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Stochastic Investment Modelling: a Multiple Time-Series Approach

Published online by Cambridge University Press:  10 June 2011

W.S. Chan
W.S. Chan
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. Tel: + 852-2859-2466; Fax: + 852-2858-9041; E-mail: chanws@hku.hk
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Asbtract

In this paper we adopt the multiple time-series modelling approach suggested by Tiao & Box (1981) to construct a stochastic investment model for price inflation, share dividends, share dividend yields and long-term interest rates in the United Kingdom. This method has the advantage of being direct and transparent. The sequential and iterative steps of tentative specification, estimation and diagnostic checking parallel those of the well-known Box-Jenkins method in the univariate time-series analysis. It is not required to specify any a priori causality as compared to some other stochastic asset models in the literature.

Keywords

ARCH ModelsNon-Linear Threshold ModelsWilkie ModelVector Autoregressive-Moving Average ModelsTime-Series OutliersPrice InflationLong-Term Interest RatesShare Dividend YieldsShare Dividends

Information

Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 8 , Issue 3 , 01 August 2002 , pp. 545 - 591
Copyright
Copyright © Institute and Faculty of Actuaries 2002

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References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC–19, 716–723.CrossRefGoogle Scholar
Balvers, R., Wu, Y. & Gilliland, E. (2000). Mean reversion across national stock markets and parametric contrarian investment strategies. Journal of Finance, 55, 745–772.CrossRefGoogle Scholar
Bartlett, M.S. (1938). Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society, 34, 33–40.CrossRefGoogle Scholar
Black, F. (1990). How to use the holes in Black-Scholes. In The Handbook of Financial Engineering, edited by Smith, C. Jr & Smithson, C.. New York: Harper Business, 304–315.Google Scholar
Blaug, M. (1992). The methodology of economics, or how economists explain. Second edition. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Box, G.E.P. (1976). Science and statistics. Journal of the American Statistical Association, 76, 588–597.Google Scholar
Box, G.E.P. & Cox, D.R. (1964). An analysis of transformation. Journal of the Royal Statistical Society, B26, 211–252.Google Scholar
Box, G.E.P. & Jenkins, G.M. (1976). Time series analysis: forecasting and control. Second edition. Holden-Day Press, San Francisco.Google Scholar
Caldwell, B.J. (1994). Beyond positivism: economic methodology in the twentieth century. Revised edition. Routledge, London.Google Scholar
Carriére, J.F. (2001). A Gaussian process of yield rates calibrated with strips. North American Actuarial Journal, 5 (3), 19–30.CrossRefGoogle Scholar
Carter, J. (1991). The derivation and application of an Australian stochastic investment model. Transactions of the Institute of Actuaries of Australia, 1, 315–428.Google Scholar
Chambers, J.M., Mallows, C.L. & Stuck, B.W. (1976). A method for simulating stable random variables. Journal of the American Statistical Association, 71, 340–344.CrossRefGoogle Scholar
Chan, K.S. & Tong, H. (1990). On likelihood ratio tests for threshold autoregression. Journal of the Royal Statistical Society, B52, 469–476.Google Scholar
Chan, W.S. (1992). A note on time series model specification in the presence of outliers. Journal of Applied Statistics, 19, 117–124.CrossRefGoogle Scholar
Chan, W.S. (1994). On portmanteau goodness-of-fit tests in robust time series modelling. Computational Statistics, 9, 301–310.Google Scholar
Chan, W.S. (1998a). Forecasting Australian retail price inflation: a multiple time series approach. Australian Actuarial Journal, II.2, 127–141.Google Scholar
Chan, W.S. (1998b). Outlier analysis of annual retail price inflation: a cross-country study. Journal of Actuarial Practice, 6, 149–172.Google Scholar
Chan, W.S. & Wang, S. (1998). The Wilkie model for retail price inflation revisited. B.A.J. 4, 637–652.Google Scholar
