Structural Breaks In Time Series Research Articles

Unveiling the influence of COVID-19 on the online retail market: A comprehensive exploration

The global economy has experienced significant disruptions due to the COVID-19 pandemic, profoundly impacting production and consumption patterns. This paper examines the effect of the pandemic on consumer goods prices, focusing on a sample of hand sanitizers, soap, disinfectants, and baking yeasts. The selection of these products was motivated by multiple and comprehensive criteria, where we considered various factors such as changes in consumption patterns during the pandemic, the relevance of these products in household consumption, consumer behavior, availability of historical price data, their significance in daily domestic life, and their utility in the prevention of the disease. Employing a time-series analysis, the study investigates the relationship between product prices and the S&P 500 index, as well as the presence of structural breaks in the time series. The results reveal a significant correlation between all prices in the sample and the S&P 500 index, indicating the index's efficacy as an indicator of the overall economic state. Moreover, the study identifies a single structural break in each price time series, coinciding with the onset of the COVID-19 pandemic. Notably, hand sanitizers, soap, and disinfectants exhibit particularly substantial price jumps near the time of the break. These findings offer crucial insights into the impact of the COVID-19 pandemic on consumer prices, which can guide policy decisions aimed at mitigating the pandemic's economic consequences.

A Combination of Fuzzy Techniques and Chow Test to Detect Structural Breaks in Time Series

In a series of papers, we suggested a non-statistical method for the detection of structural breaks in a time series. It is based on the applications of special fuzzy modeling methods, namely Fuzzy transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). In this paper, we combine our method with the principles of the classical Chow test, which is a well-known statistical method for testing the presence of a structural break. The idea is to construct testing statistics similar to that of the Chow test which is formed from components of the first-degree F-transform. These components contain an estimation of the average values of the tangents (slopes) of the time series over an imprecisely specified time interval. In this paper, we illustrate our method and its statistical test on a real-time series and compare it with three classical statistical methods.

Functional Estimation and Change Detection for Nonstationary Time Series

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null hypothesis of no change. In this article, estimators for integrated parameters of locally stationary time series are constructed and a corresponding functional central limit theorem is established, enabling change-point inference for a broad class of parameters under mild assumptions. The proposed framework covers all parameters which may be expressed as nonlinear functions of moments, for example kurtosis, autocorrelation, and coefficients in a linear regression model. To perform feasible inference based on the derived limit distribution, a bootstrap variant is proposed and its consistency is established. The methodology is illustrated by means of a simulation study and by an application to high-frequency asset prices.

Detection of Structural Breaks in Time Series Using Fuzzy Techniques

Detection of Structural Breaks in Time Series Using Fuzzy Techniques

The EU Enlargement and Income Convergence: Central and Eastern European Countries vs. Western Balkan Countries

Objective: This article analyses the stochastic convergence of income per capita between the Western Balkan (WB) and the Central and Eastern European (CEE) countries compared to developed EU countries (EU15). Research Design & Methods: Stochastic convergence implies that all shocks in country’s income relative to the average income of the group are only temporary. In order to test stochastic convergence, the tests of the unit root were used. The Augmented Dickey-Fuller (ADF) test is supplemented with the Zivot-Andrews (ZA) unit root test, which allows for the structural breaks in time series of income per capita. Findings: Results confirm the existence of stochastic convergence of income per capita toward the EU15 average in the cases of the Czech Republic, Slovakia, Poland, Slovenia, Estonia, Latvia and Romania. Income convergence is not found in the case of the Western Balkan countries. Implications & Recommendations: While income convergence toward the EU15 average level was found in the case of 7 CEE countries, it was not found in the case of any WB country. This could be a proof of the importance of further support to reforms in the Western Balkan countries. Contribution & Value Added: The scientific contribution of the article is reflected in the fact that the existing literature dealing with income convergence of the Western Balkan countries toward the income of the EU15 countries is still very limited in number, as is the number of studies that compare convergence of income per capita toward the EU15 between the Western Balkan and CEE countries.

Measuring Business Cycles: A Review

This article summarizes the main findings on problems related to the measurement and identification of business cycles. The aim of this study is to define and identify the determinants of business cycles. This paper provides an overview of the methodology and its future course. Our investigation suggests that some methodological frameworks are available in the literature, but none is perfect. A new development in the field lies in spectral analysis methods for measuring business cycles, which may have advantages over existing methodologies (nonlinearity, stationarity issues). We feel that fractional integration is important in the proper monitoring and explanation of business cycles. Spectral analysis techniques have also proved to be useful for addressing the problems of stationarity and structural breaks in time series when analyzing business cycles. Another important issue that is excluded when studying business cycles is that the link between cycles and economic growth is presumed to be non-existent, implying money neutrality.

