FIN 532. Fama (1975) AER: Expected real interest rates are

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1 FIN 532 Inflation & Interest Rates Fama (1975) AER: Expected real interest rates are (approximately) constant over time, so: E( t t-1 ) = R t E(r) where E( t 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. *. * ***. *** **. * **. * *. * **. * * **. * **. * ** * ***. **

2 Autocorrelations of Changes in CPI Inflation Changes in CPI Inflation *****. ***** ** ** *. ** * * * *. ** * ** *. ** * * Autocorrelations of CPI Inflation (SA) Changes in CPI Inflation. **. ** ***. ** *. * **. ** **. * ***. * **. * **. * **. * ***. * ** **

3 Autocorrelations of Changes in CPI Inflation (SA) Changes in CPI Inflation ****. **** * ** *. ** * ** *. ** * * *. * * * *. * * * Autocorrelations of Tbill Yield Nominal Tbill Yield. *******. ******* *******. ** *******. * ******* ******* * ******* * ****** ******. * ****** * ****** * ****** *****. *

4 Autocorrelations of Real Tbill Yield Real Tbill Yield *. * *. * *. * *. * *. * *. * **. ** Autocorrelations of Real Tbill Yield (SA) Real Tbill Yield *. * *. * *. * *. * * *. *

5 Predict Inflation with Tbill Yields LS // Dependent Variable 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 *. * *. * *. * *. * *. * *. * **. **

6 Predict Inflation (SA) with Tbill Yields LS // Dependent Variable 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) *. * *. * *. * *. * * *. *

7 Specification Check: Include Lagged Inflation with Tbill Yields, LS // Dependent Variable 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 t Prob(F-statistic) ti ti Specification Check: Include Lagged Inflation (SA) with Tbill Yields, LS // Dependent Variable 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 t Prob(F-statistic) ti ti

8 ARIMA(0,1,1) Model for CPI Inflation LS // Dependent Variable is DCPI Convergence achieved after 9 iterations C 1.87E E-0518E 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 t Prob(F-statistic) ti ti Inverted MA Roots.93 Autocorrelations of ARIMA Residuals Q-statistic probabilities adjusted for 1 ARMA term(s) *. * *. * *. * *. * *. * * *. *

9 ARIMA(0,1,1) Model for CPI Inflation LS // Dependent Variable 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 t Prob(F-statistic) ti ti Inverted MA Roots.91 Autocorrelations of ARIMA Residuals (SA) Q-statistic probabilities adjusted for 1 ARMA term(s) *. * *. * *. * *. * * *. * *

10 Composite Regression & ARIMA Model LS // Dependent Variable 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 t Prob(F-statistic) ti ti Composite Regression & ARIMA Model (SA) LS // Dependent Variable 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 t Prob(F-statistic) ti ti

11 Combined Regression & ARIMA Model LS // Dependent Variable 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 likelihoodlih F-statistic ti ti Durbin-Watson stat Prob(F-statistic) Inverted MA Roots.99 Combined Regression & ARIMA Model (SA) LS // Dependent Variable 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 likelihoodlih F-statistic ti ti Durbin-Watson stat Prob(F-statistic) Inverted MA Roots

12 FIN 532 Return to FIN 532 Home page:

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