Structural Changes In Time Series Research Articles

The Fourier approach and testing for cointegration in LSTAR model

This paper proposes a new logistic smooth transition autoregressive (LSTAR) cointegration test by combining the Fourier function to catch the structural changes that occur over time and the LSTAR model to consider the nonlinearity. Logistic and exponential functions are the main transition functions defining the nonlinearity in STAR models since the exponential smooth transition autoregressive (ESTAR) and LSTAR models can explain the different structures of economic variables. The Fourier approach is a simple and effective way to model the structural changes in time series as an alternative to dummy variables. The most significant advantage of the method is that it does not require prior knowledge about the date, number of breaks, or forms. Monte Carlo simulation results show that the proposed test has good size and power properties for different sample sizes and parameters. The results also revealed that the power performance of the proposed test and the Fourier ESTAR test offered by Güriş and Sedefoğlu (2022) are close to each other. The steps of the Fourier-based tests are illustrated by providing an empirical example of testing the validity of the purchasing power parity (PPP) hypothesis in Türkiye.

Power of weighted test statistics for structural change in time series

Power of weighted test statistics for structural change in time series

Detecting Structural Changes in Time Series by Using the BDS Test Recursively: An Application to COVID-19 Effects on International Stock Markets

Structural change tests aim to identify evidence of a structural break or change in the underlying generating process of a time series. The BDS test has its origins in chaos theory and seeks to test, using the correlation integral, the hypothesis that a time series is generated by an identically and independently distributed (IID) stochastic process over time. The BDS test is already widely used as a powerful tool for testing the hypothesis of white noise in the residuals of time series models. In this paper, we illustrate how the BDS test can be implemented also in a recursive manner to evaluate the hypothesis of structural change in a time series, taking advantage of its ability to test the IID hypothesis. We apply the BDS test repeatedly, starting with a sub-sample of the original time series and incrementally increasing the number of observations until it is applied to the full sample time series. A structural change in the unknown underlying generator model is detected when a change in the trend shown by this recursively computed BDS statistic is detected. The strength of this recursive BDS test lies in the fact that it does not require making any assumptions about the underlying time series generator model. We ilustrate the power and potential of this recursive BDS test through an application to real economic data. In this sense, we apply the test to assess the structural changes caused by the COVID-19 pandemic in international financial markets. Using daily data from the world’s top stock indices, we have detected strong and statistically significant evidence of two major structural changes during the period from June 2018 to June 2022. The first occurred in March 2020, coinciding with the onset of economic restrictions in the main Western countries as a result of the pandemic. The second occurred towards the end of August 2020, with the end of the main economic restrictions and the beginning of a new post-pandemic economic scenario. This methodology to test for structural changes in a time series is easy to implement and can detect changes in any system or process behind the time series even when this generating system is not known, and without the need to specify or estimate any a priori generating model. In this sense, the recursive BDS test could be incorporated as an initial preliminary step to any exercise of time series modeling. If a structural change is detected in a time series, rather than estimating a single predictive model for the full-sample time series, efforts should be made to estimate different predictive models, one for the time before and one for the time after the detected structural change.

Subsampling ratio tests for structural changes in time series with heavy-tailed AR(p) errors

In this article, we consider that issues related to the mean and trend of heavy-tailed AR(p) series are possibly subject to change at most once at some unknown point in time. Under the inspiration of Shao (J. Time Ser. Anal., 2011, 32, 598–606), two ratio statistics are constructed to test whether unknown changes have occurred. It is shown that asymptotic distributions of these test statistics under the no-change null hypothesis are functional for Lévy processes and their consistencies are given under the alternative. To avoid the nuisance parameter, we provide a subsampling method that returns more accurate critical values for these tests. The validity of the subsampling algorithm is proved. A simulation study shows the subsampling-based ratio tests achieve the correct empirical sizes and comparable empirical powers in large samples. Finally, two practical applications using real data set are presented.

Impact of the COVID-19 Pandemic on Objectively Measured Physical Activity and Sedentary Behavior Among Overweight Young Adults: Yearlong Longitudinal Analysis.

