The impact of estimation methods and data frequency on the results of long memory assessment

• Autorzy: Brania K. , Gurgul H.

Identyfikatory

DOI

10.7494/manage.2015.16.1.7

• Języki publikacji: EN

Abstrakty

EN

The main goal of this paper is to examine the effects of selected methods of estimation (the Geweke and Porter-Hudak, modified Geweke and Porter-Hudak, Whittle, R/S Rescaled Range Statistic, aggregated variance, aggregated absolute value, and Peng’s variance of residuals methods) and data frequency on properties of Hurst exponents for stock returns, volatility, and trading volumes of 43 companies and eight stock market indices. The calculations have been performed for a time series of log-returns, squared log-returns, and log-volume (based on hourly and daily data) by nine methods. Descriptive statistics and distribution laws of Hurst exponents depend on the method of estimation and, to some extent, on data frequency (daily and hourly). While by and large in log-returns no long memory has been detected, some estimation methods confirm the existence of long memory in squared log-returns. All of the applied estimation methods show long memory in log-volume data.

Słowa kluczowe

EN

stock returns; volatility; trading volume; Hurst exponent; long memory

• Wydawca: Wydawnictwa AGH
• Czasopismo: Managerial Economics
• Rocznik: 2015
• Tom: Vol. 16, no. 1
• Strony: 7--37
• Opis fizyczny: Bibliogr. 56 poz., tab.

Twórcy

autor

Brania K.

• Jagiellonian University in Cracow, Faculty of Mathematics and Computer Science

autor

Gurgul H.

• AGH University of Science and Technology, Faculty of Management, Department of Application of Mathematics in Economics

