In this paper the class of ARCH(âˆž) models is generalized to the nonstationary class of ARCH(âˆž) models with time-varying coefficients. For fixed time points, a stationary approximation is givenâ€¦ (More)

We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations,â€¦ (More)

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financialâ€¦ (More)

In this paper our object is to show that a certain class of nonstationary random processes can locally be approximated by stationary processes. The class of processes we are considering includes theâ€¦ (More)

There exists very few results on mixing for nonstationary processes. However, mixing is often required in statistical inference for nonstationary processes, such as time-varying ARCH (tvARCH) models.â€¦ (More)

We consider a zero mean discrete time series, and define its discrete Fourier transform at the canonical frequencies. It can be shown that the discrete Fourier transform is asymptoticallyâ€¦ (More)

It is well known that the discrete Fourier transform (DFT) of a second order stationary time series between two distinct Fourier frequencies are asymptotically uncorrelated. In contrast we show thatâ€¦ (More)

In this paper we consider tests for nonlinear time series, which are motivated by the notion of serial dependence. The proposed tests are based on comparisons with the quantile spectral density,â€¦ (More)

In this paper general quadratic forms of nonstationary, Î±-mixing time series are considered. Under relatively weak mixing and moment assumptions, asymptotic normality of these forms are derived. Theâ€¦ (More)

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point t âˆ’ 1 withâ€¦ (More)