Parameter stability and semiparametric inference in time varying auto-regressive conditional heteroscedasticity models
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2017 · Volume 79 · Issue 5
Abstract
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.
Keywords
Auto-regressive conditional heteroscedasticity processes, Kernel smoothing, Locally stationary time series, Semiparametric inference
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