Bandwidth selection for functional time series prediction

Antoniadis, Anestis; Paparoditis, Efstathios; Sapatinas, Theofanis

doi:10.1016/j.spl.2008.10.028

Cited by 21 publications

(12 citation statements)

References 6 publications

(2 reference statements)

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“…However, its performance may depend on different choices of the number of PLS components. Thus, a cross-validation approach of Yao and Tong (1998), Racine (2000), and Antoniadis et al (2009) may be proposed to determine the optimum number of PLS components.…”

Section: Data Analysesmentioning

confidence: 99%

On function-on-function regression: partial least squares approach

Beyaztaş

Shang

2020

Environ Ecol Stat

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Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood, and maximum penalized likelihood, have been proposed to estimate such function-onfunction regression models. However, these estimation techniques produce unstable estimates in the case of degenerate functional data or are computationally intensive. To overcome these issues, we proposed a partial least squares approach to estimate the model parameters in the functionon-function regression model. In the proposed method, the B-spline basis functions are utilized to convert discretely observed data into their functional forms. Generalized cross-validation is used to control the degrees of roughness. The finite-sample performance of the proposed method was evaluated using several Monte-Carlo simulations and an empirical data analysis. The results reveal that the proposed method competes favorably with existing estimation techniques and some other available function-on-function regression models, with significantly shorter computational time.Recent advances in computer storage and data collection have enabled researchers in diverse branches of science such as, for instance, chemometrics, meteorology, medicine, and finance, recording data of characteristics varying over a continuum (time, space, depth, wavelength, etc.). Given the complex nature of such data collection tools, the availability of functional data, in which observations are sampled over a fine grid, has progressively increased. Consequently, the interest in functional data analysis (FDA) tools is significantly increasing over the years. Silverman (2002, 2006), Ferraty and Vieu (2006), Horvath and Kokoszka (2012) and Cuevas (2014) provide excellent overviews of the research on theoretical developments and case studies of FDA tools.Functional regression models in which both the response and predictors consist of curves known as, function-on-function regression, have received considerable attention in the literature. The main goal of these regression models is to explore the associations between the functional response and the functional predictors observed on the same or potentially different domains as the response function. In this context, two key models have been considered: the varying-coefficient model and the function-on-function regression model (FFRM). The varying-coefficient model assumes that the functional response Y (t) and functional predictors X (t) are observed in the same domain. Its estimation and test procedures have been studied by numerous authors, including Fan and Zhang among many others. In contrast, the FFRM considers cases in which the functional response Y (t) for a given continuum t depends on the full trajectory of the predictors X (s). Compared with the varying-coefficient model, the FFRM is more natural; therefore, we restrict our attent...

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Section: Data Analysesmentioning

confidence: 99%

On function-on-function regression: partial least squares approach

Beyaztaş

Shang

2020

Environ Ecol Stat

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“…First, a method based on empirical prediction-risk minimisation is explored by Antoniadis et al (2009): oracle inequalities are proved, but the criterion is specic to functional time series prediction. Then, inspired both by the advances about the Lepski methods (Goldenshluger and Lepski, 2011) and model selection, Chagny and Roche (2014) investigate a global bandwidth selection method to estimate a cumulative distribution function (c.d.f.…”

Section: G Chagny and A Rochementioning

confidence: 99%

Adaptive estimation in the functional nonparametric regression model

Chagny

Roche

2016

Journal of Multivariate Analysis

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In this paper, we consider nonparametric regression estimation when the predictor is a functional random variable (typically a curve) and the response is scalar. Starting from a classical collection of kernel estimates, the bias-variance decomposition of a pointwise risk is investigated to understand what can be expected at best from adaptive estimation. We propose a fully data-driven local bandwidth selection rule in the spirit of the Goldenshluger and Lepski method. The main result is a nonasymptotic risk bound which shows the optimality of our tuned estimator from the oracle point of view. Convergence rates are also derived for regression functions belonging to Hölder spaces and under various assumptions on the rate of decay of the small ball probability of the explanatory variable. A simulation study also illustrates the good practical performances of our estimator.

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“…Step 4) The SSP is obtained by (6), where the weights , , are determined by (7) where the kernel function is the Gaussian kernel and the bandwidth are selected by the empirical risk of prediction methodology [22]. Finally, the computational algorithm related to the above implementation as well as the overall numerical study presented above has been carried out in the MATLAB 7.7.0 programming environment.…”

Section: B Implementation Of the Sspmentioning

confidence: 99%

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

Paparoditis

Sapatinas

2013

IEEE Trans. Power Syst.

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A novel functional time-series methodology for shortterm load forecasting is introduced. 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 latter is selected in a manner that captures the expected qualitative and quantitative characteristics of the load segment to be predicted. As an illustration, the suggested functional time-series forecasting methodology is applied to historical daily load data in Cyprus. Its performance is compared with some recently proposed alternative methodologies for short-term load forecasting.

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Bandwidth selection for functional time series prediction

Cited by 21 publications

References 6 publications

On function-on-function regression: partial least squares approach

On function-on-function regression: partial least squares approach

Adaptive estimation in the functional nonparametric regression model

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

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