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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-13T15:31:38","documenter_version":"1.3.0"}}
{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-13T15:44:07","documenter_version":"1.3.0"}}
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vlines!(axs[1], t_transitions[j], color = Cycled(1), linewidth = 3)
push!(figvec, fig)
end
figvec[1]</code></pre><img src="04e32464.png" alt="Example block output"/><p>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&#39;s check another case:</p><pre><code class="language-julia hljs">figvec[2]</code></pre><img src="809214dc.png" alt="Example block output"/><p>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&#39;s resilience.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ks_paleojump/">« Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries</a><a class="docs-footer-nextpage" href="../../api/">API »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 15:31">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
figvec[1]</code></pre><img src="04e32464.png" alt="Example block output"/><p>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&#39;s check another case:</p><pre><code class="language-julia hljs">figvec[2]</code></pre><img src="809214dc.png" alt="Example block output"/><p>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&#39;s resilience.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ks_paleojump/">« Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries</a><a class="docs-footer-nextpage" href="../../api/">API »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 15:44">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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density!(ax, q; label = &quot;D_KS = $(D_KS)&quot;)
end
axislegend(ax)
fig</code></pre><img src="f2819d31.png" alt="Example block output"/><h2 id="Perform-the-sliding-window-analysis"><a class="docs-heading-anchor" href="#Perform-the-sliding-window-analysis">Perform the sliding window analysis</a><a id="Perform-the-sliding-window-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Perform-the-sliding-window-analysis" title="Permalink"></a></h2><p>This is just a straightforward call to <a href="../../api/#TransitionsInTimeseries.estimate_changes"><code>estimate_changes</code></a>. In fact, it is even simpler than the tutorial. Here we skip completely the &quot;indicator&quot; estimation step, and we evaluate the change metric directly on input data. We do this by simply passing <code>nothing</code> as the indicators.</p><pre><code class="language-julia hljs">using TransitionsInTimeseries
fig</code></pre><img src="74d766ad.png" alt="Example block output"/><h2 id="Perform-the-sliding-window-analysis"><a class="docs-heading-anchor" href="#Perform-the-sliding-window-analysis">Perform the sliding window analysis</a><a id="Perform-the-sliding-window-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Perform-the-sliding-window-analysis" title="Permalink"></a></h2><p>This is just a straightforward call to <a href="../../api/#TransitionsInTimeseries.estimate_changes"><code>estimate_changes</code></a>. In fact, it is even simpler than the tutorial. Here we skip completely the &quot;indicator&quot; estimation step, and we evaluate the change metric directly on input data. We do this by simply passing <code>nothing</code> as the indicators.</p><pre><code class="language-julia hljs">using TransitionsInTimeseries

config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500)

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fig = visualize_results(results)
axDKS = content(fig[2,1])
vlines!(axDKS, results.t_change[vec(flags)], color = (&quot;red&quot;, 0.25))
fig</code></pre><img src="49311be6.png" alt="Example block output"/><p>We could proceed with a lot of preprocessing as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>) but we skip this here for the sake of simplicity.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../logistic/">« Permutation entropy for dynamic regime changes</a><a class="docs-footer-nextpage" href="../do-events/">Dansgaard-Oescher events and Critical Slowing Down »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 15:31">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
fig</code></pre><img src="49311be6.png" alt="Example block output"/><p>We could proceed with a lot of preprocessing as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>) but we skip this here for the sake of simplicity.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../logistic/">« Permutation entropy for dynamic regime changes</a><a class="docs-footer-nextpage" href="../do-events/">Dansgaard-Oescher events and Critical Slowing Down »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 15:44">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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surromethod = RandomFourier()
overplot_surrogate_significance!(fig, surromethod)

