Testing for long memory in the presence of a general trend

Liudas Giraitis · Piotr S. Kokoszka · Remigijus Leipus

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Complex Systems and Time Series Analysis Financial Risk and Volatility Modeling Time Series Analysis and Forecasting

Abstract

The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharyaet al.(1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo's (1991) modifiedR/Stest. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool theR/S-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger thanN-½, whereNis the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so.

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References

1992Testing the null hypothesis of stationarity against the alternative of a unit root 2012The Econometrics of Financial Markets 1997The Econometrics of Financial Markets 1997Further evidence on breaking trend functions in macroeconomic variables 1991Long-Term Memory in Stock Market Prices 1989Long-term Memory in Stock Market Prices 1992Nonstationarity and Level Shifts With an Application to Purchasing Power Parity 1990Testing for a Unit Root in a Time Series With a Changing Mean

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