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EXACT LOCAL WHITTLE ESTIMATION IN LONG MEMORY TIME SERIES WITH MULTIPLE POLES

Published online by Cambridge University Press:  05 March 2020

Josu Arteche
Josu Arteche*
Affiliation:
University of the Basque Country UPV/EHU
*
Address correspondence to Josu Arteche, Department of Econometrics and Statistics, University of the Basque Country UPV/EHU, Bilbao 48015 Spain; e-mail: [email protected].
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Abstract

A generalization of the Exact Local Whittle estimator in Shimotsu and Phillips (2005, Annals of Statistics 33, 1890–1933) is proposed for jointly estimating all the memory parameters in general long memory time series that possibly display standard, seasonal, and/or other cyclical strong persistence. Consistency and asymptotic normality are proven for stationary, nonstationary, and noninvertible series, permitting straightforward standard inference of interesting hypotheses such as the existence of unit roots and equality of memory parameters at some or all seasonal frequencies, which can be used as a prior test for the application of seasonal differencing filters. The effects of unknown deterministic terms are also discussed. Finally, the finite sample performance is analyzed in an extensive Monte Carlo exercise and an application to an U.S. Industrial Production index.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 6 , December 2020 , pp. 1064 - 1098
Copyright
© Cambridge University Press 2020

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Footnotes

*

Research was supported by the Spanish Ministry of Science and Innovation and ERDF grant ECO2016-76884-P, and UPV/EHU Econometrics Research Group, Basque Government grant IT1359-19. The author thanks the Editor, Co-Editor, three anonymous referees, Javier García-Enríquez, Rajendra Bhansali, Carlos Velasco, Javier Hualde, and Tomás del Barrio for useful constructive comments.

