We consider nonparametric estimation of the parameter functions a i () , i = 1; : : : ; p , of a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions a i , the empirical wavelet coeecients are derived from the time series data as the solution of a least squares minimization problem. In order to allow the a i to be functions of inhomogeneous ...

We derive a method of approximating a nonstationary process by a time-varying autoregressive model of order (TVAR( )). This method is based on the Dym–Gohberg band matrix extension technique, and for an -variate arbitrary nondegenerate covariance matrix it gives the unique TVAR( ) model. For adaptive applications, this method requires a sample size that is comparable with the TVAR( ) model orde...

We propose a novel recursive system identification algorithm for linear autoregressive systems with skewed innovations. The algorithm is based on the variational Bayes approximation of the model with a multivariate normal prior for the model coefficients, multivariate skew-normally distributed innovations, and matrix-variatenormal–inverse-Wishart prior for the parameters of the innovation distr...

We consider nonparametric estimation of the parameter functions a i () , i = 1; : : : ; p , of a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions a i , the empirical wavelet coeecients are derived from the time series data as the solution of a least squares minimization problem. In order to allow the a i to be functions of inhomogeneous ...

Based on a vector autoregressive model and dynamic conditional correlation generalized heteroskedasticity model, this study explores the relation between international crude oil market Chinese energy stock market. The findings suggest positive one-way spillover effect of returns China’s returns. Furthermore, two markets is time varying.

S U M M A R Y Recent studies show that the frequency content of continuous passive recordings contains useful information for the study of hydraulic fracturing experiments as well as longstanding applications in volcano and global seismology. The short-time Fourier transform (STFT) is usually used to obtain the time–frequency representation of a seismic trace. Yet, this transform has two main d...

The Bidirectional Texture Function (BTF) is the recent most advanced representation of visual properties of surface materials. It specifies their altering appearance due to varying illumination and viewing conditions. Corresponding huge BTF measurements require a mathematical representation allowing simultaneously extremal compression as well as high visual fidelity. We present a novel Markovia...