Bibliografia

• [1] Agiakloglou, C., Newbold, P. and Wohar, M. (1993) ‘Bias in an estimator of the fractional difference parameter’, Journal of Time Series Analysis, vol. 14, pp. 235–246.
• [2] An, S. and Bloomfield, P. (1993) Cox and Reid’s modification in regression models with correlated errors, Technical Report, North Carolina State University.
• [3] Andrews, D.W.K. and Guggenberger, P. (2003) ‘A bias-reduced log-periodogram regression estimator for the long memory parameter’, Econometrica, vol. 71, pp. 675–712.
• [4] Andrews, D.W.K. and Sun, Y. (2004) ‘Adaptive local polynomial Whittle estimation of long-range dependence’, Econometrica, vol. 72, pp. 569–614.
• [5] Aydogan, K. and Booth, G.G. (1988) ‘Are there long cycles in common stock returns?’, Southern Economic Journal, vol. 55, pp. 141–149.
• [6] Baillie, R.T. (1996) ‘Long memory processes and fractional integration in econometrics’, Journal of Econometrics, vol. 73, pp. 5–59.
• [7] Barkoulas, J.T. and Baum, C.F. (1996) ‘Long term dependence in stock returns’, Economics Letters, vol. 53, pp. 253–259.
• [8] Barkoulas, J.T, Labys, W.C. and Onochie, J. (1997) ‘Fractional dynamics in international commodity prices’, Journal of Futures Markets, vol. 17, pp. 161–189.
• [9] Beran, J.A. (1992) ‘Statistical methods for data with long-range dependence’, Statistical Science, vol. 7, pp. 404–427.
• [10] Beran, J.A. (1994) Statistics for Long memory Processes, London: Chapman and Hall.
• [11] Beveridge, S. and Oickle, C. (1997) ‘Long memory in the Canadian stock market’, Applied Financial Economics, pp. 667–672.
• [12] Bollerslev, T. and Jubinski, D. (1999) ‘Equity trading volume volatility: latent information arrivals and common long-run dependencies’, Journal of Business & Economic Statistics, vol. 17, pp. 9–21.
• [13] Bollerslev, T. and Mikkelsen, H.O. (1996) ‘Modeling and pricing long memory in stock market volatility’, Journal of Econometrics, vol. 73, pp. 151–184.
• [14] Booth, G.G., Kaen, F.R. and Koveos, P.E. (1982) ‘R/S analysis of foreign exchange markets under two international monetary regimes’, Journal of Monetary Economics, vol. 10, pp. 407–415.
• [15] Cheung, Y.W. and Lai, K.S. (1993) ‘Do gold market returns have long memory?’, Financial Review, vol. 28, pp. 181–202.
• [16] Cheung, Y.W. and Lai, K.S. (1995) ‘A search for long memory in international stock market returns’, Journal of International Money and Finance, vol. 14, pp. 597–615.
• [17] Cheung, Y.W., Lai, K. and Lai, M. (1993) ‘Are there long cycles in foreign stock returns?’, Journal of International Financial Markets, Institutions and Money, vol. 3, pp. 33–47.
• [18] Clark, P.K. (1973) ‘A subordinated stochastic process model with finite variance for speculative prices’, Econometrica, vol. 41, pp. 135–155.
• [19] Copeland, T. (1976) ‘A model of asset trading under the assumption of sequential information arrival’, Journal of Finance, vol. 31, pp. 135–155.
• [20] Cox, D.R. and Reid, N. (1987) ‘Parameter orthogonality and approximate conditional inference (with discussion)’, Journal of the Royal Statistical Society Series B, vol. 49, pp. 1–39.
• [21] Crato, N. (1994) ‘Some international evidence regarding the stochastic memory of stock returns’, Applied Financial Economics, vol. 4, pp. 33–39.
• [22] Darrat, A.F., Rahman, S. and Zhong, M. (2003) ‘Intraday trading volume and return volatility of the DJIA stocks: A note’, Journal of Banking and Finance, vol. 27, pp. 2035–2043.
• [23] Doornik, J.A. and Ooms, M. (2003) ‘Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models’, Computational Statistics and Data Analysis, vol. 42, pp. 333–348.
• [24] Fama, E.F. (1970) ‘Efficient capital markets: A review of theory and empirical work’, Journal of Finance, vol. 25, pp. 383–417.
• [25] Fang, H., Lai, K. and Lai, M. (1994) ‘Fractal structure in currency futures prices’, Journal of Futures Markets, vol. 14, pp. 169–181.
• [26] Geweke, J. and Porter-Hudak, S. (1983) ‘The estimation and application of long memory time series models’, Journal of Time Series Analysis, vol. 4, pp. 221–238.
• [27] Granger, C.W.J. and Joyeux, R. (1980) ‘An introduction to long memory time series models and fractional differencing’, Journal of Time Series Analysis, vol. 1, pp. 15–29.
• [28] Granger, C.W.J. and Zhuanxin, D. (1996) ‘Varieties of long memory models’, Journal of Econometrics, vol. 73, pp. 61–67.