BackgroundThe COVID-19 pandemic has impacted multiple aspects of daily living, including behaviors associated with occupation, transportation, and health. It is unclear how these changes to daily living have impacted physical activity and sedentary behavior.ObjectiveIn this study, we add to the growing body of research on the health impact of the COVID-19 pandemic by examining longitudinal changes in objectively measured daily physical activity and sedentary behavior among overweight or obese young adults participating in an ongoing weight loss trial in San Diego, California.MethodsData were collected from 315 overweight or obese (BMI: range 25.0-39.9 kg/m2) participants aged from 18 to 35 years between November 1, 2019, and October 30, 2020, by using the Fitbit Charge 3 (Fitbit LLC). After conducting strict filtering to find valid data on consistent wear (>10 hours per day for ≥250 days), data from 97 participants were analyzed to detect multiple structural changes in time series of physical activity and sedentary behavior. An algorithm was designed to detect multiple structural changes. This allowed for the automatic identification and dating of these changes in linear regression models with CIs. The number of breakpoints in regression models was estimated by using the Bayesian information criterion and residual sum of squares; the optimal segmentation corresponded to the lowest Bayesian information criterion and residual sum of squares. To quantify the changes in each outcome during the periods identified, linear mixed effects analyses were conducted. In terms of key demographic characteristics, the 97 participants included in our analyses did not differ from the 210 participants who were excluded.ResultsAfter the initiation of the shelter-in-place order in California on March 19, 2021, there were significant decreases in step counts (−2872 steps per day; 95% CI −2734 to −3010), light physical activity times (−41.9 minutes; 95% CI −39.5 to −44.3), and moderate-to-vigorous physical activity times (−12.2 minutes; 95% CI −10.6 to −13.8), as well as significant increases in sedentary behavior times (+52.8 minutes; 95% CI 47.0-58.5). The decreases were greater than the expected declines observed during winter holidays, and as of October 30, 2020, they have not returned to the levels observed prior to the initiation of shelter-in-place orders.ConclusionsAmong overweight or obese young adults, physical activity times decreased and sedentary behavior times increased concurrently with the implementation of COVID-19 mitigation strategies. The health conditions associated with a sedentary lifestyle may be additional, unintended results of the COVID-19 pandemic.

Analyses of structural changes in ecological time series (ASCETS)

• ASCETS provides boundaries and confidence for changes in indicator states. • ASCETS can be applied to a wide range of univariate time-series of ecological indicators. • ASCETS enable integration of different indicators and aggregations across geographical areas. • ASCETS is useful for risk assessment and for an ecosystem approach to management. Assessing status of natural resources and ecosystem components is pivotal for management, where indicators or indices often are used as proxies of ecological state. Many indicators, however, lack reference points and are associated with sampling errors and environmental noise, limiting their usefulness in management. Here we present a method for assessing state changes in ecological indicator from time-series: Analyses of Structural Changes in Ecological Time Series (ASCETS) . ASCETS enables both quantitative boundary levels for changes in indicator states (e.g. for management targets), and the confidence for a change in state during an assessment period. Thereby it can be used in risk assessments and is suitable for aggregation or integration of different indicator states across sites, or for an ecosystem based approach to management. With extended information about ecological state during a reference period, ASCETS can support reference levels for defining ecological status of an indicator. ASCETS first identifies structural changes in time-series to determine reference periods with coherent indicator dynamics. Next, from the observed indicator values during the reference period, a distribution of resampled median values is used to set boundary levels as a tolerable range of indicator variation reflecting the same state as during the reference period. Finally, a confidence of a change in indicator state is evaluated during an assessment period as the proportion of resampled median values of the assessment period overlapping the boundary levels of the reference period. Simulations indicate ASCETS correctly detects changes in indicator state when changes in indicator values are at least twice as large as the coefficient of variation, with a false rate of changes around 5%. We apply ASCETS to indicators for bird and fish communities used within the Marine Strategy Framework Directive to illustrate how indicator boundary levels can be set where reference levels may be ecologically and analytically troublesome. An R-script is provided for further use and modification. We propose ASCETS as a flexible and generic method for assessing changes in ecological states from time-series to support identification of management targets.

