Seasonal and Periodic Long Memory Models in the In�ation Rates

Ben Nasr, Adnen and Trabelsi, Abdelwahed (2005): Seasonal and Periodic Long Memory Models in the In�ation Rates.

Abstract

This paper considers the application of long memory processes to describe inflation with seasonal behaviour. We use three different long memory models taking into account the seasonal pattern in the data. Namely, the ARFIMA model with deterministic seasonality, the ARFISMA model, and the periodic ARFIMA (PARFIMA) model. These models are used to describe the inflation rates of four different countries, USA, Canada, Tunisia, and South Africa. The analysis is carried out using the Sowell's (1992) maximum likelihood techniques for estimating ARFIMA model and using the approximate maximum likelihood method for the estimation of the PARFIMA process. We implement a new procedure to obtain the maximum likelihood estimates of the ARFISMA model, in which dummies variables on additive outliers are included. The advantage of this parametric estimation method is that all parameters are estimated simultaneously in the time domain. For all countries, we find that estimates of differencing parameters are significantly different from zero. This is evidence in favour of long memory and suggests that persistence is a common feature for inflation series. Note that neglecting the existence of additive outliers may possibly biased estimates of the seasonal and periodic long memory models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Long memory; Fractional integration; Seasonality; Periodic models; inflation
• Subjects: E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E31 - Price Level ; Inflation ; Deflation; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Andél, J., 1986, "Long memory time series models," Kybernetika, 22(2), 105-123.

Arteche, J. and Robinson, P. M., 1998, "Seasonal and cyclical long memorye," STICERD Discussion Paper, 360, 1-30.

Baillie, R.T., Chung, C.F. and Tieslau, M.A., 1996, "Analysing Inflation by the Fractionally Integrated ARFIMA-GARCH Model," Journal of Applied Econometrics, 11, 23-40.

Baillie Richard T., Young Wook Han, and Tae-Go Kwon, 2002, "Further long memory properties of inflationary shocks," Southern Economic Journal, 68 (3), 496-510.

Ball, L., and S.G. Cecchetti, 1990, "Inflation and uncertainty at short and long horizons," Brookings papers on Economic Activity, 215-254.

Barsky, R.B., 1987, "The Fisher hypothesis and the forecastibility and persistence of inflation,"Journal of Monetary Economics, 19, 3-24.

Baum, C.F., Barkoulas, J.T. and Caglayan, M., 1999, "Persistence in International Inflation Rates," Southern Economic Journal, 65, 900-913.

Beran, J., 1995, "Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models," Journal of Royal Statistical Society B, 57, 659-672.

Box, G.E.P. and G.M. Jenkins, 1970, "Time Series Analysis: Forecasting and Control," San Francisco: Holden-Day.

Brunner, A.D., and G.D. Hess, 1993, "Are higher levels of inflation less predictable? A state-dependent conditional heteroskedasticity approach," Journal of Business and Economic Statistics, 11, 187-197.

Chan, N. H. and W. Palma, 1998, "State space modeling of long-memory processes," Annals of Statistics, 26, 719-740.

Cheung, Y. W., 1993, "Long memory in foreign-exchange rates," Journal of Business and Economic Statistics, 11, 93-101.

Franses, P.H. and Ooms, M., 1997, "A Periodic Long Memory Model for Quarterly UK Inflation," International Journal of Forecasting, 13, 119--128.

Geweke, J.F. and Porter-Hudak, S.,1983, "The Estimation and Application of Long Memory Time Series Models," Journal of Time Series Analysis, 4, 221-238.

Granger, C.W.J. and Joyeux, R., 1980, "An Introduction to Long-Memory Time Series and Fractional Differencing," Journal of Time Series Analysis, 1, 15-39.

Hassler, U., 1994, "Misspecification of long memory seasonal time series," Journal of Time Series Analysis, 15, 19-30.

Hassler, U. and Wolters, J., 1995, "Long Memory in Inflation Rates: International Evidence," Journal of Business and Economic Statistics, 13, 37-45.

Hosking, J., 1981, "Fractional differencing," Biometrika, 68, 165-176.

Hurst, H. E., 1951, "Long Term Storage Capacity of Reservoirs," Transactions of the American Society of Civil Engineers, 116, 770-799.

Lo, A. W., 1991, "Long Term Memory in Stock Market Prices," Econometrica, 59, 1279-1313.

MacDonald, R, and P.D. Murphy, 1989, "Testing for the long run relationship between nominal interest rates and inflation using cointegration techniques," Applied Economics, 21, 439-447.

Ooms, M., 1995, "Flexible seasonal long memory and economic time series. Technical Report 9515/A, Econometric Institute," Erasmus University.

Porter-Hudak, S., 1990, "An application of the seasonal fractionally differenced model to the monetary aggregate," Journal of the American Statistical Association, 85, 338-344.

Reisen, V. A , Cribari N., F. and Jensen, M., 2003, "Long Memory inflationary dynamics; The case of Brazil," Studies in Nonlinear Dynamics and Econometrics, 7 (3), Article 3.

Robinson, P.M., 1995, "Gaussian semi-parametric estimation of long-range dependence," Annals of Statistics, 23, 1630-1661.

Rose, A.K., 1980, "Is the real interest rate stable?," Journal of Finance, 43, 1095-1112.

Sowell, F., 1992, "Maximum Likelihood Estimation of Stationary Univariate Fractionally Integrated Time Series Models", Journal of Econometrics, 53, 165-188.

Vogelsang, T.J., 1999, "Two Simple Procedures for Testing for a Unit Root When There are Additive Outliers," Journal of Time Series Analysis, 20, 237-252.