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Specification testing in nonparametric AR‐ARCH models
Author(s) -
Hušková Marie,
Neumeyer Natalie,
Niebuhr Tobias,
Selk Leonie
Publication year - 2019
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12337
Subject(s) - mathematics , heteroscedasticity , conditional variance , autoregressive model , nonparametric statistics , econometrics , series (stratigraphy) , conditional independence , consistency (knowledge bases) , statistics , independence (probability theory) , autoregressive conditional heteroskedasticity , star model , asymptotic distribution , goodness of fit , arch , time series , autoregressive integrated moving average , discrete mathematics , volatility (finance) , paleontology , civil engineering , estimator , engineering , biology
In this paper, an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. Tests for the model assumption of independence of innovations from past time series values are suggested. Tests based on weighted L 2 ‐distances of empirical characteristic functions are considered as well as a Cramér–von Mises‐type test. The asymptotic distributions under the null hypothesis of independence are derived, and the consistency against fixed alternatives is shown. A smooth autoregressive residual bootstrap procedure is suggested, and its performance is shown in a simulation study.