arXiv subjects

Efstathios Paparoditis

Publications and source records attributed to Efstathios Paparoditis.

26 records · Page 2Linked to original sources

arXiv2017

EstimatedWold Representation and Spectral Density-Driven Bootstrap for Time Series

The second-order dependence structure of purely nondeterministic stationary process is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process. This relation together with some spectral density estimator is used in order to obtain consistent estimators of these coefficients. A spectral density-driven bootstrap for time series is then developed which uses the entire sequence of estimated MA coefficients together with appropriately generated pseudo innovations in order to obtain a bootstrap pseudo time series. It is shown that if the underlying process is linear and if the pseudo innovations are generated by means of an i.i.d. wild bootstrap which mimics, to the necessary extent, the moment structure of the true innovations, this bootstrap proposal asymptotically works for a wide range of statistics. The relations of the proposed bootstrap procedure to some other bootstrap procedures, including the autoregressive-sieve bootstrap, are discussed. It is shown that the latter is a special case of the spectral density-driven bootstrap, if a parametric autoregressive spectral density estimator is used. Simulations investigate the performance of the new bootstrap procedure in finite sample situations. Furthermore, a real-life data example is presented.

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arXiv2017

Sieve Bootstrap for Functional Time Series

A bootstrap procedure for functional time series is proposed which exploits a general vector autoregressive representation of the time series of Fourier coefficients appearing in the Karhunen-Loève expansion of the functional process. A double sieve-type bootstrap method is developed which avoids the estimation of process operators and generates functional pseudo-time series that appropriately mimic the dependence structure of the functional time series at hand. The method uses a finite set of functional principal components to capture the essential driving parts of the infinite dimensional process and a finite order vector autoregressive process to imitate the temporal dependence structure of the corresponding vector time series of Fourier coefficients. By allowing the number of functional principal components as well as the autoregressive order used to increase to infinity (at some appropriate rate) as the sample size increases, a basic bootstrap central limit theorem is established which shows validity of the bootstrap procedure proposed for functional finite Fourier transforms. Some numerical examples illustrate the good finite sample performance of the new bootstrap method proposed.

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arXiv2016

Bootstrap-Based K-Sample Testing For Functional Data

We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing methodology is simple and easy to implement. It resamples the original dataset in such a way that the null hypothesis of interest is satisfied and it can be potentially applied to a wide range of testing problems and test statistics of interest. Furthermore, it can be utilized to the case where more than two populations of functional data are considered. We illustrate the bootstrap procedure by considering the important problems of testing the equality of mean functions or the equality of covariance functions (resp. covariance operators) between two populations. Theoretical results that justify the validity of the suggested bootstrap-based procedure are established. Furthermore, simulation results demonstrate very good size and power performances in finite sample situations, including the case of testing problems and/or sample sizes where asymptotic considerations do not lead to satisfactory approximations. A real-life dataset analyzed in the literature is also examined.

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arXiv2012

On the range of validity of the autoregressive sieve bootstrap

We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. Our main theorem provides a simple and effective tool in assessing whether the AR-sieve bootstrap is asymptotically valid in any given situation. In effect, the large-sample distribution of the statistic in question must only depend on the first and second order moments of the process; prominent examples include the sample mean and the spectral density. As a counterexample, we show how the AR-sieve bootstrap is not always valid for the sample autocovariance even when the underlying process is linear.

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arXiv2012

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.

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arXiv2010

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.

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arXiv2008

Goodness-of-fit tests for Markovian time series models: Central limit theory and bootstrap approximations

New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that of the model class postulated under the null hypothesis. The model specification under the null allows for Markovian models, the transition mechanisms of which depend on an unknown vector of parameters and an unspecified distribution of i.i.d. innovations. Asymptotic properties of the test statistic are derived and the critical values of the test are found using appropriate bootstrap schemes. General properties of the bootstrap for Markovian processes are derived. A new central limit theorem for triangular arrays of weakly dependent random variables is obtained. For the proof of stochastic equicontinuity of multidimensional empirical processes, we use a simple approach based on an anisotropic tiling of the space. The finite-sample behavior of the proposed test is illustrated by some numerical examples and a real-data application is given.

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arXiv2005

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.

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