# Nonstationary Time Series Analysis and Cointegration

By Colin P. Hargreaves | Go to book overview

9. APPLICATION

Inder and Silvapulle ( 1992) used cointegration methods to test if the Fisher effect applies in Australia. One question related to this is whether nominal interest rates and inflation are cointegrated. Consider the equation
it = β0 + β1πt + ut (39)
where it is the nominal interest rate and πt is the inflation rate. Inder and Silvapulle ( 1992) treat (39) as a long-run relationship which implies that the interest rate and the inflation rate are cointegrated. They use the augmented Dickey-Fuller test to test for cointegration between the series as represented by the change in the log of CPI for inflation and the bank accepted bill rate for interest rates. The estimated parameters for equation (37) were β + ̂0 = 7.2275 and β + ̂1 = -0.4387, and the Dickey- Fullert statistic was -2.5921. Compared with a 10% critical value of -2.84, it can be seen that the null hypothesis of no cointegration could not be rejected.

However, it is possible that the failure to reject the null hypothesis was due only to lack of power of the Dickey-Fuller test, rather than true non-cointegration. To check this, we computed

to test the null hypothesis of cointegration. We chose the lag length l by following Inder ( 1991), who suggested choosing the largest significant lag in the autocorrelation function of the OLS residuals. For this application, this gave a choice of l = 4. We obtained , which when compared to the 1% critical value of 0.5497 allows rejection of the null hypothesis of cointegration. This provides further evidence for the results of Inder and Silvapulle ( 1992) rejecting the cointegration hypothesis.

REFERENCES

ENGLE, R. F. and C. W. J. GRANGER ( 1987), "'Cointegration and Error Correction: Representation, Estimation and Testing'", Econometrica, 55, pp. 251-76.

INDER, B. ( 1991), "'Some Strong Evidence for a Unit Root in Economic Time Series'", Mimeo, Monash University.

INDER, B. and P. SILVAPULLE ( 1992), "'Does the Fisher Effect Apply in Australia?'", Working Paper No. 5/92, Monash University.

JOHANSEN, S. ( 1988), "'Statistical Analysis of Cointegration Vectors'", Journal of Economic Dynamics and Control, 12, pp. 231-54.

KING, M. L. and G. H. HILLIER ( 1985), "'Locally Best Invariant Tests of the Error Covariance Matrix of the Linear Regression Model'", Journal of the Royal Statistical Society B, 47, pp. 98-102.

KWIATKOWSKI, D., P. C. B. PHILLIPS, P. SCHMIDT and Y. SHIN ( 1992), "'Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure are We that Economic Time Series Have a Unit Root?'", Journal of Econometrics, 54, pp. 159-78.

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Nonstationary Time Series Analysis and Cointegration

• Title Page iii
• Contents v
• List of Figures vii
• List of Tables xiii
• List of Contributors xv
• Foreword xvii
• 1 - Introduction 1
• References 8
• 2 - Towards a Theory of Economic Forecasting 9
• Appendix 48
• References 50
• 3 - Bayes Models and Forecasts of Australian Macroeconomic Time Series 53
• References 86
• 4 - A Review of Methods of Estimating Cointegrating Relationships 87
• References 129
• 5 - A Test of the Null Hypothesis of Cointegration 133
• References 151
• 6 - Modelling Seasonal Variation 153
• References 176
• 7 - Cointegration, Seasonality, Encompassing, and the Demand for Money in the Uk 179
• Appendix A. the Data 214
• Appendix B. Sequential Reduction Analysis 216
• References 220
• 8 - Evaluating a Real Business Cycle Model 225
• Appendix 252
• References 254
• 9 - Misspecification Versus Bubbles in the Cagan Hyperinflation Model 257
• References 281
• 10 Regime Switching with Time-Varying Transition Probabilities 283
• Appendix 299
• References 302
• Name Index 303
• Subject Index 307
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