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Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series. (English) Zbl 1041.62506
Summary: In this paper we modify the general hypothesis studied by Robinson (1989) for semi-/nonparametric time-series models, and present a consistent testing procedure for the modified hypothesis. As examples, we provide consistent tests for the portfolio conditional mean-variance efficiency hypothesis, for the omitted variables in a multivariate nonparametric time-series regression model, and for the two original examples in Robinson. The asymptotic distributions under the null and Pitman local alternatives are established by invoking central limit theorems for Hilbert-valued-dependent random arrays. To approximate the critical values of the general test, we modify the conditional Monte-Carlo approach of Hansen (1996) and the stationary bootstrap of Politis and Romano (1994), and show that both work asymptotically.

62G08 Nonparametric regression and quantile regression
62P20 Applications of statistics to economics
62G10 Nonparametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Full Text: DOI
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