Detecting structural breaks in time series via genetic algorithms

Detecting structural breaks is an essential task for the statistical analysis of time series, for example, for fitting parametric models to it. In short, structural breaks are points in time at which the behaviour of the time series substantially changes. Typically, no solid background knowledge of the time series under consideration is available. Therefore, a black-box optimization approach is our method of choice for detecting structural breaks. We describe a genetic algorithm framework which easily adapts to a large number of statistical settings. To evaluate the usefulness of different crossover and mutation operations for this problem, we conduct extensive experiments to determine good choices for the parameters and operators of the genetic algorithm. One surprising observation is that use of uniform and one-point crossover together gave significantly better results than using either crossover operator alone. Moreover, we present a specific fitness function which exploits the sparse structure of the break points and which can be evaluated particularly efficiently. The experiments on artificial and real-world time series show that the resulting algorithm detects break points with high precision and is computationally very efficient. A reference implementation with the data used in this paper is available as an applet at the following address: http://www.imm.dtu.dk/~pafi/TSX/. It has also been implemented as package SBRect for the statistics language R.

Previsão do volume exportado para a fruticultura brasileira via análise de séries temporais: uma abordagem ARIMA/GARCH

O objetivo deste trabalho foi propor modelos de previsão econométricos para o volume exportado da fruticultura brasileira, com vistas a auxiliar o planejamento e controle de sua produção, motivado também pela constatação de poucos estudos publicados tratando desse tema. Nesse sentido, empregou-se os modelos ARIMA/GARCH, considerando-se, outrossim, a ocorrência de uma sazonalidade estocástica multiplicativa nessas séries históricas. Foram coletadas 300 observações de peso líquido (kg) exportado entre jan/1989 a dez/2013 das seguintes frutas: abacaxi, banana, laranja, limão-lima, maçã, mamão, manga, melancia, melão e uva, cujo critério de seleção foi a sua importância na pauta de exportação frutícola, pois representavam 97% do total de dólares recebidos e 99% do volume vendido em 2010, de uma população de 28 tipos de frutas exportadas. Os resultados indicam que só não foi observada a existência de sazonalidade multiplicativa de 12 meses na banana e na manga. Por outro lado, foram identificadas dois grupos de frutas: (1) as que são exportadas continuamente, e (2) as que possuem picos de exportação. Sobre a qualidade dos modelos de previsão, eles foram considerados satisfatórios para seis das dez frutas analisadas. Quanto à volatilidade, verificou-se uma alta persistência das séries da banana e do mamão, apontando para a existência de uma quebra estrutural na série de dados, que pode estar associada às crises econômicas ocorridas nos últimos 17 anos.

Testing of breakdates in agricultural prices of selected representatives of animal production

This paper deals with an investigation of breakdates in agricultural prices. A structural break has occurred if at least one of the model parameters has changed at some date. This date is a breakdate. Ignoring structural breaks in time series can lead to serious problems with economic models of time series. The aim is to determine the number and date of the breakdates in individual time series and connect them with changes in the market and economic environment. The time series of agricultural price relating to animal production, namely the prices of pork, beef, chicken, milk and eggs, are analyzed for the period from January 1996 to December 2011. The autoregressive model (AR) model of Box-Jenkins methodology and stability testing according to Quandt or Wald statistics are used for the purposes of this paper. Multiple breakdates are found in the case of eggs (September 1998, May 2004), milk (October 1999, December 2007) and chicken (October 2002, February 2005) prices. One breakdate was detected in the prices of beef (April 2002) and none in the case of pork prices. The results show the importance of multiple breakdate testing. The Quandt statistic provides one possible way of applying a multiple approach. All breakdates which were confirmed using these statistics can be associated with changes in the agri-food market and economic environment. Information about the date of changes in the time series can be used for other unbiased modelling in more complex models.

Linkages among the US energy futures markets

This study investigates the price linkage among the US major energy sources, considering structural breaks in time series, to provide information for diversifying the US energy sources. We find that only a weak linkage sustains among crude oil, gasoline, heating oil, coal, natural gas, uranium and ethanol futures prices. This implies that the US major energy source markets are not integrated as one primary energy market. Our tests also reveal that uranium and ethanol futures prices have very weak linkages with other major energy source prices. This indicates that the US energy market is still at a stage where none of the probable alternative energy source markets are playing the role as substitute or complement markets for the fossil fuel energy markets.

Structural breaks in time series

This paper gives an account of some of the recent work on structural breaks in time series models. In particular, we show how procedures based on the popular cumulative sum, CUSUM, statistics can be modified to work also for data exhibiting serial dependence. Both structural breaks in the unconditional and conditional mean as well as in the variance and covariance/correlation structure are covered. CUSUM procedures are nonparametric by design. If the data allows for parametric modeling, we demonstrate how likelihood approaches may be utilized to recover structural breaks. The estimation of multiple structural breaks is discussed. Furthermore, we cover how one can disentangle structural breaks (in the mean and/or the variance) on one hand and long memory or unit roots on the other. Several new lines of research are briefly mentioned.

