the window views with the given stride. You can use this directly with map, such as map(std, WindowViewer(x, ...)) would give you the moving-window-timeseries of the std of x.

    If not given, the keywords width, stride are respectively taken as default_window_width(x) and 1.

    source
    TransitionsInTimeseries.windowmapFunction
    windowmap(f::Function, x::AbstractVector; kwargs...) → mapped_f

    A shortcut for first generating a wv = WindowViewer(x; kwargs...) and then applying mapped_f = map(f, wv). If x is accompanied by a time vector t, you probably also want to call this function with t instead of x and with one of mean, midpoint, midvalue as f to obtain a time vector for the mapped_f output.

    source
    TransitionsInTimeseries.windowmap!Function
    windowmap!(f::Function, out, x::AbstractVector; kwargs...)

    Same as windowmap, but writes the output in-place in out.

    source

    Load data

    TransitionsInTimeseries.load_linear_vs_doublewellMethod
    load_linear_vs_doublewell()

    Load prototypical data from a linear and a double-well model to test some indicators.

    source

    Visualization

    TransitionsInTimeseries.plot_indicator_changesFunction
    plot_indicator_changes(res) → (fig, axs)

    Return fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults has been visualised.

    Keyword arguments:

    • colors = default_colors sets the colors of the line plots that are to

    be cycled through. The default correspond to the color scheme of Julia Dynamics.

    • `indicatornames = defaultindicatorlabel(res), chametricnames =

    defaultchametriclabel(res)sets the labels for the indicators and the change metrics, with the default inferring them from the names ofres.config.indicatorsandres.config.change_metrics`.

    • accent_linewidth = 3 sets the line width for the original signals (the

    surrogates have linewidth = 1)

    source
    TransitionsInTimeseries.plot_significance!Function
    plot_significance!(axs, res, signif)

    Update the axs::Matrix{Axis} of a figure obtained with plot_indicator_changes(res) with the signif::SurrogatesSignificance.

    Keyword arguments:

    • flags = nothing provides the significance flags, for instance obtained by

    thresholding the pvalues.

    • nsurro = 20 sets the number of surrogates to plot.
    source
    TransitionsInTimeseries.plot_changes_significanceFunction
    plot_changes_significance(res, signif) → (fig, axs)

    Return fig::Figure and axs::Matrix{Axis}, on which res::ChangesResults and signif::SurrogatesSignificance have been visualised. The source code is as simple as:

    fig, axs = plot_indicator_changes(res; kwargs...)
    +plot_significance!(axs, res, signif; kwargs...)

    For more information, refer to plot_indicator_changes and plot_significance!.

    source

    Utils

    default_window_width
    diff --git a/dev/devdocs/index.html b/dev/devdocs/index.html index 1a1419d..a9cef4b 100644 --- a/dev/devdocs/index.html +++ b/dev/devdocs/index.html @@ -1,2 +1,2 @@ -Developer's documentation · TransitionsInTimeseries.jl

    Developer's documentation

    This documentation addresses users that would like to contribute to the software by either solving bugs, improving documentation, or adding new methods. All contributions come in the form of Pull Requests, for which we strongly advise to follow good practices in scientific code, which means that they are properly formatted, documented, tested, etc.

    New indicators or change metrics

    As explained already in e.g., SlidingWindowConfig, new indicators or change metrics are standard Julia functions, so you only need to define such a function (and document it, test it, etc.).

    New pipeline for estimating changes

    This means to contribute a fundamentally new "pipeline" for estimating/detecting transitions in timeseries. This new pipeline defines what a "transition" means. To add a new pipeline follow these steps:

    1. Define a new subtype of ChangesConfig
    2. Define a new subtype of ChangesResults
    3. Add a method for estimate_changes which accepts the new ChangesConfig subtype you defined and returns the ChangesResults subtype you defined.

    And that's it!

    Optionally you can further extend:

    • TransitionsInTimeseries.plot_indicator_changes with the new ChangesResults type you defined. Note the plotting functions are in the ext folder of the repository.
    • significant_transitions(res::ChangesResults, signif::Significance) with your new ChangesResults type and as many Significance subtypes you have the capacity to extend for.

