**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32870

##### Small Sample Bootstrap Confidence Intervals for Long-Memory Parameter

**Authors:**
Josu Arteche,
Jesus Orbe

**Abstract:**

**Keywords:**
bootstrap,
confidence interval,
log periodogram regression,
long memory.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1083581

**References:**

[1] Velasco, C., 1999. Non stationary log-periodogram regression. J. Econometrics 91, 325-371.

[2] Geweke, J. and Porter-Hudak, S., 1983. The estimation and application of long-memory time series models. J. Time Ser. Anal. 4, 221-238.

[3] Robinson, P.M., 1995. Log-periodogram regression of time series with long-range dependence. Ann. Statist. 23, 1048-1072.

[4] Hurvich, C.M., Deo, R. and Brodsky, J., 1998. The mean squared error of Geweke and Porter-Hudak-s estimator of the memory parameter in a long-memory time series. J. Time Ser. Anal. 19, 19-46.

[5] Phillips, P.C.B., 2007. Unit root log periodogram regression. J. Econometrics 138, 104-124.

[6] Kim, C.S. and Phillips, P.C.B., 2006. Log periodogram regression: The nonstationary case. Cowles Foundation Discussion Paper No. 1587.

[7] Phillips, P.C.B. and Shimotsu, K., 2004. Local Whittle estimation in nonstationary and unit root cases. Ann. Statist. 32, 656-692.

[8] Arteche, J., 2004, Gaussian Semiparametric Estimation in Long Memory in Stochastic Volatility and Signal Plus Noise Models. J. Econometrics 119, 131-154.

[9] Giraitis, L., Robinson, P.M. and Samarov, A., 2000. Adaptive semiparametric estimation of the memory parameter. J. Multiv. Anal. 72, 183-207.

[10] Hurvich, C.M., 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. J. Time Ser. Anal. 20, 331-341.

[11] Hassler, U. and Wolters, J., 1995. Long memory in inflation rates: International evidence. J. Business Econ. Stat. 13, 37-45.

[12] Diebold, F.X. and Rudebush, G., 1989. Long memory and persistence in aggregate output. J. Monet. Econ. 24, 189-209.

[13] Diebold, F.X. and Rudebush, G., 1991. Is consumption too smooth: Long memory and the Deaton paradox. Rev. Econ. Statist. 73, 1-9.

[14] Sowell, F., 1992a. Maximum likelihood estimation of stationary univariate fractionally integrated time series models. J. Econometrics 53, 165-188.

[15] Arteche, J. and Robinson, P.M., 2000. Semiparametric inference in seasonal and cyclical long memory processes. J. Time Ser. Anal. 21, 1-27.

[16] Sowell, F., 1992b. Modeling long-run behaviour with the fractional ARIMA model. J. Monet. Econ. 29, 277-302.

[17] Andrews, D.W.K., Lieberman, O. and Marmer, V., 2006. Higher-order improvements of the parametric bootstrap for long-memory time series. J. Econometrics 133, 673-702.

[18] Andersson, M.K. and Gredenhoff, M.P., 1998. Robust testing for fractional integration using the bootstrap. Working Paper Series in Economics and Finance 218, Stockholm School of Economics, Sweden.

[19] Hidalgo, J., 2003. An alternative bootstrap to moving blocks for time series regression models. J. Econometrics 117, 369-399.

[20] Silva, E.M., Franco, G.C., Reisen, V.A. and Cruz, F.R.B., 2006. Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models. Comput. Statist. Data Anal. 51, 1002-1011.

[21] Arteche, J. and Orbe, J., 2005. Bootstrapping the log-periodogram regression. Econ. Letters 86, 70-85.

[22] Agiakloglou, C., Newbold, P. and Wohar, M., 1993. Bias in an estimator of the fractional difference parameter. J. Time Ser. Anal. 14, 235-246.

[23] Paparoditis, E. and Politis, D., 1999. The local bootstrap for periodogram statistics. J. Time Ser. Anal. 20, 193-222.

[24] Efron, B., 1982. The jackknife, the bootstrap, and other resampling plans. Volume 38 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM.

[25] Efron, B., 1987. Better bootstrap confidence intervals. J. Amer. Statistical Assoc. 82, 171-200.

[26] Mackinnon, J.G. and Smith, A.A., 1998. Approximate bias correction in econometrics. J. Econometrics 85, 205-230.

[27] Efron, B., 1979. Bootstrap methods: Another look at the jackknife. Ann. Statist. 7, 1-26.

[28] Davidson, R. and MacKinnon, J.G., 2006. Bootstrap methods in econometrics. In: Mills, T.C. and Patterson, K.D. (eds.), Palgrave Handbooks of Econometrics: Volume 1, Econometric Theory. Palgrave Macmillan, 812-838.

[29] K┬¿unsch, H.R., 1989. The jackknife and the bootstrap for general stationary observations. Ann. Statist. 17, 1217-1261.

[30] Liu, R.Y. and Singh, K., 1992. Moving blocks jackknife and bootstrap capture weak dependence. In: LePage, R. and Billard, L.(Eds.) Exploring the limits of bootstrap. Wiley, New York, 225-248.

[31] Lahiri, S.N., 1999. Theoretical comparisons of block bootstrap methods. Ann. Statist. 27, 386-404.

[32] Kilian, L., 1998. Small sample confidence intervals for impulse response functions. Rev. Econ. Statist. 80, 218-230.

[33] Shao, J. and Tu, D., 1995. The jackknife and bootstrap. Springer Verlag: New York.

[34] Efron, B. and Tibshirani, R.J., 1993. An introduction to the bootstrap. Chapman and Hall: New York.

[35] Davison, A.C. and Hinkley, D.V., 1997. Bootstrap methods and their application. Cambridge University Press: Cambridge.

[36] Arteche, J., 2006. Semiparametric estimation in perturbed long memory series. Comput. Statist. Data Anal. 51, 2118-2141.

[37] Hurvich, C.M., Moulines, E. and Soulier, P., 2005. Estimating long memory in volatility. Econometrica 73, 1283-1328.

[38] Sun, Y. and Phillips, P.C.B., 2003. Nonlinear log-periodogram regression for perturbed fractional processes. J. Econometrics 115, 355-389.

[39] Andrews, D.W.K. and Guggenberger, P., 2003. A bias-reduced logperiodogram regression estimator for the long-memory parameter. Econometrica 71, 675-712.