Chang, I., Tiao, G.C. & Chen, C. (1988). Estimation of time series parameters in presence of outliers. Technometrics, 30, 193–204.CrossRefGoogle Scholar
Chatfield, C. (1985). The initial examination of data (with discussion). Journal of the Royal Statistical Society, A148, 214–253.CrossRefGoogle Scholar
Chatfield, C. (1995). Model uncertainty, data mining and statistical inference (with discussion). Journal of the Royal Statistical Society, A158, 419–465.CrossRefGoogle 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, 284–297.Google Scholar
Clarkson, R.S. (1991). A non-linear stochastic model for inflation. Transactions of the 2nd AFIR International Colloquium, Brighton, 3, 233–253.Google Scholar
Daykin, C.D., Pentikäinen, T. & Pesonen, M. (1994). Practical risk theory for actuaries. Chapman and Hall, London.Google Scholar
Deaves, R. (1993). Modelling and predicting Canadian inflation and interest rates. Canadian Institute of Actuaries, Canada.Google Scholar
Duffie, D. (1996). Dynamic asset pricing theory. Second edition. Princeton University Press, New Jersey.Google Scholar
Durbin, J. & Koopman, S.J. (2000). Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives. Journal of the Royal Statistical Society, B62, 3–56.CrossRefGoogle Scholar
Efron, B. (1986). Why isn't everyone a Bayesian? The American Statistician, 40, 1–5.CrossRefGoogle Scholar
Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007.CrossRefGoogle Scholar
Fama, E.F. (1990). Term structure forecasts of interest rates, inflation and real returns. Journal of Monetary Economics, XXV, 59–76.CrossRefGoogle Scholar
Fama, E.F. & French, K.R. (1988). Permanent and temporary components of stock prices. Journal of Political Economy, 96, 246–273.CrossRefGoogle Scholar
Feller, W. (1966). An introduction to probability theory and its applications, Vol. 2. New York: John Wiley & Sons.Google Scholar
Finkelstein, G.S. (1997). Maturity guarantees revisited: allowing for extreme stochastic fluctuations using stable distributions. B.A.J. 3, 411–482.Google Scholar
Ford, A., Benjamin, S., Gillespie, R.C., Hager, D.P., Loades, D.H., Rowe, B.N., Ryan, J.P., Smith, P. & Wilkie, A.D. (1980). Report of the Maturity Guarantees Working Party. J.I.A. 107, 101–212.Google Scholar
Frees, E., Kung, Y.C., Rosenberg, M., Young, V. & Lai, S.W. (1997). Forecasting social security actuarial assumptions. North American Actuarial Journal, 1, 49–77.CrossRefGoogle Scholar
Hausman, D. (1992). The inexact and separate science of economics. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Huber, P.P. (1995). A review of the Wilkie's stochastic asset model. Actuarial Research Paper No. 70, Department of Actuarial Science & Statistics, The City University, London.Google Scholar
Huber, P.P. (1997). A review of the Wilkie's stochastic investment model. B.A.J. 3, 181–210.Google Scholar
Huber, P.P. & Verrall, R.J. (1999). The need for theory in actuarial economic models. B.A.J. 5, 377–395.Google Scholar
Hull, J.C. (2000). Options, futures, & other derivatives. Fourth edition. Prentice Hall, New Jersey.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
Jorion, P. & Sweeney, R. (1996). Mean reversion in real exchange rates: evidence and implications for forecasting. Journal of International Money and Finance, 15, 535–550.CrossRefGoogle Scholar
Kemp, M.H.D. (1997). Actuaries and derivatives. B.A.J. 3, 51–162.Google Scholar
Kemp, M.H.D. (2000). Pricing derivatives under the Wilkie model. B.A.J. 6, 621–635.Google Scholar
Klein, G.E. (1993). The sensitivity of cash-flow analysis to the choice of statistical model for interest rate changes. Transactions of the Society of Actuaries, XLV, 79–186.Google Scholar
Ledolter, J. (1989). The effect of additive outliers on the forecasts from ARIMA models. International Journal of Forecasting, 5, 231–240.CrossRefGoogle Scholar
Leamer, E.E. (1978). Specification searches: ad hoc inference with experimental data. Wiley & Sons, New York.Google Scholar
