The wavelet scaling approach to forecasting: Verification on a large set of Noisy data

Abstract

In the paper, we undertake a detailed empirical verification of wavelet scaling as a forecasting method through its application to a large set of noisy data. The method consists of two steps. In the first, the data are smoothed with the help of wavelet estimators of stochastic signals based on the idea of scaling, and, in the second, an AR(I)MA model is built on the estimated signal. This procedure is compared with some alternative approaches encompassing exponential smoothing, moving average, AR(I)MA and regularized AR models. Special attention is given to the ways of treating boundary regions in the wavelet signal estimation and to the use of biased, weakly biased and unbiased estimators of the wavelet variance. According to a collection of popular forecast accuracy measures, when applied to noisy time series with a high level of noise, wavelet scaling is able to outperform the other forecasting procedures, although this conclusion applies mainly to longer time series and not uniformly across all the examined accuracy measures.

A Wavelet Evaluation of Some Leading Business Cycle Indicators for the German Economy

“…Paying more attention to out-of-sample forecast evaluation is a further research prospect, especially using the principal components weights to generate a CLI for a future period and to evaluate this CLI out of sample. In this context, the concept of targeted predictors from Bruzda ( 2020 ) may also be invoked and evaluated by the wavelet analysis tools. Nowcasting may also be a further application area, but is more in the domain of the discrete wavelet transform as already applied in Gallegati ( 2014b ).…”

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