Size properties of Lagrange Multiplier cointegration tests in the presence of structural breaks

The size properties of the recently advanced Lagrange Multiplier (LM) cointegration tests in the presence of structural breaks in time series are investigated. It is shown that misspecification of the types of breaks is liable to spurious rejection. In contrast, severe undersizing may result when ignoring the presence of any break.

Bayesian Inference about the Types of Structural Breaks When There Are Different Breaks in Many Parameters

I propose a Bayesian approach to making an inference about complicated patterns of structural breaks in time series. Structural break models in the literature are mainly considered for a simple case in which all the parameters under the structural changes are restricted to have breaks at the same dates. Unlike the existing literature, the proposed method in this paper allows multiple parameters such as intercept, persistence, and/or residual variance to undergo mutually independent structural breaks at different dates with the different number of breaks across parameters. To estimate the complex structural break models considered in this paper, structural breaks in the multiple parameters are interpreted as regime transitions as in Chib (1998). The regime for each parameter is then indicated by a corresponding discrete latent variable which follows a first-order Markov process. A Markov-chain Monte Carlo scheme is developed to estimate and compare the complex structural break models, which are potentially non-nested, in an efficient and tractable way. I apply this approach to postwar U.S. inflation and find strong support for an autoregressive model with two structural breaks in residual variance and no break in intercept and persistence.

Identifying Structural Breaks in Stochastic Mortality Models

In recent years the issue of life expectancy has become of upmost importance to pension providers, insurance companies and the government bodies in the developed world. Significant and consistent improvements in mortality rates and hence life expectancy have led to unprecedented increases in the cost of providing for older ages. This has resulted in an explosion of stochastic mortality models forecasting trends in mortality data in order to anticipate future life expectancy and hence quantify the costs of providing for future ageing populations. Many stochastic models of mortality rates identify linear trends in mortality rates by time, age and cohort and forecast these trends into the future using standard statistical methods. The modeling approaches used fail to capture the effects of any structural change in the trend and thus potentially produce incorrect forecasts of future mortality rates. In this paper we look at a range of leading stochastic models of mortality and test for structural breaks in the trend time series. We find that in almost all cases structural breaks in the time series are present and when allowing for these the resulting forecasts are significantly improved.

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Testing for Structural Breaks in Small Samples

In a recent paper, Bai and Perron (2006) demonstrate that their approach for testing for multiple structural breaks in time series works well in large samples, but they found substantial deviations in both the size and power of their tests in smaller samples. We propose modifying their methodology to deal with small samples by using Monte Carlo simulations to determine sample-specific critical values under the each time the test is run. We draw on the results of our simulations to offer practical suggestions on handling serial correlation, model misspecification, and the use of alternative test statistics for sequential testing. We show that, for most types of data generating processes in samples with as low as 50 observations, our proposed modifications perform substantially better.

Testing for Structural Breaks in Small Samples

In a recent paper, Bai and Perron (2006) demonstrate that their approach for testing for multiple structural breaks in time series works well in large samples, but they found substantial deviations in both the size and power of their tests in smaller samples. We propose modifying their methodology to deal with small samples by using Monte Carlo simulations to determine sample-specific critical values under the each time the test is run. We draw on the results of our simulations to offer practical suggestions on handling serial correlation, model misspecification, and the use of alternative test statistics for sequential testing. We show that, for most types of data generating processes in samples with as low as 50 observations, our proposed modifications perform substantially better.

Additional sources of bias in half-life estimation

Recently, an increasing amount of attention is being paid to biases in the measurement of time series dynamics based on calculations of half-life. In particular, this issue amplifies the controversy surrounding the purchasing power parity doctrine. Cross-sectional and temporal aggregations, along with mis-specified models, were previously identified as sources of this bias. We identified several other sources of bias, namely, sampling error, incorrect approximations, and structural breaks in time series. These sources should also receive sufficient attention for a sound measurement of half-life.

Testing Integration of Macroeconomic Time Series in Transitional Socialist Economies. A Modification of Perron Test

The presence of structural breaks reduces the power of integration tests. A number of methods were suggested to improve the statistical properties of integration tests in the presence of structural breaks. The most known are Perron tests, which allow to test for the level of integration of time series with one structural break. Perron tests allow for two types of structural breaks: additive outlier an innovative outlier. These tests are, however, not very useful in testing the level of integration of macroeconomic time series in countries in transition from centrally-planned to market economy. In such case one should expect two structural breaks to affect the time series: one at the beginning and one at the end of the transformation process. Test that allows for two additive outlier type structural breaks in time series is developed in this paper. This test has superior power as compared to standard Dickey-Fuller and Perron tests. This paper provides asymptotic distribution as well as finite sample properties of proposed test. Therefore practitioners receive a reliable tool for analyzing macroeconomic processes in transitional economies.