Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T14:38:03.081Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Simple Graphical Approach to Modelling Economic Fluctuations with an Application to United Kingdom Price Inflation, 1265 to 2005

Published online by Cambridge University Press:  10 May 2011

W. S. Chan ,
M. W. Ng  and
H. Tong
W. S. Chan
Affiliation:
Department of Finance, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong., Tel: +852-2609-7715, Fax: +852-2603-6586, Email: chanws@cuhk.edu.hk
M. W. Ng
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong., Tel: +852-2859-2466, Fax: +852-2858-9041, Email: h9500301@hkusua.hku.hk
H. Tong
Affiliation:
Department of Statistics, Columbia House, London School of Economics, Houghton Street, London WC2A 2AE, U.K., Tel: +44 (0)2079-556879, Fax: +44 (0)2079-557416, Email: h.tong@lse.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Structural instability in economic time series is widely reported in the literature. It is most prevalent in such series as price indices and inflation related data. Many methods have been developed for analysing and modelling structural changes in a univariate time series model. However, most of them assume that the data are generated by one fixed type (linear or non-linear) of the time series processes. This paper proposes a strategy for modelling different segments of an economic time series by different linear or non-linear models. A graphical procedure is suggested for detecting the model change points. The proposed procedure is illustrated by modelling annual United Kingdom price inflation series over the period 1265 to 2005. Stochastic modelling of inflation rates is an important topic to actuaries for dealing with long-term index linked insurance business. The proposed method suggests dividing the U.K. inflation series into four segments for modelling. Inflation projections based on the latest segment of the data are obtained through simulations. To get a better understanding of the impact of structural changes on inflation projections we also perform a forecasting study.

Keywords

Actuarial SimulationsARIMA ModelOutliersSETAR ModelTests for Non-LinearityTime Series AnalysisU.K. Price InflationWilkie Model
Type
Papers
Information
Annals of Actuarial Science , Volume 1 , Issue 1 , March 2006 , pp. 103 - 128
Copyright
Copyright © Institute and Faculty of Actuaries 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transaction on Automatic Control, AC–9, 716–723.CrossRefGoogle Scholar
Atkinson, A., Koopman, S. & Shephard, N. (1997). Detecting shocks, outliers and breaks in time series. Journal of Econometrics, 80, 387–422.CrossRefGoogle Scholar
Balke, N. & Fomby, T. (1991). Shifting trends, segmented trends, and infrequent permanent shocks. Journal of Monetary Economics, 28, 61–85.CrossRefGoogle Scholar
Balke, N. & Fomby, T. (1994). Large shocks, small shocks, and economic fluctuations, outliers in macroeconomic time series. Journal of Applied Econometrics, 9, 181–200.CrossRefGoogle Scholar
Bizovi, K.E., Leikin, J.B., Hryhorczuk, D.O. & Frateschi, L.J. (1998). Night of the sirens: analysis of carbon monoxide-detector experience in suburban Chicago. Annals of Emergency Medicine, 31, 737–740.CrossRefGoogle ScholarPubMed
Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307–327.CrossRefGoogle Scholar
Box, G.E.P. & Jenkins, G.M. (1976). Time series forecasting and control. Second Edition. Holden-Day: San Francisco, CA.Google Scholar
Brenner, Y.S. (1961). The inflation of prices in early Sixteenth Century England. Economic History Review, 2nd series, XIV, 266–284.Google Scholar
Brenner, Y.S. (1962). The inflation of prices in England, 1551–1650. Economic History Review, 2nd series, XV, 266–284.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
Chan, W.S. (2002). Stochastic investment modelling: a multiple time series approach. British Actuarial Journal, 8, 545–591.CrossRefGoogle Scholar
Chan, W.S. & Cheung, S.H. (1994). On robust estimation of threshold autoregressions. Journal of Forecasting, 13, 37–49.CrossRefGoogle Scholar
Chan, W.S. & Ng, M.W. (2004). Robustness of alternative non-linearity tests for SETAR models. Journal of Forecasting, 23, 215–231.CrossRefGoogle Scholar
Chan, W.S. & Wang, S. (1998). Wilkie stochastic model for retail price inflation revisited. British Actuarial Journal, 4, 637–652.CrossRefGoogle Scholar
Chappell, D., Padmore, J., Mistry, P. & Ellis, C. (1996). A threshold model for the French Franc/Deutschmark exchange rate. Journal of Forecasting, 15, 155–164.3.0.CO;2-Z>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
Chen, C.W.S., McCulloch, R. & Tsay, R.S. (1997). A unified approach to estimating and modelling linear and nonlinear time series. Statistica Sinica, 7, 451–472.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
