Prueba de hipótesis sobre la existencia de una raíz fraccional en una serie de tiempo no estacionaria

Diego Lemus; Elkin Castaño

doi:10.17533/udea.le.n78a15710

Authors

Diego Lemus National University of Colombia
Elkin Castaño University of Antioquia

DOI:

https://doi.org/10.17533/udea.le.n78a15710

Keywords:

Long memory time series, fractional differencing parameter, autoregressiveapproximation, non-stationary ARFIMA process

Abstract

In this work, we present a modification of the hypothesis testing procedure for the existence of long memory in the stationary and invertible ARFIMA(p,d,q) process proposed by Castaño, Gómez and Gallón (2008). This modification allows assessing the existence of a fractional root in a non-stationary time series when the short-term ARMA component is undetermined or unknown, especially in ARFIMA(p,d,q) processes. We validate, via Monte Carlo simulations, the analytical results and demonstrate the good performance of the proposed test in terms of both power and size, in comparison to other well-known tests in the literature.

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Author Biographies

Diego Lemus, National University of Colombia

Master of Science - Statistics. School of Statistics, Faculty of Sciences, National University of Colombia, Medellín Headquarters.

Elkin Castaño, University of Antioquia

Associate professor at the School of Statistics, Faculty of Sciences, National University of Colombia - Medellín Headquarters and professor at the Faculty of Economic Sciences, University of Antioquia.

References

Beran, Jan (1993). “Fitting long-memory models by generalized linear regression”, Biometrika, Vol. XXC, No. 4, pp. 817–822.

Beran, Jan (1994). Statistics for Long-Memory Processes, Nueva York, Chapman & Hall.

Castaño, Elkin; Gómez, Karol y Gallón, Santiago (2008). “Una nueva prueba para el parámetro de diferenciación fraccional”, Revista Colombiana de Estadística, Vol. XXXI, pp. 67–84.

Dolado, Juan; Gonzalo, Jesús y Mayoral, Laura. (2002). “A fractional dickey-fuller test for unit roots”, Econometrica, Vol. LXX, No. 5, pp. 1963–2006.

Geweke, John y Porter-Hudak, Susan (1983). “The estimation and application of long-memory time series models”, Journal of Time Series Analysis, Vol. IV, No. 4, pp. 221–238.

Granger, Clive y Joyeux, Roselyne (1980). “An introduction to long-memory time series and fractional differencing”, Journal of Time Series Analysis, Vol. I, pp. 15–29.

Granger, Clive (1980). “Long memory relationships and the aggregation of dynamic models”, Journal of Econometrics, Vol. XIV, No. 2, pp. 227–238. Hosking, Jonathan (1981). “Fractional differencing”, Biometrika, Vol. LXVIII, No. 1, pp. 165–176.

Lobato, Ignacio y Velasco, Carlos (2007). “Efficient wald tests for fractional unit roots”, Econometrica, Vol. LXXV, No. 2, pp. 575–589.

Mayoral, Laura (2007). “Minimum distance estimation of stationary and non-stationary arfima processes”, The Econometrics Journal, Vol. X, No. 1, pp. 124–148.

Robinson, Peter (1995). “Log-periodogram regression of time series with long range dependence”, The Annals of Statistics, Vol. XXIII, No. 3, pp. 1048–1072.

Said, Said y Dikey, David (1984), “Testing for unit roots in autoregressivemoving average models of unknown order”, Biometrika, Vol. LXXI, No. 3, pp. 599–607.

Tanaka, Katsuto (1999), “The non-stationary fractional unit root”, Econometric Theory, Vol. XV, No. 4, pp. 549–582.

Velasco, Carlos (1999), “Gaussian semiparametric estimation of non-stationary time series”, Journal of Time Series Analysis, Vol. XX, No. 1, pp. 87–127.