References

REFERENCES

Abadir, K.M., Distaso, W., & Giraitis, L. (2007) Nonstationarity-extended Local Whittle estimation. Journal of Econometrics 141, 1353–1384.CrossRefGoogle Scholar
Abadir, K.M., Caggiano, G., & Talmain, G. (2013) Nelson–Plosser revisited: The ACF approach. Journal of Econometrics 175, 22–34.CrossRefGoogle Scholar
Arteche, J. (2000) Gaussian semiparametric estimation in seasonal/cyclical long memory time series. Kybernetika 36, 279–310.Google Scholar
Arteche, J. (2002) Semiparametric robust tests on seasonal or cyclical long memory time series. Journal of Time Series Analysis 23, 251–286.Google Scholar
Arteche, J. & Robinson, P.M. (1999) Seasonal and cyclical long memory. In Ghosh, S. (ed.) Asymptotics, Nonparametrics and Time Series. pp. 115–148, Marcel Dekker, New York, NY.Google Scholar
Arteche, J. & Robinson, P.M. (2000) Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis 21, 1–25.Google Scholar
Arteche, J. & Velasco, C. (2005) Trimming and tapering semiparametric estimates in asymmetric long memory time series. Journal of Time Series Analysis 26, 581–611.CrossRefGoogle Scholar
Beaulieu, J.J. & Miron, J.A. (1993) Seasonal unit roots in aggregate U.S. data. Journal of Econometrics 55, 305–328.CrossRefGoogle Scholar
Canova, F. & Hansen, B.E. (1995) Are seasonal patterns constant over time? A test for seasonal stability. Journal of Business and Economic Statistics 13, 237–252.Google Scholar
Chan, N.H. & Terrin, N. (1995) Inference for unstable long-memory processes with applications to fractional unit roots autorregressions. Annals of Statistics 23, 1662–1683.CrossRefGoogle Scholar
Chan, N.H. & Wei, C.Z. (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16, 367–401.CrossRefGoogle Scholar
Fox, R. & Taqqu, M.S. (1986) Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics 14, 517–532.CrossRefGoogle Scholar
Ghysels, E., Lee, H.S., & Noh, J. (1994) Testing for unit roots in seasonal time series: Some theoretical extensions and a Monte Carlo investigation. Journal of Econometrics 62, 415–442.CrossRefGoogle Scholar
Giraitis, L. & Leipus, R. (1995) A generalized fractionally differencing approach in long-memory modeling. Lithuanian Mathematical Journal 35, 53–65.CrossRefGoogle Scholar
Giraitis, L., Hidalgo, J., & Robinson, P.M. (2001) Gaussian estimation of parametric spectral density with unknown pole. Annals of Statistics 29 987–1023.Google Scholar
Granger, C.W.J. (1966) The typical spectral shape of an economic variable. Econometrica 34, 150–161.Google Scholar
Hassler, U., Rodrigues, P.M.M., & Rubia, A. (2009) Testing for general fractional integration in the time domain. Econometric Theory 25, 1793–1828.CrossRefGoogle Scholar
Hidalgo, J. (2005) Semiparametric estimation for stationary processes whose spectra have an unknown pole. Annals of Statistics 33, 1843–1889.CrossRefGoogle Scholar
Hidalgo, J. & Soulier, P. (2004) Estimation of the location and exponent of the spectral singularity of a long memory process. Journal of Time Series Analysis 25, 55–81.CrossRefGoogle Scholar
Hosking, J.R.M. (1984) Modeling persistence in hydrological time series using fractional differencing. Water Resources Research 20, 1898–1908.CrossRefGoogle Scholar
Hylleberg, S., Engle, R.F., Granger, C.W.J., & Yoo, B.S. (1990) Seasonal integration and cointegration. Journal of Econometrics 44, 215–238.CrossRefGoogle Scholar
Hylleberg, S., Jørgensen, C., & Sørensen, N.K. (1993) Seasonality in macroeconomic time series. Empirical Economics 18, 321–335.Google Scholar
Hurvich, C.M. & Chen, W.W. (2000) An efficient taper for potentially overdifferenced long memory time series. Journal of Time Series Analysis 21, 155–80.CrossRefGoogle Scholar
Nielsen, M.Ø. (2004) Efficient likelihood inference in nonstationary univariate models. Econometric Theory 20, 116–146.CrossRefGoogle Scholar
Phillips, P.C.B. (1999) Discrete Fourier transforms of fractional processes, Cowles Foundation Discussion Paper No. 1243.Google Scholar
Phillips, P.C.B. (2014) Optimal estimation of cointegrated systems with irrelevant instruments. Journal of Econometrics 178, 210–224.Google Scholar
Porter-Hudak, S. (1990) An application to the seasonally fractionally differenced model to the monetary aggregates. Journal of the American Statistical Association 85, 338–344.CrossRefGoogle Scholar
Ray, B.K. (1993) Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model. International Journal of Forecasting 9, 255–269.CrossRefGoogle Scholar
Robinson, P.M. (1994) Efficient tests of nonstationary hypotheses. Journal of the American Statistical Association 89, 1420–1436.CrossRefGoogle Scholar
Robinson, P.M. (1995) Gaussian semiparametric estimation of long-range dependence. Annals of Statistics 23, 1630–1661.CrossRefGoogle Scholar
Robinson, P.M. (2005) The distance between rival nonstationary fractional processes. Journal of Econometrics 128, 283–300.Google Scholar
Shao, X. (2010) Nonstationarity-extended Whittle estimation. Econometric Theory 26, 1060–1087.CrossRefGoogle Scholar
Shao, X. & Wu, W.B. (2007) Local Whittle estimation of fractional integration for nonlinear processes. Econometric Theory 23, 899–929.CrossRefGoogle Scholar
Shimotsu, K. (2010) Exact Local Whittle estimation of fractional integration with unknown mean and time trend. Econometric Theory 26, 501–540.CrossRefGoogle Scholar
Shimotsu, K. & Phillips, P.C.B. (2005) Exact Local Whittle estimation of fractional integration. Annals of Statistics 33, 1890–1933.CrossRefGoogle Scholar
Shimotsu, K. & Phillips, P.C.B. (2006) Local Whittle estimation of fractional integration and some of its variants. Journal of Econometrics 103, 209–233.CrossRefGoogle Scholar
Velasco, C. (1999) Gaussian semiparametric estimation of non-stationary time series. Journal of Time Series Analysis 20, 87–127.CrossRefGoogle Scholar
Woodward, W.A., Cheng, Q.C., & Gray, H.L. (1998) A k-factor GARMA long memory model. Journal of Time Series Analysis 19, 485–504.CrossRefGoogle Scholar
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