fig</code></pre><img src="fb0b8392.png" alt="Example block output"/><h2 id="Different-surrogates"><a class="docs-heading-anchor" href="#Different-surrogates">Different surrogates</a><a id="Different-surrogates-1"></a><a class="docs-heading-anchor-permalink" href="#Different-surrogates" title="Permalink"></a></h2><p>Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn&#39;t contain any information highlighting the <em>local</em> dynamics or information that preserves the local changes of dynamical behavior.</p><p>A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides <strong>stricter</strong> surrogate-based significance) is for example <code>RelativePartialRandomization</code>.</p><p>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.</p><pre><code class="language-julia hljs">surromethod = RelativePartialRandomization(0.25)
fig</code></pre><img src="3a741e68.png" alt="Example block output"/><h2 id="Different-surrogates"><a class="docs-heading-anchor" href="#Different-surrogates">Different surrogates</a><a id="Different-surrogates-1"></a><a class="docs-heading-anchor-permalink" href="#Different-surrogates" title="Permalink"></a></h2><p>Random Fourier surrogates perserve the power spectrum of the timeseries, but the power spectrum is a property integrated over the whole timeseries. It doesn&#39;t contain any information highlighting the <em>local</em> dynamics or information that preserves the local changes of dynamical behavior.</p><p>A surrogate type that does a better job in preserving local sharp changes in the timeseries (and hence provides <strong>stricter</strong> surrogate-based significance) is for example <code>RelativePartialRandomization</code>.</p><p>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.</p><pre><code class="language-julia hljs">surromethod = RelativePartialRandomization(0.25)
fig = plot_change_metrics()
overplot_surrogate_significance!(fig, surromethod, &quot;gray&quot;)
fig</code></pre><img src="8fb14a64.png" alt="Example block output"/><p>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.</p><h2 id="Simpler-Significance"><a class="docs-heading-anchor" href="#Simpler-Significance">Simpler Significance</a><a id="Simpler-Significance-1"></a><a class="docs-heading-anchor-permalink" href="#Simpler-Significance" title="Permalink"></a></h2><p>Arguably, exactly because we are using the <a href="../../api/#TransitionsInTimeseries.difference_of_means"><code>difference_of_means</code></a> as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using <a href="../../api/#TransitionsInTimeseries.SurrogatesSignificance"><code>SurrogatesSignificance</code></a> we may use the simpler and much faster <a href="../../api/#TransitionsInTimeseries.SigmaSignificance"><code>SigmaSignificance</code></a>, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.</p><pre><code class="language-julia hljs">fig = plot_change_metrics()
fig</code></pre><img src="721b55f7.png" alt="Example block output"/><p>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.</p><h2 id="Simpler-Significance"><a class="docs-heading-anchor" href="#Simpler-Significance">Simpler Significance</a><a id="Simpler-Significance-1"></a><a class="docs-heading-anchor-permalink" href="#Simpler-Significance" title="Permalink"></a></h2><p>Arguably, exactly because we are using the <a href="../../api/#TransitionsInTimeseries.difference_of_means"><code>difference_of_means</code></a> as a change metric, we may want to be less strict and more simple with our tests for significance. Instead of using <a href="../../api/#TransitionsInTimeseries.SurrogatesSignificance"><code>SurrogatesSignificance</code></a> we may use the simpler and much faster <a href="../../api/#TransitionsInTimeseries.SigmaSignificance"><code>SigmaSignificance</code></a>, which simply claims significant time points whenever a change metric exceeds some pre-defined factor of its timeseries standard deviation.</p><pre><code class="language-julia hljs">fig = plot_change_metrics()
flags = significant_transitions(results, SigmaSignificance(factor = 5.0))

# Plot the flags
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)
end
content(fig[1, 1]).title = &quot;significance from std&quot;
fig</code></pre><img src="056afaf1.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorial/">« Tutorial</a><a class="docs-footer-nextpage" href="../ks_paleojump/">Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 15:31">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
fig</code></pre><img src="056afaf1.png" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorial/">« Tutorial</a><a class="docs-footer-nextpage" href="../ks_paleojump/">Kolmogorov-Smirnov test for detecting transitions in paleoclimate timeseries »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 15:44">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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