    New pipeline for estimating significance

    Statistically significant changes are "transitions". However, what "significant" means is not universal. There are different ways to test for significance and TransitionsInTimeseries.jl allows various methods.

    To add a new pipeline for estimating significance follow these steps:

    1. Define a new subtype of Significance
    2. Extend significant_transitions(res::ChangesResults, signif::Significance) with your new type and as many ChangesResults subtypes as you have capacity for.

    And that's it! Unfortunately so far we have found no way to make the significant_transitions code agnostic of the changes result, so you would need to add a method manually for every ChangesResults.

    Optionally you can further extend TransitionsInTimeseries.plot_significance! (which you can find in the ext folder) for visualizing the significance results.

    +Developer's documentation · TransitionsInTimeseries.jl

    Developer's documentation

    This documentation addresses users that would like to contribute to the software by either solving bugs, improving documentation, or adding new methods. All contributions come in the form of Pull Requests, for which we strongly advise to follow good practices in scientific code, which means that they are properly formatted, documented, tested, etc.

    New indicators or change metrics

    As explained already in e.g., SlidingWindowConfig, new indicators or change metrics are standard Julia functions, so you only need to define such a function (and document it, test it, etc.).

    New pipeline for estimating changes

    This means to contribute a fundamentally new "pipeline" for estimating/detecting transitions in timeseries. This new pipeline defines what a "transition" means. To add a new pipeline follow these steps:

    1. Define a new subtype of ChangesConfig
    2. Define a new subtype of ChangesResults
    3. Add a method for estimate_changes which accepts the new ChangesConfig subtype you defined and returns the ChangesResults subtype you defined.

    And that's it!

    Optionally you can further extend:

    • TransitionsInTimeseries.plot_indicator_changes with the new ChangesResults type you defined. Note the plotting functions are in the ext folder of the repository.
    • significant_transitions(res::ChangesResults, signif::Significance) with your new ChangesResults type and as many Significance subtypes you have the capacity to extend for.

    New pipeline for estimating significance

    Statistically significant changes are "transitions". However, what "significant" means is not universal. There are different ways to test for significance and TransitionsInTimeseries.jl allows various methods.

    To add a new pipeline for estimating significance follow these steps:

    1. Define a new subtype of Significance
    2. Extend significant_transitions(res::ChangesResults, signif::Significance) with your new type and as many ChangesResults subtypes as you have capacity for.

    And that's it! Unfortunately so far we have found no way to make the significant_transitions code agnostic of the changes result, so you would need to add a method manually for every ChangesResults.

    Optionally you can further extend TransitionsInTimeseries.plot_significance! (which you can find in the ext folder) for visualizing the significance results.

    diff --git a/dev/examples/do-events/index.html b/dev/examples/do-events/index.html index bc1d694..065af80 100644 --- a/dev/examples/do-events/index.html +++ b/dev/examples/do-events/index.html @@ -188,4 +188,4 @@ vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3) push!(figvec, fig) end -figvec[1]Example block output

    It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

    figvec[2]
    Example block output

    Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

    +figvec[1]Example block output

    It here appears that not all transitions are preceeded by a significant increase of variance and AC1, even in the case of clean and evenly sampled time series. Let's check another case:

    figvec[2]
    Example block output

    Same here! Although CLIMBER-X does not represent real DO-events, the above-performed analysis might be hinting at the fact that not all DO transitions can be forecasted with CSD. Nonetheless, performing a CSD analysis can inform on the evolution of a system's resilience.

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    Perform the sliding window analysis

    This is just a straightforward call to estimate_changes. In fact, it is even simpler than the tutorial. Here we skip completely the "indicator" estimation step, and we evaluate the change metric directly on input data. We do this by simply passing nothing as the indicators.

    using TransitionsInTimeseries
    +fig
    Example block output

    Perform the sliding window analysis

    This is just a straightforward call to estimate_changes. In fact, it is even simpler than the tutorial. Here we skip completely the "indicator" estimation step, and we evaluate the change metric directly on input data. We do this by simply passing nothing as the indicators.

    using TransitionsInTimeseries
     
     config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500)
     
    @@ -65,4 +65,4 @@
     fig = visualize_results(results)
     axDKS = content(fig[2,1])
     vlines!(axDKS, results.t_change[vec(flags)], color = ("red", 0.25))
    -fig
    Example block output

    We could proceed with a lot of preprocessing as in (Bagniewski et al., 2021) but we skip this here for the sake of simplicity.