• [29] Greene, M.T. and Fielitz, B.D. (1977) ‘Long-term dependence in common stock returns’, Journal of Financial Economics, vol. 5, pp. 339–349.
• [30] Helms, B.P., Kaen, F.R. and Rosenman, R.E. (1984) ‘Memory in commodity futures contracts’, Journal of Futures Market, vol. 4, pp. 559–567.
• [31] Henry, M. and Robinson, P.M. (1996) ‘Bandwidth choice in Gaussian semiparametric estimation of long range dependence’, in Robinson, P.M. and Rosenblatt, M. (eds) Athens Conference on Applied Probability and Time Series Analysis, Volume II: Time Series Analysis, In Memory of E. J. Hannan, New York, Springer, pp. 220–232.
• [32] Hiemstra, C. and Jones, J.D. (1997) ‘Another look at long memory in common stock returns’, Journal of Empirical Finance, vol. 4, pp. 373–401.
• [33] Hosking, J.R.M. (1981) ‘Fractional differencing’, Biometrika, vol. 68, pp. 165–176.
• [34] Hurst, H.R. (1951) ‘Long-term storage capacity of reservoirs’, Transactions of the American Society of Civil Engineers, vol. 1, pp. 519–543.
• [35] Hurvich, C.M., Deo, R.S. and Brodsky, J. (1998) ‘The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long memory time series’, Journal of Time Series Analysis, vol. 19, pp. 19–46.
• [36] Kim, C. S. and Philips, P.C.B. (1999) Log periodogram regression in the nonstationary case, Mimeo, Yale University.
• [37] Koop, G., Ley, E., Osiewalski, J. and Steel, M.F.J. (1997) ‘Bayesian analysis of long memory and persistence using ARFIMA models’, Journal of Econometrics, vol. 76, pp. 149–169.
• [38] Künsch, H.R. (1987) ‘Statistical aspects of self-similar processes’, in Prokhorov, Y. and Sazanov, V.V. (eds), Proceedings of the First World Congress of the Bernoulli Society. Utrecht, VNU Science Press, pp. 67–74.
• [39] Lo, A.W. (1991) ‘Long-term memory in stock market prices’, Econometrica, vol. 59, pp. 1279–1313.
• [40] Lobato, I.N. (1999) ‘A semiparametric two-step estimator in a multivariate long memory model’, Journal of Econometrics, vol. 90, pp. 129–153.
• [41] Lobato, I.N. and Velasco, C. (2000) ‘Long memory in stock-market trading volume’, Journal of Business & Economic Statistics, vol. 18 (4), pp. 410–427.
• [42] Mandelbrot, B.B. (1971) ‘When can a price be arbitraged efficiently? A limit to the validity of the random walk and martingale models’, Review of Economics and Statistics, vol. 53, pp. 225–236.
• [43] Mandelbrot, B.B. and Van Ness J.W. (1968) ‘Fractional Brownian Motion, Fractional Noises and Applications’, SIAM Review, vol. 10 (4), pp. 422–437.
• [44] Nielsen, M.Ø. (2004) ‘Efficient likelihood inference in nonstationary univariate models, Econometric Theory, vol. 20, pp. 116–146.
• [45] Palma W. (2007) Long memory time series. Theory and methods, New York: Wiley Interscience.
• [46] Peng C.K., Buldyrev S.V., Simons M., Stanley H.E. and Goldberger A.I. (1994) ‘Mosaic organization of DNA nucleotides’, Physical Review E, vol. 49, pp. 1685–1698.
• [47] Phillips, P.C.B. and Shimotsu, K. (2004) ‘Local Whittle estimation in nonstationary and unit root cases’, Annals of Statistics, vol. 34 (2), pp. 656–692.
• [48] Robinson, P.M. (1995a) ‘Log-periodogram regression of time series with long range dependence’, Annals of Statistics, vol. 23, pp. 1048–1072.
• [49] Robinson, P.M. (1995b) ‘Gaussian semiparametric estimation of long range dependence’, Annals of Statistics, vol. 23, pp. 1630–1661.
• [50] Shimotsu, K. and Phillips, P.C.B. (2002a) ‘Pooled log periodogram regression’, Journal of Time Series Analysis, vol. 23, pp. 57–93.
• [51] Shimotsu, K. and Phillips, P.C.B. (2002b) ‘Exact local Whittle estimation of fractional integration’, Cowles Foundation Discussion Paper 1367.
• [52] Sowell, F.B. (1992) ‘Maximum likelihood estimation of stationary univariate fractionally integrated time series models’, Journal of Econometrics,vol. 53, pp. 165–188.
• [53] Tanaka, K. (1999) ‘The nonstationary fractional unit root’, Econometric Theory, vol. 15, pp. 549–582.
• [54] Taqqu M.S., Teverovsky V. and Willinger W. (1995) ‘Estimators for long-range dependence: an empirical study’ Fractals, vol. 3(4), pp. 785–798.
• [55] Velasco, C. (1999a) ‘Non-stationary log-periodogram regression’, Journal of Econometrics, vol. 91, pp. 325–371.
• [56] Velasco, C. (1999b) ‘Gaussian semiparametric estimation of non-stationary time series’, Journal of Time Series Analysis, vol. 20, pp. 87–127.

Uwagi

Financial support for this paper from the National Science Centre of Poland (Research Grant DEC- -2012/05/B/HS4/00810).