A nonparametric approach to detecting changes in variance in locally stationary time series

Chapman, Jamie-Leigh; Eckley, Idris A.; Killick, Rebecca

doi:10.1002/env.2576

Cited by 11 publications

(8 citation statements)

References 30 publications

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“…Foremost, this paper examines mean shift changepoints only; that is, while series mean levels are allowed to abruptly shift, the variances and correlations of the series are held constant (stationary) in time. Changepoints can also occur in variances (volatilities) (Chapman et al, 2020), in the series' correlation structures (Davis et al, 2006), or even in the marginal distribution of the series (Gallagher et al, 2012). Secondarily, the simulation results reported here are for Gaussian series only.…”

Section: Introductionmentioning

confidence: 93%

A Comparison of Single and Multiple Changepoint Techniques for Time Series Data

Shi¹,

Gallagher²,

Lund³

et al. 2021

Preprint

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This paper describes and compares several prominent single and multiple changepoint techniques for time series data. Due to their importance in inferential matters, changepoint research on correlated data has accelerated recently. Unfortunately, small perturbations in model assumptions can drastically alter changepoint conclusions; for example, heavy positive correlation in a time series can be misattributed to a mean shift should correlation be ignored. This paper considers both single and multiple changepoint techniques. The paper begins by examining cumulative sum (CUSUM) and likelihood ratio tests and their variants for the single changepoint problem; here, various statistics, boundary cropping scenarios, and scaling methods (e.g., scaling to an extreme value or Brownian Bridge limit) are compared. A recently developed test based on summing squared CUSUM statistics over all times is shown to have realistic Type I errors and superior detection power. The paper then turns to the multiple changepoint setting. Here, penalized likelihoods drive the discourse, with AIC, BIC, mBIC, and MDL penalties being considered. Binary and wild binary segmentation techniques are also compared. We introduce a new distance metric specifically designed to compare two multiple changepoint segmentations. Algorithmic and computational concerns are discussed and simulations are provided to support all conclusions. In the end, the multiple changepoint setting admits no clear methodological winner, performance depending on the particular scenario. Nonetheless, some practical guidance will emerge.

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Section: Introductionmentioning

confidence: 93%

A Comparison of Single and Multiple Changepoint Techniques for Time Series Data

Shi¹,

Gallagher²,

Lund³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In addition, several studies are ongoing to detect CPs elaborately. [45] proposed an algorithm to understand the structural change of volatility based on a wavelet, and [46] developed a new algorithm suitable for farm animal behavior patterns. Beyond the typical usage of estimating the severe change in time-series, several studies also investigated to detect a smooth change, verifying the effectiveness of the model to the non-normal distribution data [47], [48].…”

Section: Introductionmentioning

confidence: 99%

Unsupervised Change Point Detection and Trend Prediction for Financial Time-Series Using a New CUSUM-Based Approach

et al. 2022

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The aim of this research is to propose a binary segmentation algorithm to detect the change points in financial time-series based on the Iterative Cumulative Sum of Squares (ICSS). The proposed algorithm, entitled KW-ICSS, utilizes the non-parametric Kruskal-Wallis test in cross-validation procedures. In this regard, KW-ICSS can quickly detect the change points in non-normally distributed time-series with a small number of observations after the change points than the state-of-the-art ICSS algorithm, entitled AIT-ICSS. For the simulated financial time-series whose true location of the change point is known, KW-ICSS detects the change points with the average true positive rate of 81% for the different number of change points, whereas AIT-ICSS only exhibits 72.57%. Also, KW-ICSS's mean absolute deviation between the true and detected change points is less than that of AIT-ICSS for different significance levels. The experiment also finds that the significance level, the model parameter, should be set to less than 10%. For the real-world financial time-series whose true location of change points is unknown, KW-ICSS's robust detection of change points is observed from fewer detected change points and longer intervals between them. Furthermore, KW-ICSS's trend prediction for the short-term future performs with an average of 92.47% accuracy, whereas AIT-ICSS shows 90.69%. Therefore, we claim that KW-ICSS successfully improves AIT-ICSS.INDEX TERMS Unsupervised learning, change point detection, iterative cumulative sum of squares, Kruskal-Wallis.

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“…The model has been successfully applied for a number of tasks in time series analysis, including forecasting (Fryzlewicz et al ., 2003), changepoint analysis (Killick et al ., 2013), stationarity testing (Nason, 2013) and clustering/classification (Hargreaves et al ., 2018; Wilson et al ., 2019). This particular approach to modelling has shown to provide improved analytic insights in areas such as medicine (Sanderson et al ., 2010; Park et al ., 2014), biology (Hargreaves et al ., 2019) and environmental science (Chapman et al ., 2020). A comprehensive overview of second‐order non‐stationary time series modelling can be found in Dahlhaus (2012).…”

Section: Introductionmentioning

confidence: 99%

Trend locally stationary wavelet processes

McGonigle

Killick

Nunes

2022

Journal Time Series Analysis

Self Cite

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Most time series observed in practice exhibit first-as well as second-order non-stationarity. In this article we propose a novel framework for modelling series with simultaneous time-varying first-and second-order structure, removing the restrictive zero-mean assumption of locally stationary wavelet processes and extending the applicability of the locally stationary wavelet model to include trend components. We develop an associated estimation theory for both first-and second-order time series quantities and show that our estimators achieve good properties in isolation of each other by making appropriate assumptions on the series trend. We demonstrate the utility of the method by analysing the global mean sea temperature time series, highlighting the impact of the changing climate.

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A nonparametric approach to detecting changes in variance in locally stationary time series

Cited by 11 publications

References 30 publications

A Comparison of Single and Multiple Changepoint Techniques for Time Series Data

A Comparison of Single and Multiple Changepoint Techniques for Time Series Data

Unsupervised Change Point Detection and Trend Prediction for Financial Time-Series Using a New CUSUM-Based Approach

Trend locally stationary wavelet processes

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