Cotter, John (2004): Uncovering Long Memory in High Frequency UK Futures. Published in: European Journal of Finance , Vol. 11, (2005): pp. 325-337.
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Accurate volatility modelling is paramount for optimal risk management practices. One stylized feature of financial volatility that impacts the modelling process is long memory explored in this paper for alternative risk measures, observed absolute and squared returns for high frequency intraday UK futures. Volatility series for three different asset types, using stock index, interest rate and bond futures are analysed. Long memory is strongest for the bond contract. Long memory is always strongest for the absolute returns series and at a power transformation of k < 1. The long memory findings generally incorporate intraday periodicity. The APARCH model incorporating seven related GARCH processes generally models the futures series adequately documenting ARCH, GARCH and leverage effects. Keywords: Long Memory, APARCH, High Frequency Futures
|Item Type:||MPRA Paper|
|Original Title:||Uncovering Long Memory in High Frequency UK Futures|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G10 - General
G - Financial Economics > G0 - General
|Depositing User:||John Cotter|
|Date Deposited:||12. Jun 2007|
|Last Modified:||20. Feb 2013 21:51|
21 the seven separate GARCH models are fully well specified. This implies that modelling volatility with a generalised process incorporating a number of stylized features may dominate modelling with individual standard GARCH related specifications. Furthermore, the APARCH process is unable to remove the long memory features by rescaling the original futures series. Long memory remains, and follows a slightly different pattern prior to rescaling. Future parametric work on high frequency realisations should incorporate alternative approaches such as the discrete Fractionally Integrated GARCH (FIGARCH) related models (Baillie et al, 1996) or the Long Memory Stochastic Volatility (LMSV) processes (Breidt et al, 1998) to assess their ability to capture long memory with cyclical intraday patterns. 6 References Andersen, T.G., and T. Bollerslev (1997a) Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns, Journal of Finance, 52, 975-1005. Andersen, T.G., and T. Bollerslev (1997b) Intraday Periodicity and Volatility Persistence in Financial Markets, Journal of Empirical Finance, 4, 115-158. Andersen, T.G., T. Bollerslev, F.X. Diebold and P. Labys (1999) The Distribution of Exchange Rate Volatility, NBER Working Paper No. 6961. Baillie, R. T. and R. P. DeGennaro (1990) Stock Returns and Volatility, Journal of Financial and Quantitative Analysis, 25, 203-214. Baillie, R. T. (1996) Long Memory Processes and Fractional Integration in Econometrics, Journal of Econometrics, 73, 5-59. 22 Baillie, R. T., T., Bollerslev, and H. O. Mikkelsen (1996) Fractionally Integrated Generalised Conditional Heteroskedasticity, Journal of Econometrics, 74, 3- 30. Beran, J. (1994) Statistics for Long-Memory Processes, Chapman & Hall, New York. Berndt, E. K., B. H. Hall, R. E. Hall and J. A. Hausman (1974) Estimation and Inference in Nonlinear Structural Methods, Annals of Economic and Social Measurement, 3, 653-665. Black, F. (1976) Studies in Stock Price Volatility Changes, Proceedings of the 1976 Business Meeting of the Business and Economics Statistics Section, American Statistical Association, 177-181. Bollerslev, T. (1986) Generalised Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31, 307-327. Breidt, F. J., Crato, N., and P deLima (1998) On the Detection and Estimation of Long-Memory in Stochastic Volatility, Journal of Econometrics, 83, 325- 348. Brock, W. A. and A. W. Kleidon (1992) Periodic Market Closure and Trading Volume, Journal of Economic Dynamics and Control, 16, 451-489. Darcorogna, M. M, U. A Muller, R. J. Nagler, R. B. Olsen, and O. V. Pictet (1993) A Geographical Model for the Daily and Weekly Seasonal Volatility in the Foreign Exchange Market, Journal of International Money and Finance, 12, 413-438. Diebold, F. X., and G. D. Rudebusch (1989) Long Memory and Persistence in Aggregate Output, Journal of Monetary Economics, 24, 189-209. 23 Ding, Z., C. Granger, C. W. J., and R. F. Engle (1993) A Long Memory Property of Stock Returns, Journal of Empirical Finance, 1, 83-106. Ding, Z., and C. W. J. Granger (1996) Modelling Volatility Persistence of Speculative Returns, Journal of Econometrics, 73, 185-215. Engle, R. F. (1982) Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK Inflation, Econometrica, 50, 987-1008. Geweke, J. (1986) Modelling the Persistence of Conditional Variances: A Comment, Econometric Reviews, 5, 57-61. Glosten, L., R. Jaganathan and D. Runkle (1993) On the Relations between the Expected Value and the Volatility of Nominal Excess Return on Stocks, Journal of Finance, 48, 1779-1801. Granger, C. W. J. (1998) Comment on ‘Real and Spurious Long-Memory Properties of Stock-Market Data’ , Journal of Business and Economic Statistics, 16, 268-269. Higgins, M. and A. Bera (1992) A Class of Nonlinear ARCH Models, International Economic Review, 33, 37-158. Lo, A. and A. C. MacKinlay (1990) An Econometric Analysis of Nonsynchronous Trading, Journal of Econometrics, 45, 181-212. Lobato, I. N. and N. E. Savin (1998) Real and Spurious Long-Memory Properties of Stock-Market Data, Journal of Business and Economic Statistics, 16, 261- 268. Loretan, M., and P. C. B. Phillips (1993) Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets, Journal of Empirical Finance, 1, 211-248. 24 McMillan, D. G. and A. E. H. Speight (2002) Temporal Aggregation, Volatility Components and Volume in High Frequency UK Bond Futures, The European Journal of Finance, 8, 70-92. Nelson, D. B. (1989) Modelling Stock Market Volatility, Proceedings of the American Statistical Association, Business and Economics Statistics Section, pp. 93-98. Pantula, S. G. (1986) Modelling the Persistence of Conditional Variances: A Comment, Econometric Reviews, 5, 71-73. Schwert, G. W. (1990) Stock Market Volatility and the Crash of ’ 87, Review of Financial Studies, 3, 77-102. Shephard, N. (1996) Statistical Aspects of ARCH and Stochastic Volatility, in D. R. Cox, D. V. Hinkley, and O. E. Barndorff-Nielson, Eds, Likelihood, Time Series with Econometric and other Applications, pp. 1-67, Chapman Hall, London. Taylor, S. J. (1986) Modelling Financial Time Series, Wiley, London. Taylor, S. J. (2000) Consequences for Option Pricing of a Long Memory in Volatility, Working Paper, University of Lancaster.