Add Factor for estimating factor models

.github/workflows/CI-stable.yml

@@ -25,6 +25,9 @@ jobs:
           - 'windows-latest'
         arch:
           - 'x64'
+        exclude:
+          - version: '1.6'
+            os: 'windows-latest'
     steps:
       - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1

Project.toml

@@ -17,19 +17,21 @@ CSV = "0.9, 0.10"
 ConfidenceBands = "0.1"
 DataFrames = "1"
 LocalProjections = "0.2"
+MAT = "0.10"
 MatrixEquations = "2"
 Roots = "1, 2"
 StatsAPI = "1.2"
 StatsBase = "0.33, 0.34"
 Tables = "1"
-julia = "1.3"
+julia = "1.6"
 
 [extras]
 CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
 ConfidenceBands = "6840a270-7180-4af9-9adc-8b0ddd17b6f2"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 LocalProjections = "8dd5e8af-b996-4a51-9681-92a36a2638c1"
+MAT = "23992714-dd62-5051-b70f-ba57cb901cac"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["CSV", "ConfidenceBands", "DataFrames", "LocalProjections", "Test"]
+test = ["CSV", "ConfidenceBands", "DataFrames", "LocalProjections", "MAT", "Test"]

data/README.md

@@ -0,0 +1,23 @@
+# Example Data
+
+Data files are provided here for the ease of testing and illustrations.
+The data may have been processed for the ease of usage.
+See [`data/src`](src/) for the source code
+that generates these files from original data.
+
+## Sources
+
+| Name | Source | File | Note |
+| :--: | :----: | :--: | :--- |
+| lpw_est_data.mat | [Li, Plagborg-Møller and Wolf (2024)](https://doi.org/10.1016/j.jeconom.2024.105722) | `DFM/Subroutines/SW_DFM_Estimation/data/hom_fac_1.xlsx` | Data are processed with [`lpw_savedata.m`](src/lpw_savedata.m) and used in [Stock and Watson (2016)](https://doi.org/10.1016/bs.hesmac.2016.04.002) |
+
+## References
+
+**Li, Dake, Mikkel Plagborg-Møller, and Christian K. Wolf.** 2024.
+"Local Projections vs. VARs: Lessons from Thousands of DGPs."
+*Journal of Econometrics*, forthcoming.
+
+**Stock, James H. and Mark W. Watson.** 2016.
+"Chapter 8---Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics."
+In *Handbook of Macroeconomics*, Vol. 2A,
+edited by John B. Taylor and Harald Uhlig, 415-525. Amsterdam: Elsevier.

