A General Limit Theory for Nonlinear Functionals of Nonstationary Time Series

Qiying Wang and Peter Phillips
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Qiying Wang: University of Sydney

No 2337R1, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self normalized statistics similar to the bimodality that can arise in t-ratio statistics based on heavy tailed data. Bimodal behavior in these statistics is due to the presence of long memory innovations and is shown to persist for very large sample sizes even though the limit theory is Gaussian when the long memory innovations are stationary. Bimodality is shown to occur even in the limit theory when the long memory innovations are nonstationary. To address these complications new self normalized versions of the test statistics are introduced that deliver improved approximations that can be used for inference.

Keywords: Bimodality; Endogeneity; Limit theory; Local time; Nonlinear functional; Nonstationarity; Sample covariance; Zero energy (search for similar items in EconPapers)
JEL-codes: C13 C23 (search for similar items in EconPapers)
Pages: 53 pages
Date: 2024-06
New Economics Papers: this item is included in nep-ets
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Working Paper: A General Limit Theory for Nonlinear Functionals of Nonstationary Time Series (2022)
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