What is What?: A Simple Time-Domain Test of Long-Memory vs. Structural Breaks

Abstract

This paper proposes a new time-domain test of a process being I(d), 0 < d ≤ 1, under the null, against the alternative of being I(0) with deterministic components subject to structural breaks at known or unknown dates, with the goal of disentangling the existing identification issue between long-memory and structural breaks. Denoting by A B (t) the different types of structural breaks in the deterministic components of a time series considered by Perron (1989), the test statistic proposed here is based on the t-ratio (or the infimum of a sequence of t-ratios) of the estimated coefficient on y t−1 in an OLS regression of ∆ d y t on a simple transformation of the above-mentioned deterministic components and y t−1 , possibly augmented by a suitable number of lags of ∆ d y t to account for serial correlation in the error terms. The case where d = 1 coincides with the Perron (1989) or the Zivot and Andrews (1992) approaches if the break date is known or unknown, respectively. The statistic is labelled as the SB-FDF (Structural Break-Fractional Dickey-Fuller) test, since it is based on the same principles as the well-known Dickey-Fuller unit root test. Both its asymptotic behavior and finite sample properties are analyzed, and two empirical applications are provided. * We are grateful to Manuel Santos and participants in seminars at IGIER (Milan), ESEM 2004 (Madrid) and Univ.de Montreal for helpful comments. Special thanks go to Benedikt Pöstcher for help in one of the proofs.

A multivariate test against spurious long memory

“…However, univariate tests are often not able to reject the null hypothesis of true long memory in volatility time series. Dolado et al (2005), for example, apply their test to absolute and squared returns of the S&P 500, without being able to indicate spurious long memory. In view of the power gains of the multivariate procedure, demonstrated in Section 4.2, we revisit the log-absolute return series of the S&P 500 and additionally consider logabsolute returns of the DAX, FTSE and NIKKEI in a multivariate setup to test for spurious long memory using the MLWS test.…”

“…Here, we focus on the literature with the null hypothesis of true long memory. Dolado et al (2005) propose a time domain test based on the testing principle of previously derived fractional Dickey Fuller tests. Shimotsu (2006) suggests two tests.…”

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

“…The Structural Break-Fractional Dickey-Fuller (SB-FDF) test is developed in Dolado et al (2005). Under the null, the process of interest is I(d), d ∈ (0, 1).…”

“…Authors find that the exchange rate volatility is driven by a true LM process. Dolado et al (2005) propose a time-domain test to verify whether a process is I(d), against the alternative of being I(0) with deterministic components subject to structural breaks at known or unknown dates. The test is applied to the study of U.S. real GNP and absolute values and squared values of S&P 500 returns, and in both cases the null of I(d) cannot be rejected at the conventional significance levels.…”

Is the Observed Persistence Spurious? A Test for Fractional Integration Versus Short Memory and Structural Breaks

“…Lazarova (2004) extends the latter framework by allowing for long memory also in the regressors. Finally, Dolado, Gonzalo and Mayoral (2005) propose an extension of the Perron (1989) and Zivot and Andrew's (1992) approaches (developed for testing I(1) vs. I(0) plus breaks with known or unknown break date, respectively) along the lines of the Fractional Dickey-Fuller test (Dolado, Gonzalo and Mayoral, 2002).…”