data/src/lpw_savedata.m

@@ -0,0 +1,267 @@
+% Modified from Li, Plagborg-Møller and Wolf (2024) for testing purposes
+% Estimation part is based on Stock and Watson (2016)
+% To run the code, download the replication repo from
+% https://github.com/dake-li/lp_var_simul
+% Place this file in the DFM folder
+% Data for testing purposes are saved to lpw_est_data.mat
+
+
+%% Content from run_dfm.m
+
+%% HOUSEKEEPING
+
+clc
+clear all
+close all
+
+addpath(genpath(fullfile('..', 'Auxiliary_Functions')))
+addpath(genpath(fullfile('..', 'Estimation_Routines')))
+addpath(genpath('Subroutines'))
+
+%% SET EXPERIMENT
+
+lag_type = 4; % No. of lags to impose in estimation, or NaN (= AIC)
+
+%% SETTINGS
+
+% Apply shared settings as well as settings specific to DGP and estimand type
+
+run(fullfile('Settings', 'shared'));
+
+%% ENCOMPASSING DFM MODEL
+
+%% Set the argument values for DFM_est
+
+n_factors = DF_model.n_fac;
+n_lags_fac = DF_model.n_lags_fac;
+n_lags_uar = DF_model.n_lags_uar;
+reorder = DF_model.reorder;
+levels = 1;
+coint_rank = DF_model.coint_rank;
+
+
+%% Content from DFM_est.m
+
+%% PREPARATIONS
+
+small = 1.0e-10;
+big = 1.0e+6;
+
+% ----------- Sample Period, Calendars and so forth
+[dnobs_m,calvec_m,calds_m] = calendar_make([1959 1],[2014 12],12);  % Monthly Calendar
+[dnobs_q,calvec_q,calds_q] = calendar_make([1959 1],[2014 4],4);    % Quarterly Calendar
+
+% -- Load Data
+load_data=1;
+datain_all;      % datain_all reads in the full dataset .. all variables, etc. saved in datain.xx
+
+%% ESTIMATION
+
+% Factor Parameters
+n_fac = n_factors;
+est_par.fac_par.nfac.unobserved = n_fac;
+est_par.fac_par.nfac.observed = 0;
+est_par.fac_par.nfac.total = n_fac + est_par.fac_par.nfac.observed;
+
+% Sampling parameters
+est_par.smpl_par.nfirst = [1959 3];       % start date
+est_par.smpl_par.nlast  = [2014 4];       % end date
+est_par.smpl_par.calvec = datain.calvec;  % calendar
+est_par.smpl_par.nper   = 4;              % number of periods a year
+
+% Factor analysis parameters
+est_par.fac_par.nt_min                  = 20;     % min number of obs for any series used to est factors
+est_par.lambda.nt_min                   = 40;     % min number of obs for any series used to estimate lamba, irfs, etc.
+est_par.fac_par.tol                     = 10^-8;  % precision of factor estimation (scaled by by n*t)
+
+% Restrictions on factor loadings to identify factors
+est_par.fac_par.lambda_constraints_est  = 1;  % no constraints on lambda
+est_par.fac_par.lambda_constraints_full = 1;  % no constraints on lambda
+
+% VAR parameters for factors
+est_par.var_par.nlag   = n_lags_fac;    % number of lags
+est_par.var_par.iconst = 1;    % include constant
+est_par.var_par.icomp  = 1;    % compute companion form of model .. excluding constant
+
+% yit equation parameters
+est_par.n_uarlag = n_lags_uar;  % number of arlags for uniqueness
+
+% Matrices for storing results
+n_series = size(datain.bpdata,2);
+
+%% Set the argument values for factor_estimation_ls_full
+
+data = datain.bpdata;
+inclcode = datain.bpinclcode;
+
+
+%% Content from factor_estimation_ls_full.m
+
+% PRELIMINARIES
+n_series = size(data,2);                    % number of series
+nfirst   = est_par.smpl_par.nfirst;         % start date
+nlast    = est_par.smpl_par.nlast;          % end date
+calvec   = est_par.smpl_par.calvec;         % calendar
+nper     = est_par.smpl_par.nper;           % number of periods a year
+n_uarlag = est_par.n_uarlag;                % number of AR lags
+ntmin    = est_par.lambda.nt_min;           % minimum number of Obs
+
+% USE SUBSET OF DATA TO ESTIMATE FACTORS
+est_data = data(:,inclcode==1);
+if levels
+    est_data = [nan(1,size(est_data,2)); diff(est_data,1,1)]; % If data is in levels, estimate factors off first differences
+end
+
+
+%% Content from factor_estimation_ls
+
+%%
+% Preliminaries
+% extract estimation parameters
+smpl_par           = est_par.smpl_par;
+lambda_constraints = est_par.fac_par.lambda_constraints_est;
+nt_min             = est_par.fac_par.nt_min;
+tol                = est_par.fac_par.tol;
+nfac_u             = est_par.fac_par.nfac.unobserved;
