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Robust bootstrap prediction intervals for univariate and multivariate autoregressive time series models.

ABSTRACT: The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications, especially in the field of econometrics. These outlying data points tend to produce high forecast errors, which reduce the forecasting performances of the existing bootstrap prediction intervals calculated based on non-robust estimators. In the univariate and multivariate autoregressive time series, we propose a robust bootstrap algorithm for constructing prediction intervals and forecast regions. The proposed procedure is based on the weighted likelihood estimates and weighted residuals. Its finite sample properties are examined via a series of Monte Carlo studies and two empirical data examples.

SUBMITTER: Beyaztas U

PROVIDER: S-EPMC9042141 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

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Publications

Robust bootstrap prediction intervals for univariate and multivariate autoregressive time series models.

Beyaztas Ufuk U Shang Han Lin HL

Journal of applied statistics 20201201 5

The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications, especially in the field of econometrics. These outlying data points tend to produce high forecast errors, which reduce the forecasting performances of the existing bootstrap prediction intervals calculated based on non-robust estimators. In the univariate and multiva ...[more]

PMID: 35707515

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Project description:A time-series is any set of N time-ordered observations of a process. In veterinary epidemiology, our focus is generally on disease occurrence (the "process") over time, but animal production, welfare or other traits might also be of interest. A common source of time-series datasets are animal disease monitoring and surveillance systems. Here, we scan the application of methods to analyse time-series data in the peer-reviewed, published literature. Based on this literature scan we focus on autocorrelation and illustrate the recommended steps using ARIMA (Autoregressive Integrated Moving Average Models) methods via analysis of a time-series of canine parvovirus (CPV) events in a pet dog population in Australia, 2009 to 2015. We conclude by identifying the barriers to the application of ARIMA methods in veterinary epidemiology and suggest some possible solutions. In the literature scan the selected 37 studies focused mostly on infectious and parasitic diseases, predominantly for analytical, rather than descriptive or predictive, purposes. Trends and seasonality were investigated, and autocorrelation analyzed, in most studies, most commonly using R software. An approach to analyzing autocorrelation using ARIMA methods was then illustrated using a time-series (week and month units) of CPV events in a pet dog population in Australia, reported to a national companion animal disease surveillance system. This time-series was derived by summing veterinarian reports of confirmed CPV diagnoses. We present data analysis output generated via the R statistical environment, and make this code available for the reader to apply to this or other time-series datasets. We also illustrate prediction of CPV events by rainfall as a covariate. Time-series analysis using ARIMA methods to understand and explore autocorrelation appears to be relatively uncommon in veterinary epidemiology. Some of the reasons might include limited availability of data of sufficient time unit length, lack of familiarity with analytical methods and available software, and how to best use the information generated. We recommend that wherever feasible, such time-series data be made available both for analysis and for methods development.

Project description:BackgroundRhythmic oscillatory activity is widely observed during a variety of subject behaviors and is believed to play a central role in information processing and control. A classic example of rhythmic activity is alpha spindles, which consist of short (0.5-2 s) bursts of high frequency alpha activity. Recent research has shown that alpha spindles in the parietal/occipital area are statistically related to fatigue and drowsiness. These spindles constitute sharp changes in the underlying statistical properties of the signal. Our hypothesis is that change point detection models can be used to identify the onset and duration of spindles in EEG. In this work we develop an algorithm that accurately identifies sudden bursts of narrowband oscillatory activity in EEG using techniques derived from change point analysis. Our motivating example is detection of alpha spindles in the parietal/occipital areas of the brain. Our goal is to develop an algorithm that can be applied to any type of rhythmic oscillatory activity of interest for accurate online detection.MethodsIn this work we propose modeling the alpha band EEG time series using discounted autoregressive (DAR) modeling. The DAR model uses a discounting rate to weigh points measured further in the past less heavily than points more recently observed. This model is used together with predictive loss scoring to identify periods of EEG data that are statistically significant.ResultsOur algorithm accurately captures changes in the statistical properties of the alpha frequency band. These statistical changes are highly correlated with alpha spindle occurrences and form a reliable measure for detecting alpha spindles in EEG. We achieve approximately 95% accuracy in detecting alpha spindles, with timing precision to within approximately 150 ms, for two datasets from an experiment of prolonged simulated driving, as well as in simulated EEG. Sensitivity and specificity values are above 0.9, and in many cases are above 0.95, for our analysis.ConclusionModeling the alpha band EEG using discounted AR models provides an efficient method for detecting oscillatory alpha activity in EEG. The method is based on statistical principles and can generally be applied to detect rhythmic activity in any frequency band or brain region.

Dataset Information

Robust bootstrap prediction intervals for univariate and multivariate autoregressive time series models.

Publications

Robust bootstrap prediction intervals for univariate and multivariate autoregressive time series models.

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