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Semi-parametric smoothing estimators for long-memory processes with added noise. (English) Zbl 1009.62075

Summary: The development of long-memory stochastic volatility (LMSV) models has increased the interest in the estimation of persistent processes observed with added noise. This paper investigates the performance of semi-parametric methods for estimating the long-memory-parameter in the long-range dependence plus noise case and demonstrates improvements obtained by preliminary smoothing and aggregation of the series.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15 Inference from stochastic processes and spectral analysis
62G07 Density estimation
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[1] Abry, P.; Veitch, D.; Flandrin, P., Long-range dependence: revisiting aggregation with wavelets, J. Time Series Anal., 19, 253-266 (1998) · Zbl 0910.62080
[2] Baillie, R. T.; Bollerslev, T.; Mikkelsen, H. O., Fractionally integrated generalized autoregressive conditional heteroskedasticity, J. Econom., 74, 3-30 (1996) · Zbl 0865.62085
[3] Beran, J., Statistics for Long Memory Processes (1994), Chapman & Hall: Chapman & Hall New York · Zbl 0869.60045
[4] Breidt, F. J.; Crato, N.; de Lima, P. J.F, The detection and estimation of long memory in stochastic volatility, J. Econom., 83, 325-348 (1998) · Zbl 0905.62116
[5] Chambers, M. J., Long memory and aggregation in macroeconomic time series. Symposium on Forecasting and Empirical Methods in Macroeconomics and Finance, Internat. Econom. Rev., 39, 1053-1072 (1998)
[6] Crato, N.; de Lima, P. J.F, Long-range dependence in the conditional variance of stock returns, Econom. Lett., 45, 3, 281-285 (1994) · Zbl 0800.62791
[7] Crato, N.; Ray, B. K., Memory in returns and volatilities of futures’ contracts, J. Futures Markets, 20, 525-544 (2000)
[8] De Lima, P., Crato, N., 1993. Long-memory in stock returns and volatilities, Proceedings of the Business and Economic Statistics Section, American Statistical Association.; De Lima, P., Crato, N., 1993. Long-memory in stock returns and volatilities, Proceedings of the Business and Economic Statistics Section, American Statistical Association.
[9] Delgado, M.; Robinson, P., New methods for the analysis of long-memory time series: applications to Spanish inflation, J. Forecasting, 13, 97-107 (1994)
[10] Deo, R.S., Hurvich, C.M., 2001. On the log periodogram regression estimator of the memory parameter in long memory stochastic volatility models. Econom. Theory, forthcoming.; Deo, R.S., Hurvich, C.M., 2001. On the log periodogram regression estimator of the memory parameter in long memory stochastic volatility models. Econom. Theory, forthcoming. · Zbl 1018.62079
[11] Ding, Z.; Granger, C.; Engle, R. F., A long memory property of stock market returns and a new model, J. Empirical Finance, 1, 83-106 (1993)
[12] Geweke, J.; Porter-Hudak, S., The estimation and application of long memory time series models, J. Time Series Anal., 4, 4, 221-238 (1983) · Zbl 0534.62062
[13] Giraitis, L.; Robinson, P. M.; Surgailis, D., Variance-type estimation of long memory, Stochastic Process. Appl., 80, 1-24 (1999) · Zbl 0955.62090
[14] Granger, C. W.J; Joyeux, R., An introduction to long-memory time series models and fractional differencing, J. Time Series Anal., 1, 15-29 (1980) · Zbl 0503.62079
[15] Hall, P.; Koul, H.; Turlach, B. A., Note on convergence rates of semiparametric estimators of dependence index, Ann. Statist., 25, 1725-1739 (1997) · Zbl 0890.62068
[16] Hosking, J. R.M, Fractional differencing, Biometrika, 68, 1, 165-176 (1981) · Zbl 0464.62088
[17] Hosking, J. R.M, Modeling persistence in hydrological time series using fractional differencing, Water Resources Res., 20, 1898-1908 (1984)
[18] Hosking, J. R.M, Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series, J. Econom., 73, 261-284 (1996) · Zbl 0854.62084
[19] Hurvich, C. M.; Deo, R. S.; Brodsky, J., The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long memory time series, J. Time Series Anal., 19, 19-46 (1998) · Zbl 0920.62108
[20] Hurvich, C. M.; Deo, R. S., Plug-in selection of the number of frequencies in regression estimates of the memory parameter of a long-memory time series, J. Time Series Anal., 20, 331-341 (1999) · Zbl 0933.62095
[21] Pérez, A.; Ruiz, E., Finite sample properties of a QML estimator of stochastic volatility models with long memory, Econom. Lett., 70, 157-164 (2001) · Zbl 1110.62335
[22] Ray, B. K.; Tsay, R. S., Size effects on common long-range dependence in stock volatilities, J. Business Econom. Statist., 18, 254-262 (2000)
[23] Robinson, P. M., Log-periodogram regression of time series with long range dependence, Ann. Statist., 23, 1048-1072 (1995) · Zbl 0838.62085
[24] Robinson, P. M., Gaussian semiparametric estimation of long range dependence, Ann. Statist., 23, 1630-1661 (1995) · Zbl 0843.62092
[25] Robinson, P. M.; Henry, M., Long and short memory conditional heteroskedasticity in estimating the memory parameter on levels, Econom. Theory, 15, 299-336 (1999) · Zbl 1054.62584
[26] Teles, P., Wei, W.W.S., Crato, N., 1999. The use of aggregate time series in testing for long memory. Bulletin of the International Statistical Institute, 52nd Session, 1999, pp. 341-342.; Teles, P., Wei, W.W.S., Crato, N., 1999. The use of aggregate time series in testing for long memory. Bulletin of the International Statistical Institute, 52nd Session, 1999, pp. 341-342.
[27] Taqqu, M.S., Teverovsky, V., 1998. On estimating the intensity of long-range dependence in finite and infinite variance time series. A Practical Guide to Heavy Tails, Birkhäuser, Boston, pp. 177-217.; Taqqu, M.S., Teverovsky, V., 1998. On estimating the intensity of long-range dependence in finite and infinite variance time series. A Practical Guide to Heavy Tails, Birkhäuser, Boston, pp. 177-217. · Zbl 0922.62091
[28] Wright, J., A new estimator of the fractionally integrated stochastic volatility model, Econom. Lett., 63, 295-303 (1999) · Zbl 0922.90032
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