Clements, M. & Hendry, D. (1995). Macro-economic forecasting and modelling. Economic Journal, 105, 1001–1013.CrossRefGoogle Scholar
Clements, M. & Hendry, D. (1996). Intercept corrections and structural change. Journal of Applied Econometrics, 11, 475–494.3.0.CO;2-9>CrossRefGoogle Scholar
Clements, M. & Smith, J. (1997). The performance of alternative forecasting methods for SETAR models. International Journal of Forecasting, 13, 463–475.CrossRefGoogle Scholar
Clements, M. & Smith, J. (1999). A Monte Carlo study of the forecasting performance of empirical SETAR models. Journal of Applied Econometrics, 14, 123–141.3.0.CO;2-K>CrossRefGoogle Scholar
Daykin, C.D. & Hey, G.B. (1990). Managing uncertainty in a general insurance company. Journal of the Institute of Actuaries, 117, 173–277.CrossRefGoogle Scholar
De Brouwer, G. & Ericsson, N.R. (1998). Modelling inflation in Australia. Journal of Business and Economic Statistics, 16, 433–449.Google Scholar
De Jong, P. & Penzer, J. (1998). Diagnosing shocks in time series. Journal of the American Statistical Association, 93, 796–806.CrossRefGoogle Scholar
De Gooijer, J.G. (2001). Cross-validation criteria for SETAR model selection. Journal of Time Series Analysis, 22, 267–281.CrossRefGoogle Scholar
De Gooijer, J.G. & Vidiella-i-Anguera, A. (2003). Nonlinear stochastic inflation modelling using SEASETARs. Insurance: Mathematics and Economics, 32, 3–18.Google Scholar
Dempster, M.A.H., Germano, M., Medova, E.A. & Villaverde, M. (2003). Global asset liability management. British Actuarial Journal, 9, 137–216.CrossRefGoogle Scholar
Dicks-Mireaux, L.A. & Dow, J.C.R. (1959). The determinants of wage inflation: United Kingdom, 1946–1956. Journal of the Royal Statistical Society, A 122, 145–184.CrossRefGoogle Scholar
Embrechts, P., Resnick, S.I. & Samorodnitsky, G. (1999). Extreme value theory as a risk management tool. North American Actuarial Journal, 3, 30–41.CrossRefGoogle Scholar
Fisher, F.J. (1965). Influenza and inflation in Tudor England. Economic History Review, 2nd Series, XVIII, 120–129.CrossRefGoogle Scholar
Foster, R.S. (1994). A stochastic evaluation of the short-range economic assumptions in the 1994 OASDI trustees report. Actuarial Study No. 109, Baltimore, MD: Social Security Administration.Google Scholar
Franses, P.H. & Van Dijk, D. (2000). Nonlinear time series models in empirical finance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Friedman, M. (1977). Nobel lecture: Inflation and unemployment. Journal of Political Economy, 85, 451–473.CrossRefGoogle 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. Journal of the Institute of Actuaries, 119, 173–228.CrossRefGoogle Scholar
Granger, C. & Andersen, A. (1978). An introduction to bilinear time series models. Vandehoek and Ruprecht: Gottingen.Google Scholar
Hamilton, J. (1989). A new approach to the economic analysis of nonstationary time-series and the business cycle. Econometrica, 57, 357–384.CrossRefGoogle Scholar
Hardy, M.R. (2001). A regime-switching model of long-term stock returns. North American Actuarial Journal, 5, 41–53.CrossRefGoogle Scholar
Hardy, M.R. (2003). Investment guarantees: modelling and risk management for equity-linked life insurance. John Wiley & Sons, New York.Google Scholar
Hendry, D. (2001). Modelling U.K. inflation, 1875–1991. Journal of Applied Econometrics, 16, 255–275.CrossRefGoogle Scholar
Hill, E.D. & Long, W.B. (2001). Tudor England: an encyclopedia. London: Garland Publishing, Inc.Google Scholar
Huber, P.P. (1997). A review of the Wilkie's stochastic investment model. British Actuarial Journal, 3, 181–210.CrossRefGoogle Scholar
Jarque, C.M. & Bera, A.K. (1980). Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters, 6, 255–259.CrossRefGoogle Scholar
Junttila, J. (2001). Structural breaks, ARIMA model and Finnish inflation forecasts. International Journal of Forecasting, 17, 203–230.CrossRefGoogle Scholar
Kepetanios, G. (2000). Small sample properties of the conditional last squares estimator in SETAR models. Economics Letters, 69, 267–276.CrossRefGoogle Scholar
Kitts, A. (1990). Comment on a model of retail price inflation. Journal of the Institute of Actuaries, 117, 104–412.CrossRefGoogle Scholar
Krager, H. & Kugler, P. (1993). Nonlinearities in foreign exchange markets: a different perspective. Journal of International Money and Finance, 12, 195–208.CrossRefGoogle Scholar
Lai, S.W. & Frees, E.W. (1995). Examining changes in reserves using stochastic interest models. Journal of Risk and Insurance, 62, 535–574.CrossRefGoogle Scholar
Liu, L.M. (1996). Modelling and forecasting time series using SCA-EXPERT capabilities. Scientific Computing Associates: Chicago.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
