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%% Specify AR Lags When Estimating FGLS Coefficients and Standard Errors % Suppose the sensitivity of the U.S. Consumer Price Index (CPI) to changes % in the paid compensation of employees (COE) is of interest. This example % enhances the analysis outlined in the example <docid:econ_ug.buicqm4-12>. % Copyright 2015 The MathWorks, Inc. %% % Load the U.S. macroeconomic data set. load Data_USEconModel %% % The series are nonstationary. Stabilize them by applying the log, and % then the first difference. CPI = diff(log(DataTable.CPIAUCSL)); COE = diff(log(DataTable.COE)); %% % Regress |CPI| onto |COE| including an intercept to obtain OLS estimates. % Plot correlograms for the residuals. Mdl = fitlm(COE,CPI); u = Mdl.Residuals.Raw; figure; subplot(2,1,1) autocorr(u); subplot(2,1,2); parcorr(u); %% % The correlograms suggest that the innovations have significant AR % effects. According to <docid:econ_ug.bs7alhb>, the innovations seem to % comprise an AR(3) series. %% % Estimate the regression coefficients using FGLS. By default, |fgls| % assumes that the innovations are autoregressive. Specify that the % innovations are AR(3) using the |'arLags'| name-value pair argument. [coeff,se] = fgls(CPI,COE,'arLags',3,'display','final'); %% % If the COE series is exogenous with respect to the CPI, then the FGLS % estimates (|coeff|) are consistent and asymptotically more efficient than % the OLS estimates.