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Parameter stability and semiparametric inference in time varying auto‐regressive conditional heteroscedasticity models
Author(s) -
Truquet Lionel
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12221
Subject(s) - heteroscedasticity , autoregressive model , arch , semiparametric regression , parametric statistics , econometrics , semiparametric model , mathematics , inference , autoregressive–moving average model , stability (learning theory) , nonparametric statistics , statistical hypothesis testing , autoregressive conditional heteroskedasticity , kernel (algebra) , conditional variance , computer science , statistics , artificial intelligence , machine learning , volatility (finance) , civil engineering , engineering , combinatorics
Summary We develop a complete methodology for detecting time varying or non‐time‐varying parameters in auto‐regressive conditional heteroscedasticity (ARCH) processes. For this, we estimate and test various semiparametric versions of time varying ARCH models which include two well‐known non‐stationary ARCH‐type models introduced in the econometrics literature. Using kernel estimation, we show that non‐time‐varying parameters can be estimated at the usual parametric rate of convergence and, for Gaussian noise, we construct estimates that are asymptotically efficient in a semiparametric sense. Then we introduce two statistical tests which can be used for detecting non‐time‐varying parameters or for testing the second‐order dynamics. An information criterion for selecting the number of lags is also provided. We illustrate our methodology with several real data sets.