Comparing permutation entropy functions to detect structural changes in time series

Entropy can be taken as a measure of the complex dynamical behavior. In this paper, we consider different entropy functions and the permutation symbolic dynamics and we apply them to find structural changes in time series. We analyze what entropy functions are more suitable to show changes in simulated time series where the structural changes are know. Applications to seismic real data and economic data series are shown to illustrate how this type of tools can be used.

Dimension Reduction of Multi-Spectral Satellite Image Time Series to Improve Deforestation Monitoring

In recent years, sequential tests for detecting structural changes in time series have been adapted for deforestation monitoring using satellite data. The input time series of such sequential tests is typically a vegetation index (e.g., NDVI), which uses two or three bands and ignores all other bands. Being limited to a vegetation index will not benefit from the richer spectral information provided by newly launched satellites and will bring two bottle-necks for deforestation monitoring. Firstly, it is hard to select a suitable vegetation index a priori. Secondly, a single vegetation index is typically affected by seasonal signals, noise and other natural dynamics, which decrease its power for deforestation detection. A novel multispectral time series change monitoring method that combines dimension reduction methods with a sequential hypothesis test is proposed to address these limitations. For each location, the proposed method automatically chooses a “suitable” index for deforestation monitoring. To demonstrate our approach, we implemented it in two study areas: a dry tropical forest in Bolivia (time series length: 444) with strong seasonality and a moist tropical forest in Brazil (time series length: 225) with almost no seasonality. Our method significantly improves accuracy in the presence of strong seasonality, in particular the temporal lag between disturbance and its detection.

Tests for Structural Changes in Time Series of Counts

AbstractWe propose methods for detecting structural changes in time series with discrete‐valued observations. The detector statistics come in familiar L2‐type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.

ON-LINE CHANGE MONITORING WITH TRANSFORMED MULTI-SPECTRAL TIME SERIES, A STUDY CASE IN TROPICAL FOREST

Abstract. In recent years, the methods for detecting structural changes in time series have been adapted for forest disturbance monitoring using satellite data. The BFAST (Breaks For Additive Season and Trend) Monitor framework, which detects forest cover disturbances from satellite image time series based on empirical fluctuation tests, is particularly used for near real-time deforestation monitoring, and it has been shown to be robust in detecting forest disturbances. Typically, a vegetation index that is transformed from spectral bands into feature space (e.g. normalised difference vegetation index (NDVI)) is used as input for BFAST Monitor. However, using a vegetation index for deforestation monitoring is a major limitation because it is difficult to separate deforestation from multiple seasonality effects, noise, and other forest disturbance. In this study, we address such limitation by exploiting the multi-spectral band of satellite data. To demonstrate our approach, we carried out a case study in a deciduous tropical forest in Bolivia, South America. We reduce the dimensionality from spectral bands, space and time with projective methods particularly the Principal Component Analysis (PCA), resulting in a new index that is more suitable for change monitoring. Our results show significantly improved temporal delay in deforestation detection. With our approach, we achieved a median temporal lag of 6 observations, which was significantly shorter than the temporal lags from conventional approaches (14 to 21 observations).

Erratum to: Parallel Algorithm to Detect Structural Changes in Time Series

Erratum to: Parallel Algorithm to Detect Structural Changes in Time Series

Parallel Algorithm to Detect Structural Changes in Time Series

Analysis of long time series is relevant in many current applications. These investigations are usually carried out on multiprocessor computers (supercomputers). However, supercomputer calculations are efficient only if the time-series processing algorithms are sufficiently parallelized. In this article, we propose a parallel algorithm that detects shift points of the time-series mean -- a highly important task in many applications. The algorithm breaks the time series into segments and looks for shift points on each segment using a statistical test. The critical values have been calculated for this test. An additional test reduces the number of false detections.

