On projection methods for functional time series forecasting

Elías, Antonio; Jiménez, Raúl; Shang, Han Lin

doi:10.1016/j.jmva.2021.104890

Cited by 10 publications

(9 citation statements)

References 70 publications

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“…In this section, we present a simulation study and empirical data examples to demonstrate the effectiveness of our novel methods for forecasting nonstationary FTS. We compare our algorithms with the functional seasonal naive method (SNM) and seven other popular approaches from the literature (Aue et al, 2015; Elías et al, 2022; Hyndman & Ullah, 2007; Liu et al, 2016; Shang & Kearney, 2022; Zamani et al, 2022). The simulation study evaluates the performance of our techniques in predicting nonstationary FTS with seasonality, an increasing trend (of varying strengths), or both.…”

Section: Simulation and Empirical Data Studiesmentioning

confidence: 99%

“…A semi‐functional partial linear model that combines linear and nonlinear covariates has also been introduced in Aneiros‐Pérez and Vieu (2008). In addition, projection methods that keep track of the seasonality present in FTS were developed in Elías et al (2022) to predict cyclic FTS in a model‐free fashion. The first projection method leverages a functional variant of the k‐nearest neighbour's algorithm used to forecast time series data.…”

Section: Introductionmentioning

confidence: 99%

“…A semi-functional partial linear model that combines linear and nonlinear covariates has also been introduced in Aneiros- Pérez and Vieu (2008). In addition, projection methods that keep track of the seasonality present in FTS were developed in Elías et al (2022) Since the aforementioned SSA-based techniques have been successful in forecasting time series data, here, we develop two FSSAbased algorithms to forecast FTS. In a nutshell, the proposed methods leverage patterns extracted by the FSSA algorithm that are present in the sub-intervals of the FTS to make predictions using novel, functional recurrence relations.…”

mentioning

confidence: 99%

“…We also introduce a model-free goodness-of-prediction tool for the proposed algorithms that is based on a bootstrap approach. We further compare the proposed methods to the algorithms presented in Aue et al (2015), Hyndman and Ullah (2007), Zamani et al (2022), Liu et al (2016), Elías et al (2022) and Shang and Kearney (2022) in terms of prediction accuracy and computation time taken to obtain forecasts. We perform the comparisons using simulated and empirical data.…”

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confidence: 99%

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Functional time series forecasting: Functional singular spectrum analysis approaches

Trinka,

Haghbin,

Lin Shang

et al. 2023

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We introduce two novel nonparametric forecasting methods designed for functional time series (FTS), namely, functional singular spectrum analysis (FSSA) recurrent and vector forecasting. Our algorithms rely on extracted signals obtained from the FSSA method and innovative recurrence relations to make predictions. These techniques are model‐free, capable of predicting nonstationary FTS and utilize a computational approach for parameter selection. We also employ a bootstrap algorithm to assess the goodness‐of‐prediction. Through comprehensive evaluations on both simulated and real‐world climate data, we showcase the effectiveness of our techniques compared to various parametric and nonparametric approaches for forecasting nonstationary stochastic processes. Furthermore, we have implemented these methods in the Rfssa R package and developed a shiny web application for interactive exploration of the results.

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Section: Simulation and Empirical Data Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Functional time series forecasting: Functional singular spectrum analysis approaches

Trinka,

Haghbin,

Lin Shang

et al. 2023

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“…In addition, Gao et al (2019) addresses the scenario where the functional time series is multivariate or high‐dimensional. Elias et al (2022) uses a nonparametric way to predict future curves by using the nearest ones. Furthermore, Alaverez Liebana (2017) has outlined a review of other approaches to analyzing functional time series.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear prediction of functional time series

Wang

Cao

2023

Environmetrics

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We propose a nonlinear prediction (NOP) method for functional time series.Conventional methods for functional time series are mainly based on functional principal component analysis or functional regression models. These approaches rely on the stationary or linear assumption of the functional time series. However, real data sets are often nonstationary, and the temporal dependence between trajectories cannot be captured by linear models. Conventional methods are also hard to analyze multivariate functional time series. To tackle these challenges, the NOP method employs a nonlinear mapping for functional data that can be directly applied to multivariate functions without any preprocessing step. The NOP method constructs feature space with forecast information, hence it provides a better ground for predicting future trajectories. The NOP method avoids calculating covariance functions and enables online estimation and prediction. We examine the finite sample performance of the NOP method with simulation studies that consider linear, nonlinear and nonstationary functional time series. The NOP method shows superior prediction performances in comparison with the conventional methods. Three real applications demonstrate the advantages of the NOP method model in predicting air quality, electricity price and mortality rate.

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Depth-based reconstruction method for incomplete functional data

2022

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The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, most reconstruction methods rely on estimating the covariance matrix or the components of its eigendecomposition, which may be difficult. In particular, the estimation accuracy might be affected by the complexity of the covariance function, the noise of the discrete observations, and the poor availability of complete discrete functional data. We introduce a non-parametric alternative based on depth measures for partially observed functional data. Our simulations point out that the benchmark methods perform better when the data come from one population, curves are smooth, and there is a large proportion of complete data. However, our approach is superior when considering more complex covariance structures, non-smooth curves, and when the proportion of complete functions is scarce. Moreover, even in the most severe case of having all the functions incomplete, our method provides good estimates; meanwhile, the competitors are unable. The methodology is illustrated with two real data sets: the Spanish daily temperatures observed in different weather stations and the age-specific mortality by prefectures in Japan. They highlight the interpretability potential of the depth-based method.

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On projection methods for functional time series forecasting

Cited by 10 publications

References 70 publications

Functional time series forecasting: Functional singular spectrum analysis approaches

Functional time series forecasting: Functional singular spectrum analysis approaches

Nonlinear prediction of functional time series

Depth-based reconstruction method for incomplete functional data

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