+nfac_o             = est_par.fac_par.nfac.observed;
+nfac_t             = est_par.fac_par.nfac.total;
+if nfac_o > 0;
+  w = est_par.fac_par.w;
+end;
+
+% Estimate factors with unbalanced panel by LS -- standardize data first
+  % Sample period
+  [istart, iend] = smpl_HO(smpl_par);
+  istart = max(istart,1);
+  iend = min(iend,size(est_data,1));
+
+  % Estimate Factors 
+  xdata = est_data(istart:iend,:);
+  nt = size(xdata,1);
+  ns = size(xdata,2);
+
+  % Mean and Standard Deviation
+  xmean = nanmean(xdata)';                                  % mean (ignoring NaN)
+  mult = sqrt((sum(~isnan(xdata))-1)./sum(~isnan(xdata)));  % num of non-NaN entries for each series
+  xstd = (nanstd(xdata).*mult)';                            % std (ignoring NaN)
+  xdata_std = (xdata - repmat(xmean',nt,1))./repmat(xstd',nt,1);   % standardized data
+
+  if nfac_o > 0;
+      wdata = w(istart:iend,:);
+      if sum(sum(isnan(wdata))) ~= 0;
+          error('w contains missing values over sample period, processing stops');
+      end;
+  end;
+
+  n_lc = 0;            % number of constrains placed on lambda
+  if size(lambda_constraints,2) > 1;
+     lam_c_index = lambda_constraints(:,1);     % Which row of lambda: Constraints are then R*lambda = r
+     lam_c_R = lambda_constraints(:,2:end-1);   % R matrix
+     lam_c_r = lambda_constraints(:,end);       % r value
+     lam_c_r_scl = lam_c_r./xstd(lam_c_index);  % Adjusted for scaling
+     n_lc = size(lambda_constraints,1);
+  end;
+
+  % Compute Total Sum of Squares
+  tss = 0;
+  nobs = 0;
+  for is = 1:ns;
+      tmp = xdata_std(:,is);     % select series
+      tmp = tmp(isnan(tmp)==0);  % drop NaN
+      tss = tss+sum(tmp.^2);     % add to tss
+      nobs = nobs+size(tmp,1);   % add to n*T
+  end;
+
+  % Estimate factors using balanced panel
+  if nfac_u > 0;
+   xbal = packr(xdata_std')';
+   %[coef,score,latent]=princomp(xbal);
+   [coef,score,latent] = pca(xbal);
+   f = score(:,1:nfac_u);
+   fa = f;
+   if nfac_o > 0;
+      fa = [wdata f];
+   end;
+   lambda = NaN*zeros(ns,nfac_t);
+  else;
+   fa = wdata;
+  end;
+
+  diff = 100;
+  ssr = 0;
+  while diff>tol*(nt*ns)
+      ssr_old = ssr;
+    for i = 1:ns; 
+        tmp=packr([xdata_std(:,i) fa]);
+        if size(tmp,1) >= nt_min;
+  	       y=tmp(:,1);
+     	     x=tmp(:,2:end);
+           xxi = inv(x'*x);
+           bols = xxi*(x'*y);
+           b = bols;
+           if n_lc > 0;
+             % Check for restrictions and impose;
+             ii = lam_c_index == i;
+             if sum(ii) > 0;
+                 R = lam_c_R(ii==1,:);
+                 r_scl = lam_c_r_scl(ii==1,:);
+                 tmp1 = xxi*R';
+                 tmp2 = inv(R*tmp1);
+                 b = bols - tmp1*tmp2*(R*bols-r_scl);
+             end;
+           end;
+           lambda(i,:)= b';
+        end;
+    end;
+    edata = xdata_std;
+    if nfac_u > 0;
+       if nfac_o > 0;
+          edata = xdata_std - fa(:,1:nfac_o)*lambda(:,1:nfac_o)';
+       end;
+       for t = 1:nt;
+          tmp=packr([edata(t,:)' lambda(:,nfac_o+1:end)]);
+          y=tmp(:,1);
+     	    x=tmp(:,2:end);
+          b = x\y;
+          f(t,:) = b';
+       end; 
+       fa = f;
+       if nfac_o > 0;
+         fa = [wdata f];
+       end;
+    end;
+    % Compute residuals 
+    e = xdata_std-fa*lambda';
+    ssr = sum(nansum(e.^2));
+    diff = abs(ssr_old - ssr);
+  end;
+
+  f_est = fa;
+
+  % Compute R2 for each series
+  r2vec = NaN*zeros(ns,1);
+  for i = 1:ns;
+      tmp=packr([xdata_std(:,i) f_est]);
+      if size(tmp,1) >= nt_min;
+  	    y=tmp(:,1);
+        x=tmp(:,2:end);
+        b = x\y;
+        e = y -x*b;
+        r2_ssr = e'*e;
+        r2_tss = y'*y;
+        r2vec(i) = 1-r2_ssr/r2_tss;
+      end;
+  end;
+
+  fac_est = NaN(size(est_data,1),nfac_t);
+  fac_est(istart:iend,:)=f_est;
+  lambda = lambda.*repmat(xstd,1,nfac_t);
+
+  lsout.fac = fac_est;   lsout.lambda = lambda;
+  lsout.tss = tss;       lsout.ssr = ssr;
+  lsout.r2vec = r2vec;   lsout.nobs = nobs;
+  lsout.nt = nt;         lsout.ns = ns;
+
+%% Save the data
+save("../lpw_est_data.mat", 'est_data')
+

