Testing temporal constancy of the spectral structure of a time series

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly time-varying spectral structure. The test is based on a comparison between the sample spectral density calculated locally on a moving window of data and a global spectral density estimator based on the whole stretch of observations. Asymptotic properties of the nonparametric estimators involved and of the test statistic under the null hypothesis of stationarity are derived. Power properties under the alternative of a time-varying spectral structure are discussed and the behavior of the test for fixed alternatives belonging to the locally stationary processes class is investigated.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ179 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Short-Term Load Forecasting: The Similar Shape Functional Time Series Predictor

We introduce a novel functional time series methodology for short-term load forecasting. The prediction is performed by means of a weighted average of past daily load segments, the shape of which is similar to the expected shape of the load segment to be predicted. The past load segments are identified from the available history of the observed load segments by means of their closeness to a so-called reference load segment, the later being selected in a manner that captures the expected qualitative and quantitative characteristics of the load segment to be predicted. Weak consistency of the suggested functional similar shape predictor is established. As an illustration, we apply the suggested functional time series forecasting methodology to historical daily load data in Cyprus and compare its performance to that of a recently proposed alternative functional time series methodology for short-term load forecasting.Comment: 22 pages, 6 Figures, 1 Tabl

Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

We propose a general bootstrap procedure to approximate the null distribution of nonparametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy to verify conditions, we establish asymptotic validity of the proposed bootstrap procedure. We apply a version of this procedure together with a new statistic in order to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The test statistic proposed is based on a L2-distance between the nonparametrically estimated individual spectral densities and an overall, 'pooled' spectral density, the later being obtained using the whole set of m time series considered. The effects of the dependence between the time series on the power behavior of the test are investigated. Some simulations are presented and a real-life data example is discussed. --

A Functional Wavelet-Kernel Approach for Continuous-time Prediction

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where observations are segments of the observed process considered as curves. These curves are assumed to lie within a space of possibly inhomogeneous functions, and the discretized times series dataset consists of a relatively small, compared to the number of segments, number of measurements made at regular times. We thus consider only the case where an asymptotically non-increasing number of measurements is available for each portion of the times series. We estimate conditional expectations using appropriate wavelet decompositions of the segmented sample paths. A notion of similarity, based on wavelet decompositions, is used in order to calibrate the prediction. Asymptotic properties when the number of segments grows to infinity are investigated under mild conditions, and a nonparametric resampling procedure is used to generate, in a flexible way, valid asymptotic pointwise confidence intervals for the predicted trajectories. We illustrate the usefulness of the proposed functional wavelet-kernel methodology in finite sample situations by means of three real-life datasets that were collected from different arenas