    +figExample block output

    We could proceed with a lot of preprocessing as in (Bagniewski et al., 2021) but we skip this here for the sake of simplicity.

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    Different surrogates

    Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

    A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

    A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

    surromethod = RelativePartialRandomization(0.25)
    +fig
    Example block output

    Different surrogates

    Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn't contain any information highlighting the local dynamics or information that preserves the local changes of dynamical behavior.

    A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides stricter surrogate-based significance) is for example RelativePartialRandomization.

    A much better alternative is to use block-shuffled surrogates, which preserve the short term local temporal correlation in the timeseries and hence also preserve local short term sharp changes in the dynamic behavior.

    surromethod = RelativePartialRandomization(0.25)
     fig = plot_change_metrics()
     overplot_surrogate_significance!(fig, surromethod, "gray")
    -fig
    Example block output

    Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

    Simpler Significance

    Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

    fig = plot_change_metrics()
    +fig
    Example block output

    Our results have improved. In the permutation entropy, we see only two transitions detected as significant, which is correct: only two real dynamical transitions exist in the data. In the other two indicators we also see fewer transitions, but as we have already discussed, no results with the other indicators should be taken into meaningful consideration, as these indicators are simply inappropriate for what we are looking for here.

    Simpler Significance

    Arguably, exactly because we are using the difference_of_means as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using SurrogatesSignificance we may use the simpler and much faster SigmaSignificance, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.

    fig = plot_change_metrics()
     flags = significant_transitions(results, SigmaSignificance(factor = 5.0))
     
     # Plot the flags
    @@ -125,4 +125,4 @@
         )
     end
     content(fig[1, 1]).title = "significance from std"
    -fig
    Example block output +figExample block output diff --git a/dev/index.html b/dev/index.html index cc10e73..381eb71 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -TransitionsInTimeseries.jl · TransitionsInTimeseries.jl

    TransitionsInTimeseries.jl

    TransitionsInTimeseries.jl

    TransitionsInTimeseriesModule

    TransitionsInTimeseries.jl

    CI codecov Package Downloads

    TransitionsInTimeseries.jl is a free and open-source software to easily analyse transitions within timeseries in a reproducible, performant, extensible and reliable way. In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

    1. Provide the analysis pipelines with new indicators, which can be either self-written or imported from other packages. In particular, the latter offers thousands of metrics that can indicate transitions right out of the box.
    2. Add new analysis pipelines for finding transitions.
    3. Add new ways for significance testing.

    TransitionsInTimeseries is a registered Julia package and can be installed by running:

    ] add TransitionsInTimeseries

    All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

    Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

    source
    Star us on GitHub!

    If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

    Content

    Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

    • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
    • Makes the surrogate analysis to test for significance under the hub.
    • Can be easily extended by any user without touching the source code.
    • Reduces the programming overhead for any researcher willing to benchmark new methods.
    • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
    • Increases trustworthiness thanks to a large test suite.
    Similar projects

    An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

    Approaches

    Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

    +TransitionsInTimeseries.jl · TransitionsInTimeseries.jl

    TransitionsInTimeseries.jl

    TransitionsInTimeseries.jl

    TransitionsInTimeseriesModule

    TransitionsInTimeseries.jl

    CI codecov Package Downloads

    TransitionsInTimeseries.jl is a free and open-source software to easily analyse transitions within timeseries in a reproducible, performant, extensible and reliable way. In contrast to other existing software with similar target application, TransitionsInTimeseries.jl defines a generic interface for how to find transitions and how to test for significance. Within this interface, it is easy to expand the software in three orthogonal ways:

    1. Provide the analysis pipelines with new indicators, which can be either self-written or imported from other packages. In particular, the latter offers thousands of metrics that can indicate transitions right out of the box.
    2. Add new analysis pipelines for finding transitions.
    3. Add new ways for significance testing.

