Unit Root Tests under Time-Varying Variances

By Giuseppe Cavaliere. 2005

155 citations recorded by the source corpus.

Abstract The paper provides a general framework for investigating the effects of permanent changes in the variance of the errors of an autoregressive process on unit root tests. Such a framework – which is based on a novel asymptotic theory for integrated and near integrated processes with heteroskedastic errors – allows to evaluate how the variance dynamics affect the size and the power function of unit root tests. Contrary to previous studies, it is shown that non-constant variances can both inflate and deflate the rejection frequency of the commonly used unit root tests, both under the null and under the alternative, with early negative and late positive variance changes having the strongest impact on size and power. It is also shown that shifts smoothed across the sample have smaller impacts than shifts occurring as a single abrupt jump, while periodic variances have a negligible effect even when a small number of cycles take place over a given sample. Finally, it is proved that the locally best invariant (LBI) test of a unit root against level stationarity is robust to heteroskedasticity of any form under the null hypothesis.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/399f79356526eab2884accfcbff3d21bd3fc4968

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Citations in the corpus

Unit Root Testing in Heteroscedastic Panels Using the Cauchy Estimator (2012, background): “Following Cavaliere and Taylor (2007), the εt are unconditionally heteroscedastic.”
Inference in Autoregression under Heteroskedasticity (2006, unknown): “ Cavaliere (2004) provides further discussion of the variance patterns that are allowed.”
HETEROSKEDASTIC TIME SERIES WITH A UNIT ROOT (2009, background): “This result constitutes a substantial generalization of previous results given by Cavaliere (2004) and Cavaliere and Taylor (2007) for the case of purely deterministic and nonexplosive volatility.”
Adaptive Estimation of Autoregressive Models with Time-Varying Variances (2008, background): “¶ ( 7 ) satisfies”
Time‐Transformed Unit Root Tests for Models with Non‐Stationary Volatility (2008, methodology): “As noticed in Cavaliere (2004), the consequences of non-stationary volatility are very similar to those described in Clark (1973); that is, one observes a deformation of the time domain.”
Detecting and Predicting Forecast Breakdowns (2009, methodology): “…+ 2 ( ) ¤ ¶µZ 1 0 £ 2 + 2 ( ) ¤ ¶ 1µZ 1 0 [ + ( )] ( ) ¶ 16 In order to develop intuition, we abstract from the fact that should be estimated, and we standardize all variances to equal one. by applying Lemma 1 in Cavaliere (2004) and results from the proof of Theorem 4 in Elliott and Muller (2006).”
Testing for Co-integration in Vector Autoregressions with Non-Stationary Volatility (2010, unknown): “Cavaliere and Taylor (2007) report evidence of multiple volatility breaks and trending volatility in the monthly producer price ination series from the well-known Stock and Watson (1999) database. These ndings have helped stimulate an interest amongst econometricians into analysing the e¤ects of n”
Testing for a change in persistence in the presence of non-stationary volatility☆ (2008, background): “Since Bω is Gaussian, has independent increments and unconditional variance E(Bω (s) 2) = η (s), Bω is a time-change Brownian motion; see Cavaliere (2004b) and Cavaliere and Taylor (2007a) for further discussion on such process.”
Modeling and Forecasting Medium-Term Electricity Consumption Using Component Estimation Technique (2020, background): “, prices or demand time series, the unit-root test results are weaker due the presence of periodicities and exceptionally heavy tailed data, which affect the size and power of standard unit-root tests [66,67].”
Instrumental variable and variable addition based inference in predictive regressions (2015, methodology): “Elliott and Stock (1994) proposed a Bayesian mixture procedure, Cavanagh et al. (1995) consider various tests based on conservative bounds (as refined by Campbell and Yogo, 2006).”