Longin, F.M. (2000). From value at risk to stress testing: the extreme value approach. Journal of Banking and Finance, 24, 1097–1130.CrossRefGoogle Scholar
Lucas, A. (2000). A note on optimal estimation from a risk-management perspective under possible misspecified tail behaviour. Journal of Business and Economic Statistics, 18 31–39.Google Scholar
McCulloch, R. & Tsay, R.S. (1994). Bayesian inference of trend- and difference-stationarity. Econometric Theory, 10, 596–608.CrossRefGoogle Scholar
McLeod, A.I. & Li, W.K. (1983). Diagnostic checking ARMA time series models using squared-residual autocorrelations. Journal of Time Series Analysis, 4, 269–273.CrossRefGoogle Scholar
Mitchell, Br.R. & Deane, P. (1962). Abstract of British historical statistics. Cambridge: Cambridge University Press.Google Scholar
Montgomery, A., Zarnowitz, V., Tsay, R.S. & Tiao, G. (1998). Forecasting the U.S. unemployment rate. Journal of the American Statistical Association, 93, 478–493.CrossRefGoogle Scholar
Newbold, P. (1995). Statistics for business and economics. New Jersey: Prentice-Hall.Google Scholar
Office of National Statistics (1996–2005). Annual abstract of statistics. H.M.S.O.: London. (www.statistics.gov.uk/downloads/theme_economy/Rp02.pdf)Google Scholar
Outhwaite, R.B. (1969). Inflation in Tudor and early Stuart England. London: MacMillan.Google Scholar
Peel, D.A. & Speight, A. (1994). Testing for non-linear dependence in inter-war exchange rates. Weltwirtschaftsliches Archiv, 130, 391–417.CrossRefGoogle Scholar
Phelps Brown, E.H. & Hopkins, S.V. (1956). Seven centuries of the prices of consumables, compared with builder's wages. Economica, 23, 269–312.Google Scholar
Potter, S. (1995). A nonlinear approach to U.S. GNP. Journal of Applied Econometrics, 10, 109–125.CrossRefGoogle Scholar
Roll, R. (1996). Treasury inflation-indexed bonds: the design of a new security. Journal of Fixed Income, 6, 9–27.CrossRefGoogle Scholar
Rosenberg, M.A. & Young, V.R. (1999). A Bayesian approach to understanding time series data. North American Actuarial Journal, 3, 130–143.CrossRefGoogle Scholar
Rowlatt, P.A. (1988). Analysis if the recent path of U.K. inflation. Oxford Bulletin of Economics and Statistics, 50, 335–360.CrossRefGoogle Scholar
Sargan, J.D. (1964). Wages and prices in the United Kingdom: a study in econometric methodology (with discussion). In Econometric analysis for national economic planning, Hart, P.E., Mills, G. & Whitaker, J.K. (eds). Vol. 16 of Colston Papers. Butterworth Co: London.Google Scholar
Sims, C. (1980). Macroeconomics and reality. Econometrica, 48, 1–48.CrossRefGoogle Scholar
Stock, J. & Watson, M. (1996). Evidence on structural instability in macroeconomic time series relations. Journal of Business and Economic Statistics, 14, 11–30.Google Scholar
Tiao, G. & Box, G.E.P. (1981). Modelling multiple time series with applications. Journal of the American Statistical Association, 76, 802–816.Google Scholar
Tiao, G. & Tsay, R.S. (1994). Some advances in non-linear and adaptive modelling in timeseries. Journal of Forecasting, 13, 109–131.CrossRefGoogle Scholar
Tong, H. (1978). On a threshold model. In Pattern recognition and signal processing, Chen, C.H. (ed.). Sijhoff and Noordoff: Amsterdam.Google Scholar
Tong, H. (1983). Threshold models in non-linear time series analysis. Springer-Verlag: New York.CrossRefGoogle Scholar
Tong, H. (1990). Non-linear time series: a dynamical system approach. Clarendon Press: Oxford.CrossRefGoogle Scholar
Tsay, R.S. (1988). Outliers, level shifts and variance changes in time series. Journal of Forecasting, 7, 1–20.CrossRefGoogle Scholar
Tsay, R.S. (1989). Testing and modelling threshold autoregressive processes. Journal of the American Statistical Association, 84, 231–240.CrossRefGoogle Scholar
Tsay, R.S. (1991). Detecting and modelling nonlinearity in univariate time series analysis. Statistica Sinica, 1, 431–451.Google Scholar
Whitten, S. & Thomas, G. (1999). A non-linear stochastic asset model for actuarial use. British Actuarial Journal, 5, 919–953.CrossRefGoogle Scholar
Wilkie, A.D. (1981). Indexing long-term financial contracts. Journal of the Institute of Actuaries, 108, 299–360.CrossRefGoogle Scholar
Wilkie, A.D. (1986). More on a stochastic asset model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341–403.CrossRefGoogle Scholar
Wilkie, A.D. (1995). A stochastic investment model for actuarial use. British Actuarial Journal, 1, 777–964.CrossRefGoogle Scholar
Yadav, P.K., Pope, P.F. & Paudyal, K. (1994). Threshold autoregressive modelling in finance: the price difference of equivalent assets. Mathematical Finance, 4, 205–221.CrossRefGoogle Scholar