Lee, B.S. (1995). The response of stock prices to permanent and temporary shocks to dividends. Journal of Financial and Quantitative Analysis, 30, 1–22.CrossRefGoogle 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
Ljung, G.M. & Box, G.E.P. (1978). On a measure of lack of fit in time series models. Biometrika, 65, 297–303.CrossRefGoogle Scholar
Lütkepohl, H. (1993). Introduction to multiple time series analysis. Second edition. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Malliaropulos, D. & Priestley, R. (1999). Mean reversion in Southeast Asian stock markets. Journal of Empirical Finance, 6, 355–384.CrossRefGoogle Scholar
McLeod, A.I. & Li, W.K. (1983). Diagnostic checking ARMA time-series models using squared-residual autocorrelations. Journal of Time Series Analysis, 1, 66–74.Google Scholar
Metz, M. & Ort, M. (1993). Stochastic models for the Swiss consumer's price index and the cost of the adjustment of pensions to inflation for a pension fund. Transactions of the 3rd AFIR International Colloquium, 789–806.Google Scholar
Nam, K., Pyun, C.S. & Avard, S.L. (2001). Asymmetric reverting behaviour of short-horizon stock returns: an evidence of stock market overreaction. Journal of Banking and Finance, 25, 807–824.CrossRefGoogle Scholar
Pemberton, J.M. (1999). The methodology of actuarial science. B.A.J. 5, 115–195.Google Scholar
Praetz, P.D. (1972). The distribution of share price changes. Journal of Business, 45, 49–55.CrossRefGoogle Scholar
Reinsel, G.C. (1997). Elements of multivariate time series analysis. Second edition. Springer Verlag, New York.CrossRefGoogle Scholar
Sherris, M., Tedesco, L. & Zehnwirth, B. (1999). Investment returns and inflation models: some Australian evidence. B.A.J. 5, 237–268.Google Scholar
Spahr, R.W. & Schwebach, R.G. (1998). Comparing mean reverting versus pure diffusion interest rate processes in valuing postponement options. The Quarterly Review of Economics and Finance, 38, 579–598.CrossRefGoogle Scholar
Thomson, R.J. (1996). Stochastic investment modelling: the case of South Africa. B.A.J. 2, 765–801.Google Scholar
Tiao, G.C. & Box, G.E.P. (1981). Modelling multiple time series with applications. Journal of the American Statistical Association, 76, 802–816.Google Scholar
Tiao, G.C. & Tsay, R.S. (1994). Some advances in non-linear and adaptive modelling in timeseries. Journal of Forecasting, 13, 109–131.CrossRefGoogle Scholar
Tiao, G.C., Tsay, R.S. & Wang, T. (1993). Usefulness of linear transformations in multivariate time-series. Empirical Economics, 18, 567–593.CrossRefGoogle Scholar
Tong, H. (1983). Threshold models in non-linear time series analysis. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Tong, H. (1990). Non-linear time series: a dynamical system approach. Clarendon Press, Oxford.CrossRefGoogle Scholar
Veall, M.R. (1989). Applications of computational-intensive methods to econometrics. Bulletin of the International Statistical Institute, 47, 75–88.Google Scholar
Wei, W.W.S. (1990). Time series analysis: univariate and multivariate methods. Addison-Wesley, New York.Google Scholar
Whitten, S. & Thomas, G. (1999). A non-linear stochastic asset model for actuarial use. B.A.J. 5, 919–953.Google Scholar
Wilkie, A.D. (1981). Indexing long-term financial contracts. J.I.A. 108, 299–360.Google Scholar
Wilkie, A.D. (1986). A stochastic investment model for actuarial use. T.F.A. 39, 341–403.Google Scholar
Wilkie, A.D. (1987). Stochastic investment models — theory and applications. Insurance, Mathematics and Economics, 6, 65–83.Google Scholar
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. B.A.J. 1, 777–964.Google Scholar
Wilkie, A.D. (2000). Correspondence. B.A.J. 6, 251–255.Google Scholar
Wilson, G.T. (1973). The estimation of parameters in multivariate time series models. Journal of the Royal Statistical Society, B35, 76–85.Google Scholar
Wong, C.S. & Li, W.K. (2000). On a mixture autoregressive model. Journal of the Royal Statistical Society, B62, 95–116.CrossRefGoogle Scholar
Wright, I.D. (1998). A stochastic asset model using vector auto-regression. Actuarial Research Paper No. 108, Department of Actuarial Science and Statistics, City University, London.Google Scholar