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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.

MSC:
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)
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