    TransitionsInTimeseries is a registered Julia package and can be installed by running:

    ] add TransitionsInTimeseries

    All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file.

    Alternative names for this package could have been: Early Warning Signals / Resilience Indicators / Regime-Shift Identifiers / Change-Point Detectors, or however else you want to call them!

    source
    Star us on GitHub!

    If you have found this package useful, please consider starring it on GitHub. This gives us an accurate lower bound of the (satisfied) user count.

    Content

    Multi-stable systems can display abrupt transitions between two stability regimes. To predict such transitions in real-world systems solely based on data, mathematical tools have been developed in the last decades. Numerous terminologies have been used for them, such as early warning signals, resilience indicators, regime-shift identifiers, change-point detection and transition indicators. TransitionsInTimeseries.jl sticks to the latter terminology and provides an interface that:

    • Allows a fast computation of common transition indicators with a couple of lines, as demonstrated in the example section.
    • Makes the surrogate analysis to test for significance under the hub.
    • Can be easily extended by any user without touching the source code.
    • Reduces the programming overhead for any researcher willing to benchmark new methods.
    • Eases the reproducibility thanks to a clear syntax, a simple installation and RNG-seeded surrogate generation.
    • Increases trustworthiness thanks to a large test suite.
    Similar projects

    An R toolbox and a Python library already exist. However, we believe that they are difficult to extend for the user. Furthermore, they do not offer a native performant code, as here allowed by the use of Julia.

    Approaches

    Over the last decades, research on transition indicators has largely focused on Critical Slowing Down (CSD). CSD is observed when a system approaches a Hopf, a transcritical or a fold bifurcation and consists in a resilience loss of the system. For instance this can be diagnosed by an increase of the variance and the AR1-regression coefficient, as demonstrated in the example section. However, we emphasize that this is one out of many possible approaches for obtaining transition indicators. Recent work has explored new approaches relying on nonlinear dynamics or machine learning. TransitionsInTimeseries.jl is designed to allow these cutting-edge methods and foster the development of new ones.

    diff --git a/dev/refs/index.html b/dev/refs/index.html index 71badbd..d71a1b4 100644 --- a/dev/refs/index.html +++ b/dev/refs/index.html @@ -1,2 +1,2 @@ -References · TransitionsInTimeseries.jl

    References

    +References · TransitionsInTimeseries.jl

    References

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      We can conveniently plot the information contained in results by using plot_indicator_changes:

      fig = plot_indicator_changes(results)
      Example block output

      Step 2 is to estimate significance using SurrogatesSignificance and the function significant_transitions. Finally, we can conveniently plot the results obtained by updating the figure obtained above with plot_significance!:

      signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])
       flags = significant_transitions(results, signif)
       plot_significance!(fig, results, signif, flags = flags)
      -fig
      Example block output

      Segmented windows

      The analysis shown so far relies on sliding windows of the change metric. This is particularly convenient for transition detection tasks. Segmented windows for the change metric computation are however preferable when it comes to prediction tasks. By only slightly modifying the syntax used so far, one can perform the same computations on segmented windows, as well as visualise the results conveniently:

      config = SegmentedWindowConfig(indicators, change_metrics,
      +fig
      Example block output

      Segmented windows

      The analysis shown so far relies on sliding windows of the change metric. This is particularly convenient for transition detection tasks. Segmented windows for the change metric computation are however preferable when it comes to prediction tasks. By only slightly modifying the syntax used so far, one can perform the same computations on segmented windows, as well as visualise the results conveniently:

      config = SegmentedWindowConfig(indicators, change_metrics,
           t[1:1], t[1200:1200]; whichtime = last, width_ind = 200,
           min_width_cha = 100)
       results = estimate_changes(config, input, t)
       signif = SurrogatesSignificance(n = 1000, tail = [:right, :right])
       flags = significant_transitions(results, signif)
      -fig = plot_changes_significance(results, signif)
      Example block output +fig = plot_changes_significance(results, signif)Example block output

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