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The authors deal with forecasting nonstationary time series using wavelets and kernel smoothing. Starting from a basic forecasting procedure based on the regression of the process on the nondecimated Haar wavelet coefficients of the past, the procedure was extended in various directions, including the use of an arbitrary wavelet or polynomial fitting for extrapolating low-frequency components. The authors study a further generalization of the prediction procedure dealing with multistep forecasting and combining kernel smoothing and wavelets. They finally illustrate the proposed procedure on nonstationary simulated and real data and then compare it to well-known competitors. [ABSTRACT FROM AUTHOR]

This paper deals with wavelets in time series, focusing on statistical forecasting purposes. Recent approaches involve wavelet decompositions in order to handle non-stationary time series in such context. A method, proposed by Renaud et al.,11 estimates directly the prediction equation by direct regression of the process on the Haar non-decimated wavelet coefficients depending on its past values. In this paper, this method is studied and extended in various directions. The new variants are used first for stationary data and after for stationary data contaminated by a deterministic trend. [ABSTRACT FROM AUTHOR]

We propose a new test for linearity in time series. We consider an asymptotically stationary functional AR(p) model on ℜ[sup d] of the form X[sub n] = f(X[sub n-1] , ..., X[sub n-p] ) + ξ[sub n] (n∈ N). The testing procedure is based on a suitably normalized sum of quadratic deviations between two different estimates of the function f evaluated at q distinct points of ℜ[sup dp] . The estimators are f[sub n] , a recursive version of the non-parametric kernel estimator of f, and Â[sub n] , a least squares estimator well suited to the linear case. The main result states that the test statistic has a χ[sup 2] limit distribution under the null hypothesis. A similar result is derived under the alternative hypothesis for the test statistic corrupted by a non-linear term. Our simulations indicate that our asymptotic results hold for moderate sample sizes when the testing procedure is used carefully [ABSTRACT FROM AUTHOR]