A piecewise linear model for detecting climatic trends and their structural changes with application to mesosphere/lower thermosphere winds over Collm, Germany

A piecewise linear model is developed to detect climatic trends and their structural changes in time series with a priori unknown number and positions of breakpoints (BPs). The departure (i.e., the initial noise term) of trends from time series is allowed to be interpreted by the first‐ and second‐order autoregressive models. The goodness of fit of candidate models, if the residuals are accepted as normally distributed white noise, is evaluated using the Schwarz Bayesian Information Criterion (BIC). The uncertainties of all trend parameters are estimated using the Monte‐Carlo method. The model is applied to the mesosphere and lower thermosphere (MLT) winds obtained at Collm, Germany, during 1960–2007. A persistent increase after ∼1980 of the zonal prevailing wind is observed in all seasons and hence in the zonal annual mean based on the primary models. Trends of the meridional prevailing wind are different for different seasons. Several major trend BPs are identified in the annual mean zonal and meridional winds according to BIC. However, in view of the large wind variability before the late 1970s, alternative models are considered. This provides four additional minor breaks. In some cases, the initial noise must be further interpreted by autoregressive models, suggesting that other unidentified factors may also play a role.

Market and Economic Regulation Periodicity: A Feature that Allows Prevention and Regulation

Problem statement: This study addressed the essential questions of non linear financial flows forecasting and prevention regarding the means of periodicity. Approach: We implemented some new computational tools to weigh up the presence of periodicity in 10 years financial price time series. The data consists of NYSE-Euronext listed corporations’ closing prices and East-Asian, North-American and European markets indexes closing prices. Results: Empirical evidence put forward that the tools allow considering the periodicity plus a forecasting side effect for the next months. The lengths of the cycles are determined for indexes and assets with strong disparity between the two categories. Conclusion: Extensively, the results open the road to determine structural changes in time series by allowing the calculation of the fundamental frequencies. It introduces some concepts from physics and discusses their potential usefulness in financial economics. This shows the way to detect financial and economic extreme events (burst of bubbles, companies’ failures, markets or sectors’ recessions) as to prevent them.

Markov‐Switching Estimation of Spatial Maize Price Transmission Processes between Tanzania and Kenya

We discuss the Markov-switching vector au toregressive (MS-VAR) class of nonlinear time series models that can be used to analyze recurring discrete structural changes in time series. Hamilton's (1989) seminal Markov switching (MS) model of the U.S. business cy cle triggered considerable interest in the MS approach in economics. Most empirical appli cations to date have focused on the business cy cle and financial markets, but we see potential for MS-VAR models in agricultural economics, for example, in price transmission analysis. In the following, we first provide an overview of the MS-VAR framework. We then present an illustrative application to maize price trans mission between Tanzania and Kenya. The article closes with a discussion of strengths, weaknesses, and potential uses of the MS-VAR approach in price transmission analysis.

Robust non-parametric smoothing of non-stationary time series

Motivated by the need of extracting local trends and low frequency components in non-stationary time series, this paper discusses methods of robust non-parametric smoothing. Basic approach is the combination of the parametric M-estimation with kernel and local polynomial regression methods. The result is an iterative estimator that retains a linear structure, but has kernel weights also in the direction of the prediction errors. The design of smoothing coefficients is carried out with robust cross-validation criteria and rules of thumb. The method works well both to remove the influence of patches of outliers and to detect the local breaks and persistent structural change in time series.

Detecting nonlinearity in time series by model selection criteria

This article analyzes the use of model selection criteria for detecting nonlinearity in the residuals of a linear model. Model selection criteria are applied for finding the order of the best autoregressive model fitted to the squared residuals of the linear model. If the order selected is not zero, this is considered as an indication of nonlinear behavior. The BIC and AIC criteria are compared to some popular nonlinearity tests in three Monte Carlo experiments. We conclude that the BIC model selection criterion seems to offer a promising tool for detecting nonlinearity in time series. An example is shown to illustrate the performance of the tests considered and the relationship between nonlinearity and structural changes in time series.