Semiparametric Inference And Bandwidth Choice Under Long Memory: Experimental Evidence

Yıl 2013, Cilt: 6 Sayı: 1, 27 - 41, 01.01.2013

Uwe Hassler Maya Olivares

Öz

The most widely used semiparametric estimators under fractional integration are variants of the local Whittle [LW] estimator. They are consistent for the long memory parameter d and follow a limiting normal distribution. Such properties require the bandwidth m to satisfy certain restrictions for the estimators to be “local” or semiparametric in large samples. Optimal rates for m are known and data-driven selection procedures have been proposed. A Monte Carlo study is conducted to compare the performance of the LW and the so-called exact LW estimators both in terms of experimental size when testing hypotheses about d and in terms of root mean squared error. In particular, the choice of the bandwidth is addressed. Further, competing approximations to limiting normality are compared.

Anahtar Kelimeler

Fractional integration, approximate normality, bandwidth selection

Kaynakça

• Abadir, K. M., Distaso, W. and Giraitis, L. (2007). Nonstationarity-extended local whittle estimation. Journal of Econometrics, 141, 1353–1384.
• Delgado, M. and Robinson, P. M. (1996). Optimal spectral bandwidth for long memory. Statistica Sinica, 6, 97–112.
• Fa¨y, G., Moulines, E., Roueff, F. and Taqqu, M. S. (2009). Estimators of long memory: Fourier versus wavelets. Journal of Econometrics, 151, 159–177.
• Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 4, 221–238.
• Giraitis, L., Robinson, P. M. and Samarov, A. (2000). Adaptive semiparametric estimation of the memory parameter. Journal of Multivariate Analysis, 72, 183–207.
• Granger, C. W. J. and Joyeux, R. (1980). An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis, 1, 15–29.
• Hassler, U. and Kokoszka, P. (2010). Impulse responses of fractionally integrated processes with long memory. Econometric Theory, 26, 1855–1861.
• —, Marmol, F. and Velasco, C. (2006). Residual log-periodogram inference for long-run relationships. Journal of Econometrics, 130, 165–207.
• Hauser, M. A. (1997). Semiparametric and nonparametric testing for long memory: A monte carlo study. Empirical Economics, 22, 247–271.
• Henry, M. (2001). Robust automatic bandwidth for long memory. Journal of Time Series Analysis, 22, 293–316.
• —and Robinson, P. M. (1996). Bandwidth choice in gaussian semiparametric estimation of long range dependence. In P. M. Robinson and M. Rosenblatt (eds.), Athens Conference on Applied Probability and Time Series, Vol. II, New York: Springer, pp. 220–232.
• —and Zaffaroni, P. (2003). The long-range dependence paradigm for macroeconomics and finance. In P. Doukhan, G. Oppenheim and M. S. Taqqu (eds.), Theory and Applications of Long-Range dependence, New York: Birkh¨auser Boston, pp. 417–438.
• Hosking, J. R. M. (1981). Fractional differencing. Biometrika, 68, 165–176.
• Hurvich, C. M. and Beltrao, K. I. (1994). Automatic semiparametric estimation of the memory parameter of a long memory time series. Journal of Time Series Analysis, 15, 285–302.
• — and Chen, W. W. (2000). An efficient taper for overdifferenced series. Journal of Time Series Analysis, 21, 155–180.
• — and Deo, R. S. (1999). Plug-in selection of the number of frequencies in regression estimates of the memory parameter of a long-memory time series. Journal of Time Series Analysis, 20, 331–341.
• — and Ray, B. K. (1995). Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. Journal of Time Series Analysis, 16, 17–41.
• K¨unsch, H. R. (1987). Statistical aspects of self-similar processes. In: Proceedings of the First World Congress of the Bernoulli Society, 1, 67–74.
• Marinucci, D. and Robinson, P. M. (1999). Alternative forms of fractional Brownian motion. Journal of Statistical Planning and Inference, 80, 111–122.
• Nielsen, M. Ø. and Frederiksen, P. H. (2005). Finite sample comparison of parametric, semiparametric, and wavelet estimators of fractional integration. Econometric Reviews, 24, 405–443. Robinson, P. M. (1994). Rates of convergence and optimal bandwidth in spectral analysis of processes with long range dependence. Probability Theory and Related Fields, 99, 443–473. — (1995). Gaussian semiparametric estimation of long range dependence. Annals of Statistics, 23, 1630–1661.
• —(2005). The distance between rival nonstationary fractional processes. Journal of Econometrics, 128, 283–399.
• — and Henry, M. (1999). Long and short memory conditional heteroskedasticity in estimating the memory parameter of levels. Econometric Theory, 15, 299–336.
• Shao, X. and Wu, W. B. (2007). Local whittle estimation of fractional integration for nonlinear processes. Econometric Theory, 23, 899–951.
• Shimotsu, K. (2006). Simple (but effective) tests of long memory versus structural breaks. Working Paper, Queen’s University.
• — (2010). Exact local Whittle estimation of fractional integration with unknown mean and trend. Econometric Theory, 26, 501–540.
• — and Phillips, P. C. B. (2005). Exact local Whittle estimation of fractional integration. The Annals of Statistics, 33, 1890–1933.
• Taqqu, M. S. and Teverovsky, V. (1996). Semi-parametric graphical estimation techniques for longmemory data. In P. M. Robinson and M. Rosenblatt (eds.), Athens Conference on Applied Probability and Time Series, Vol. II, New York: Springer, pp. 420–432.
• Velasco, C. (1999). Gaussian semiparametric estimation of non-stationary time series. Journal of Time Series Analysis, 20, 87–127.
• Whittle, P. (1951). Hypothesis testing in time series analysis. Almqvist and Wiksell.
• — (1953). Estimation and information in stationary time series. Arkiv f¨or Matematik, 2, 423–434.