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The Wilkie Model for Retail Price Inflation Revisited

Published online by Cambridge University Press:  10 June 2011

W.S. Chan
Affiliation:
Department of Statistics, The University of Hong Kong, Pokfulam Road, Hong Kong. Tel: + 852-2859-2466; Fax: + 852-2858-5041; E-mail; ecscws@nus.edu.sg
S. Wang
Affiliation:
SCOR Reinsurance Company, One Pierce Place, Itasca, IL 60143-4049, USA. Tel: + 1-312-663-9393: Fax: + 1-312-663-6611; E-mail: scorus/itasca/swang%5512559@mcimail.com

Abstract

A first order autoregressive model was proposed in Wilkie (1995) for the retail price inflation series as a part of his stochastic investment model. In this paper we apply time series outlier analysis to the data set and a revised model is derived. It significantly alleviates the problem of leptokurtic and positive skewed residual distribution as found in the original model. Finally, ARCH models for the original series and the outlier-adjusted data are also considered.

Type
Sessional meetings: papers and abstracts of discussions
Copyright
Copyright © Institute and Faculty of Actuaries 1998

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References

REFERENCES

Chan, W.S. (1995a). Understanding the effect of time series outliers on sample autocorrelations. TEST: A Journal of Spanish Statistics and O.R. Society, 4, 179186.Google Scholar
Chan, W.S. (1995b). Time series outliers and spurious autocorrelations. Journal of Applied Statistical Science, 3, 4051.Google Scholar
Chen, C. & Liu, L.M. (1993). Joint estimation of model parameters and outlier effects in time series. Journal of the American Statistical Association, 88, 284297.Google Scholar
Clarkson, R.S. (1991). A non-linear stochastic model for inflation. Transactions of the 2nd AFIR International Colloquium, Brighton, 3, 233253.Google Scholar
Central Statistical Office (1991). Retail prices, 1914–1990. H.M.S.O., London.Google Scholar
Central Statistical Office (1994). Annual abstract of statistics. H.M.S.O., London.Google Scholar
Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 9871007.Google Scholar
Fox, A.J. (1972). Outliers in time series. J.R.S.S., B34, 350363.Google Scholar
Geoghegan, T.J., Clarkson, R.S., Feldman, K.S., Green, S.J., Kitts, A., Lavecky, J.P., Ross, F.J.M., Smith, W.J. & Toutounchi, A. (1992). Report on the Wilkie stochastic investment model. J.I.A. 119, 173228.Google Scholar
Guerard, J.B. (1990). NYSE volume: an application of outlier analysis. Journal of Forecasting, 9, 467471.Google Scholar
Hamilton, J.D. (1994). Time series analysis. Princeton University Press, Princeton, N.J.CrossRefGoogle Scholar
Harvey, A.C. (1989). Forecasting structural time-series models, and the Kalman filter. Cambridge University Press.Google Scholar
Huber, P.P. (1997). A review of Wilkie's stochastic investment model. B.A.J. 3, 181210.Google Scholar
Jarque, C.M. & Bera, A.K. (1981). An efficient large sample test for normality of observations and regression residuals. Working Papers in Economics and Econometrics, 47, Australian National University.Google Scholar
Kitts, A. (1990). Comments on a model of retail price inflation. J.I.A. 117, 407412.Google Scholar
Liu, L.M. & Hudak, G.B. (1994). Forecasting and time series analysis using the SCA statistical system. Scientific Computing Associates Corp., Illinois 60522–4692, U.S.A.Google Scholar
Liung, G.M. (1993). On outlier detection in time series. J.R.S.S. B55, 559567.Google Scholar
Ljung, G.M. & Box, G.E.P. (1978). On a measure of lack of fit in time series models. Biometrika, 65, 297303.Google Scholar
McLeod, A.I. & Li, W.K. (1983). Diagnostic checking ARMA time series models using squared-residual autocorrelations. Journal of Time Series Analysis, 4, 269273.Google Scholar
Mitchell, B.R. & Deane, P. (1962). Abstract of British historical statistics. Cambridge University Press.Google Scholar
Muirhead, C.R. (1986). Distinguishing outlier types in time series. J.R.S.S. B48, 3947.Google Scholar
Office of National Statistics (1997). Annual abstract of statistics. H.M.S.O., London.Google Scholar
Thomas, G., Plu, G. & Thalabard, J.C. (1992). Identification of pulses in hormone time series using outlier detection methods. Statistics in Medicine, 11, 21332145.Google Scholar
Tiao, G.C. & Tsay, R.S. (1989). Model specification in multivariate time series. J.R.S.S. B51, 157213.Google Scholar
Tong, H. (1990). Non-linear time series: a dynamical system approach. Clarendon Press, Oxford.Google Scholar
Wilkie, A.D. (1986). A stochastic investment model for actuarial use. T.F.A. 39, 341403.Google Scholar
Wilkie, A.D. (1987). Stochastic investment models — theory and applications. Insurance: Mathematics and Economics, 6, 6583.Google Scholar
Wilkie, A.D. (1992). Stochastic investment models for XXIst century actuaries. Transactions of the 24th International Congress of Actuaries, Montreal, 5, 119137.Google Scholar
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. B.A.J. 1, 777964.Google Scholar