Long memory and stochastic trend

In this paper, we study a general stochastic trend model and provide conditions on the partial sums which imply the convergence of the V/S statistic. These conditions generalize those in Giraitis et al. (J. Appl. Probab. 38 (2001) 1033) obtained in the case of deterministic trend model. As a particular example of stochastic trend we study a regime switching process called mixture model. We prove that in the non-trivial cases the partial sums converge to a compound Poisson process whereas in "degenerated" cases it resembles the behavior of the I(d-1) process.

[1]  Zhijie Xiao.  Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative , 2001 .

[2]  H. Künsch.  Discrimination between monotonic trends and long-range dependence , 1986 .

[3]  C. Heyde,et al.  ON THE ROBUSTNESS TO SMALL TRENDS OF ESTIMATION BASED ON THE SMOOTHED PERIODOGRAM , 1996 .

[4]  A. Lo.  Long-Term Memory in Stock Market Prices , 1989 .

[5]  A. Skorokhod.  Random processes with independent increments , 1991 .

[6]  Ignacio N. Lobato,et al.  Real and Spurious Long-Memory Properties of Stock-Market Data , 1996 .

[7]  William R. Parke.  What is Fractional Integration? , 1999, Review of Economics and Statistics.

[8]  A simple linear time series model with misleading nonlinear properties , 1999 .

[9]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[10]  R. Leipus,et al.  Testing for long memory in the presence of a general trend , 2001, Journal of Applied Probability.

[11]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[12]  Christian Gourieroux,et al.  Memory and infrequent breaks , 2001 .

[13]  F. Diebold,et al.  Long Memory and Regime Switching , 2000 .

[14]  R. Bhattacharya,et al.  THE HURST EFFECT UNDER TRENDS , 1983 .

[15]  Timo Teräsvirta,et al.  A simple nonlinear time series model with misleading linear properties , 1999 .

[16]  R. Leipus,et al.  Rescaled variance and related tests for long memory in volatility and levels , 2003 .

[17]  Robert F. Engle,et al.  The Reviewof Economicsand Statistics , 1999 .

[18]  Ming Liu,et al.  Modeling long memory in stock market volatility , 2000 .

[19]  Clive W. J. Granger,et al.  Occasional Structural Breaks and Long Memory , 1999 .