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%% Regress the GDP onto the CPI and Examine Residuals % Regress the log GDP onto the CPI using a regression model with ARMA(1,1) % errors, and then examine the residuals. % Copyright 2015 The MathWorks, Inc. %% % Load the U.S. Macroeconomic data set and preprocess the data. load Data_USEconModel; logGDP = log(DataTable.GDP); dlogGDP = diff(logGDP); % For stationarity dCPI = diff(DataTable.CPIAUCSL); % For stationarity T = length(dlogGDP); % Effective sample size %% % Fit a regression model with ARMA(1,1) errors. ToEstMdl = regARIMA(1,0,1); EstMdl = estimate(ToEstMdl,dlogGDP,'X',dCPI); %% % Infer the residuals over all observations. By default, |infer| backcasts % for the necessary unconditional disturbances. e = infer(EstMdl,dlogGDP,'X',dCPI); %% % Plot the inferred residuals. figure plot(1:T,e,[1 T],[0 0],'r') title('{\bf Inferred Residuals}') %% % The residuals are centered around 0, but show signs of heteroscedasticity.