Testing stationarity of functional time series

Horváth, Lajos; Kokoszka, Piotr; Rice, Gregory

doi:10.1016/j.jeconom.2013.11.002

Cited by 175 publications

(157 citation statements)

References 38 publications

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“…location and or scale. Similarly as Horváth et al (2014) and Didericksen et al (2012) we considered samples with functional errors being generated by Wiener process and Brownian bridge divided into 1440 and 120 time points (24 hours divided into 1min and 12min time segments). We considered samples of equal and different sizes.…”

Section: Properties Of the Proposals -Simulation Studiesmentioning

confidence: 99%

Detecting a structural change in functional time series using local Wilcoxon statistic

2017

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Functional data analysis (FDA) (Ramsay et al. (2009);Ramsay and Silverman (2005)) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have to deal with time series of functional data, where we cannot easily decide, whether they are to be considered as homogeneous or heterogeneous. At present a discussion on adequate tests of homogenity for functional data is carried (see e.g. Flores et al. (2015)). We propose a novel statistic for detetecting a structural change in functional time series based on a local Wilcoxon statistic induced by a local depth function proposed in Paindaveine and Van Bever (2013).

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Section: Properties Of the Proposals -Simulation Studiesmentioning

confidence: 99%

Detecting a structural change in functional time series using local Wilcoxon statistic

2017

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“…The Monte Carlo test, in which the null hypothesis is stationarity, was applied to both the male and female populations. We used data from all 65 of the years in our range and performed 5000 Monte Carlo replications [32]. The p-values for the male and female populations were 0.0256 and 0.0276, respectively.…”

Section: Empirical Studiesmentioning

confidence: 99%

Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates

Gao

Shang

2017

Risks

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This study considers the forecasting of mortality rates in multiple populations. We propose a model that combines mortality forecasting and functional data analysis (FDA). Under the FDA framework, the mortality curve of each year is assumed to be a smooth function of age. As with most of the functional time series forecasting models, we rely on functional principal component analysis (FPCA) for dimension reduction and further choose a vector error correction model (VECM) to jointly forecast mortality rates in multiple populations. This model incorporates the merits of existing models in that it excludes some of the inherent randomness with the nonparametric smoothing from FDA, and also utilizes the correlation structures between the populations with the use of VECM in mortality models. A nonparametric bootstrap method is also introduced to construct interval forecasts. The usefulness of this model is demonstrated through a series of simulation studies and applications to the age-and sex-specific mortality rates in Switzerland and the Czech Republic. The point forecast errors of several forecasting methods are compared and interval scores are used to evaluate and compare the interval forecasts. Our model provides improved forecast accuracy in most cases.

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“…Work has been done on assessing whether a dataset is independent against an ergodic alternative (Horváth, Hušková, and Rice 2013), or whether two functional time series are independent (Horváth and Rice 2015a). Horváth, Kokoszka, and Rice (2014) developed test for the stationarity of functional time series, and Kokoszka and Young (2016) considered tests for stationarity around a deterministic trend. The problem of two-sample testing for equality of the mean function of two functional time series, without resorting to linearity assumptions, has been considered by Horváth, Kokoszka, and Reeder (2013), Fremdt et al (2014), and Horváth and Rice (2015b).…”

Section: Functional Data Analysismentioning

confidence: 99%

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

Tavakoli

Panaretos

2016

Journal of the American Statistical Association

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Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences in frequency and along curvelength. The approach we take is one of Fourier analysis, where the complete second-order structure of the FTS is encoded by its spectral density operator, indexed by frequency and curvelength. The comparison is broken down to a hierarchy of stages: at a global level, we compare the spectral density operators of the two FTS, across frequencies and curvelength, based on a Hilbert-Schmidt criterion; then, we localize any differences to specific frequencies; and, finally, we further localize any differences along the length of the random curves, that is, in physical space. A hierarchical multiple testing approach guarantees control of the averaged false discovery rate over the selected frequencies. In this sense, we are able to attribute any differences to distinct dynamic (frequency) and spatial (curvelength) contributions. Our approach is presented and illustrated by means of a case study in molecular biophysics: how can one use molecular dynamics simulations of short strands of DNA to infer their temporal dynamics at the scaling limit, and probe whether these depend on the sequence encoded in these strands? Supplementary materials for this article are available online.

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Testing stationarity of functional time series

Cited by 175 publications

References 38 publications

Detecting a structural change in functional time series using local Wilcoxon statistic

Detecting a structural change in functional time series using local Wilcoxon statistic

Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates

Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics

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