True Versus Spurious Long Memory: Some Theoretical Results and a Monte Carlo Comparison

Abstract

A common feature of financial time series is their strong persistence. Yet, long memory may just be the spurious effect of either structural breaks or slow switching regimes. We explore the effects of spurious long memory on the elasticity of the stock market price with respect to volatility and show how cross-sectional aggregation may generate spurious persistence in the data. We undertake an extensive Monte Carlo study to compare the performance of five tests, constructed under the null of true long memory versus the alternative of spurious long memory due to level shifts or breaks.

Keywords:

• Fractional integration
• Regime switching
• Structural break

JEL Classification:

• C15
• C22
• G10

ACKNOWLEDGMENTS

We are grateful to participants in the New York Camp Econometrics IV (The Mirror Inn, Lake Placid, NY, USA, April 3–5, 2009), in particular Badi Baltagi, Chihwa Kao, and Hashem Pesaran; the Econometric Society 2009 North American Summer Meeting (Boston University, USA, June 4–7, 2009) in particular Jean-Marie Dufour, Domenico Giannone, and Zhongjun Qu; the 15th International Conference Computing in Economics and Finance (University of Technology, Sydney, Australia, July 15–17, 2009); the 2009 Far East and South Asia Meeting of the Econometric Society (University of Tokyo, Faculty of Economics, Tokyo, Japan, August 3–5, 2009); the London–Oxbridge Time Series Workshop (Centre for International Macroeconomics and Finance, University of Cambridge, UK, October 9, 2009), in particular Andrew Harvey and Hashem Pesaran, for useful discussions and suggestions. Useful comments were provided from a lengthy discussion with Juan Dolado. We thank Morten Nielsen for useful comments especially on Section 2. We wish to thank the Editor, Esfandiar Maasoumi, an Associate Editor, and an anonymous referee for useful comments and suggestions. However, the usual disclaimer applies.

Notes

Temp. aggreg. is the “Temporal Aggregation” test with N = 4 aggregation levels. SB–FDF is the “Structural Break–Fractional Dickey–Fuller Test.” Sample split. is the “Sample Splitting” test with b = 2 subsamples. Diff. KPSS denotes the KPSS dth Differencing test, whereas Diff. PP is its Phillips–Perron version. LWL denotes the test based on the local Whittle likelihood. For each test, the null is true long memory. For the GPH and LW estimators the spectral bandwidth is . Results are based on 10,000 Monte Carlo replications.

See note to Table 3.

See note to Table 3. In addition, RLS-NS denotes the Nonstationary random level shift model, RLS-S is the stationary random level shift model, STOPBREAK is the model of Engle and Smith (1999), and MS-IID is the Markov–Switching model.

¹It is worth noticing that a number of tests, constructed under the null hypothesis of occasional breaks, are available in the literature. Bisaglia and Gerolimetto (2009) propose a test procedure based on the Box–Pierce and Ljung–Box statistics, while Berkes et al. (2006) construct a test based on the cumulative sum (CUSUM) statistic. Mayoral (2012) develops a time-domain test for non-stationary processes, under the null of I(d) versus I(0) plus trends and/or breaks. Rea et al. (2009) study the performance of the atheoretical regression trees procedure to identify breaks in LM processes. Finally, Kapetanios and Shin (2011) propose a Wald test under the null of nonstationary LM against the alternative of exponential smooth transition autoregressive processes.

See note to Table 3.

See note to Table 5.