Nonparametric time series prediction: A semi-functional partial linear modeling

Abstract

There is a recent interest in developing new statistical methods to predict time series by taking into account a continuous set of past values as predictors. In this functional time series prediction approach, we propose a functional version of the partial linear model that allows both to consider additional covariates and to use a continuous path in the past to predict future values of the process. The aim of this paper is to present this model, to construct some estimates and to look at their properties both from a theoretical point of view by means of asymptotic results and from a practical perspective by treating some real data sets. Although the literature on the use of parametric or nonparametric functional modeling is growing, as far as we know, this is the first paper on semiparametric functional modeling for the prediction of time series.

Variable selection in partial linear regression with functional covariate

“…Lemma A.1 (see Lemma 3 in [21]) Let {V i } n i=1 be a zero-mean, stationary, independent and real process verifying that ∃ r > 4 such that max 1≤i≤n E|V i | r = O (1). Assume that {a ij , i, j = 1, .…”

“…, n) are i.i.d. Model (1) was introduced in [20,21], and recent extensions to variables X ij taking also values in infinite dimensional spaces are discussed in [22]. This literature has shown that the SFPLR model combines both interesting theoretical asymptotics and good practical behaviour when the number of covariates is reasonably small.…”

Functional time series approach for forecasting very short-term electricity demand

“…The idea of forming a TS of curves from a seasonal univariate TS is not new and has been considered by several authors, including Aneiros-Pérez and Vieu [1] and Besse et al [3]. Here, we apply this idea to model and forecast very short-term electricity demand.…”

Nonparametric time series forecasting with dynamic updating

“…Recent development in functional time series forecasting include the functional autoregressive of order 1 (Bosq 2000), and functional kernel regression (Aneiros-Pérez & Vieu 2008), and functional principal component regression (Hyndman & Ullah 2007, Hyndman & Booth 2008. However, to our knowledge, there is little has been done to address the dynamic updating problem when the final curve is partially observed.…”

“…Aneiros-Pérez & Vieu (2008) assume that N can be written as N = np, where n is the number of samples and p is dimensionality. To clarify this, in the El Niño time series from 1950 to 2008, we have N = 708, n = 59, p = 12.…”