FIN 533. Autocorrelations of CPI Inflation
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1 FIN 533 Inflation & Interest Rates Fama (1975) AER: Expected real interest rates are (approximately) constant over time, so: E(r t F t-1 ) = R t E(r) where E(r t F t-1 ) is expected inflation given information available at time t-1, R t is the nominal yield on a riskless bond from t-1 to t, and E(r) is the constant expected real return on this bond Autocorrelations of CPI Inflation CPI Inflation. *. * ***. *** **. * **. * *. * **. * * **. * **. * ** * ***. ** Professor G. William Schwert 1
2 Autocorrelations of Changes in CPI Inflation Changes in CPI Inflation *****. ***** ** ** *. ** * * * *. ** * ** *. ** * * Autocorrelations of CPI Inflation (SA) Changes in CPI Inflation. **. ** ***. ** *. * **. ** **. * ***. * **. * **. * **. * ***. * ** ** Professor G. William Schwert 2
3 Autocorrelations of Changes in CPI Inflation (SA) Changes in CPI Inflation ****. **** * ** *. ** * ** *. ** * * *. * * * *. * * * Autocorrelations of Tbill Yield Nominal Tbill Yield. *******. ******* *******. ** *******. * ******* ******* * ******* * ****** ******. * ****** * ****** * ****** *****. * Professor G. William Schwert 3
4 Autocorrelations of Real Tbill Yield Real Tbill Yield *. * *. * *. * *. * *. * *. * **. ** Autocorrelations of Real Tbill Yield (SA) Real Tbill Yield *. * *. * *. * *. * * *. * Professor G. William Schwert 4
5 Predict Inflation with Tbill Yields LS // Dependent is CPINSA C INT R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Autocorrelations of Regression Residuals *. * *. * *. * *. * *. * *. * **. ** Professor G. William Schwert 5
6 Predict Inflation (SA) with Tbill Yields LS // Dependent is CPISA C INT R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Autocorrelations of Regression Residuals (SA) *. * *. * *. * *. * * *. * Professor G. William Schwert 6
7 Specification Check: Include Lagged Inflation with Tbill Yields LS // Dependent is CPINSA C INT CPINSA(-1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Specification Check: Include Lagged Inflation (SA) with Tbill Yields LS // Dependent is CPISA C INT CPISA(-1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Professor G. William Schwert 7
8 ARIMA(0,1,1) Model for CPI Inflation LS // Dependent is DCPI Convergence achieved after 9 iterations C 1.87E E MA(1) R-squared Mean dependent var 1.10E-05 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted MA Roots.93 Autocorrelations of ARIMA Residuals Q-statistic probabilities adjusted for 1 ARMA term(s) *. * *. * *. * *. * *. * * *. * Professor G. William Schwert 8
9 ARIMA(0,1,1) Model for CPI Inflation LS // Dependent is DCPISA Convergence achieved after 8 iterations C 1.71E E MA(1) R-squared Mean dependent var 1.11E-05 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted MA Roots.91 Autocorrelations of ARIMA Residuals (SA) Q-statistic probabilities adjusted for 1 ARMA term(s) *. * *. * *. * *. * * *. * * Professor G. William Schwert 9
10 Composite Regression & ARIMA Model LS // Dependent is CPINSA C PCPI INT R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Composite Regression & ARIMA Model (SA) LS // Dependent is CPISA C PCPISA INT R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Professor G. William Schwert 10
11 Combined Regression & ARIMA Model LS // Dependent is DCPI Convergence achieved after 25 iterations C 6.89E E DINT MA(1) R-squared Mean dependent var 1.10E-05 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted MA Roots.99 Combined Regression & ARIMA Model (SA) LS // Dependent is DCPISA Convergence achieved after 11 iterations C 3.02E E DINT MA(1) R-squared Mean dependent var 1.11E-05 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted MA Roots.96 Professor G. William Schwert 11
12 FIN 533 Return to FIN 533 Home page: Professor G. William Schwert 12
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