src/AutoregressiveModels.jl

@@ -2,7 +2,9 @@ module AutoregressiveModels
 
 using Base: ReshapedArray
 using LinearAlgebra: Cholesky, cholesky!, cholesky, UpperTriangular, LowerTriangular,
-    lu!, ldiv!, rdiv!, inv!, mul!, diagm, eigen!, eigen, I
+    lu!, ldiv!, rdiv!, inv!, mul!, diagm, eigen!, eigen, I,
+    BLAS.@blasfunc, BlasInt, chkstride1, LAPACK.liblapack, LAPACK.chklapackerror,
+    Algorithm, default_svd_alg, DivideAndConquer, QRIteration
 using MatrixEquations: lyapd
 using Random: randn!
 using Roots: find_zero, Brent
@@ -12,10 +14,11 @@ using Tables
 using Tables: getcolumn
 
 import Base: show
-import StatsAPI: response, modelmatrix, coef, residuals, dof_residual, fit
+import LinearAlgebra: LAPACK.gesdd!, LAPACK.gesvd!, _svd!
+import StatsAPI: response, modelmatrix, coef, residuals, dof_residual, fit, fit!, r2
 
 # Reexport objects from StatsAPI
-export response, modelmatrix, coef, residuals, dof_residual, fit
+export response, modelmatrix, coef, residuals, dof_residual, fit, fit!, r2
 
 export VARProcess,
        nvar,
@@ -46,12 +49,16 @@ export VARProcess,
        iidresiddraw!,
        bootstrap!,
 
-       ARMAProcess
+       ARMAProcess,
 
+       Factor
+
+include("lapack.jl")
 include("utils.jl")
 include("process.jl")
 include("estimation.jl")
 include("bootstrap.jl")
 include("arma.jl")
+include("factor.jl")
 
 end # module AutoregressiveModels

src/estimation.jl

@@ -350,9 +350,9 @@ The corrected estimates can be retrieved from the returned object
 with [`coefcorrected`](@ref).
 
 # Reference
-**Pope, Alun L. 1990**.
-"Biases of Estimators in Multivariate Non-Gaussian Autoregressions".
-*Journal of Time Series Analysis* 11 (3): 249-258.
+**Pope, Alun L.** 1990.
+"Biases of Estimators in Multivariate Non-Gaussian Autoregressions."
+*Journal of Time Series Analysis* 11 (3): 249--258.
 """
 function biascorrect(r::VectorAutoregression;
         offset::Real=1e-4, factor::Union{Real, Nothing}=nothing,
@@ -405,5 +405,7 @@ show(io::IO, r::VectorAutoregression) =
 
 function show(io::IO, ::MIME"text/plain", r::VectorAutoregression)
     println(io, r, " with coefficient matrix:")
-    Base.print_array(io, coef(r)')
+    M, N = displaysize(io)
+    Base.print_matrix(IOContext(io, :compact=>true, :limit=>true,
+        :displaysize=>(M-1, N)), coef(r)')
 end