The Markov-Switching Vector Autoregressive Model

The impact of oil price shocks on Tehran Stock Exchange returns: Application of the Markov switching vector autoregressive models

Jointly Determining the State Dimension and Lag Order for Markov-Switching Vector Autoregressive Models

PurposeThis study aims to analyze the impact of the crude oil market on the Toronto Stock Exchange Index (TSX).Design/methodology/approachThe focus is on detecting nonlinear relationship based on monthly data from 1970 to 2021 using Markov-switching vector auto regression (VAR) model.FindingsThe results indicate that TSX return contains two regimes: positive return (Regime 1), when growth rate of stock index is positive; and negative return (Regime 2), when growth rate of stock index is negative. Moreover, Regime 1 is more volatile than Regime 2. The findings also show the crude oil market has a negative effect on the stock market in Regime 1, while it has a positive effect on the stock market in Regime 2. In addition, the authors can see this effect in Regime 1 more significantly in comparison to Regime 2. Furthermore, two-period lag of oil price decreases stock return in Regime 1, while it increases stock return in Regime 2.Originality/valueThis study aims to address the effect of oil market fluctuation on TSX index using Markov-switching approach and capture the nonlinearities between them. To the best of the author’s knowledge, this is the first study to assess the effect of the oil market on TSX in different regimes using Markov-switching VAR model. Because Canada is the sixth-largest producer and exporter of oil in the world as well as the TSX as the Canada’s main stock exchange is the tenth-largest stock exchange in the world by market capitalization, this paper’s framework to analyze a nonlinear relationship between oil market and the stock market of Canada helps stock market players like policymakers, institutional investors and private investors to get a better understanding of the real world.

Vector Autoregressive Modal Analysis With Application To Ship Structures

An increasing number of researchers in psychology are collecting intensive longitudinal data in order to study psychological processes on an intraindividual level. An increasingly popular way to analyze these data is autoregressive time series modeling; either by modeling the repeated measures for a single individual using classic n = 1 autoregressive models, or by using multilevel extensions of these models, with the dynamics for each individual modeled at Level 1 and interindividual differences in these dynamics modeled at Level 2. However, while it is widely accepted in psychology that psychological measurements usually contain a certain amount of measurement error, the issue of measurement error is largely neglected in applied psychological (autoregressive) time series modeling: The regular autoregressive model incorporates innovations, or "dynamic errors," but not measurement error. In this article we discuss the concepts of reliability and measurement error in the context of dynamic (VAR(1)) models, and the consequences of disregarding measurement error variance in the data. For this purpose, we present a preliminary model that accounts for measurement error for constructs that are measured with a single indicator. We further discuss how this model could be used to investigate the between-person reliability of the measurements, as well as the (person-specific) within-person reliabilities and any individual differences in these reliabilities. We illustrate the consequences of assuming perfect reliability, the preliminary model, and reliabilities, using an empirical application in which we relate women's general positive affect to their positive affect concerning their romantic relationship. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Damage in real engineering often exhibits nonlinear characteristics. For example, crack opening and closing can lead to bilinear stiffness of structures. Using simple linear model will miss the nonlinear information related to damage, and reduce the damage identification reliability. To solve this problem, a new nonlinear damage identification method based on the Markov-Switching Vector Auto-Regression (MSVAR) model is proposed. This method assumes that the damage will cause nonlinear characteristics in the structural responses. Since the hidden state smooth probability of the MSVAR model can reflect nonlinear changes in the data, the smooth probability-based information entropy is used as the damage warning indicator to monitor the damage state of the structure. For cracks, their locations can be infered using the damage location vector constructed by autoregressive coefficients of the MSVAR model. The crack width is represented as the interlayer displacement at the crack location (when the smooth probability switches from 0 to 100%). A numerical example and an experimental test are introduced to verify the effectiveness of the proposed method in the identification of crack damage.

This study analyzes the effects of stress on the Uruguayan macroeconomy in the 1998Q3-2016Q2 period with the underlying idea that financial shocks propagate differently during normal than during times of stress. This behavior is captured in a multivariate framework through a Markovswitching vector auto regressive (MS-VAR) model. The evidence found so far supports the idea that financial conditions affect the macroeconomy, as they not only change the private investment long-run average growth rate but also directly modify the behavior of monetary policy.

Many nonlinear time series models have been around for a long time and have originated outside of time series econometrics. The stochastic models popular univariate, dynamic single-equation, and vector autoregressive are presented and their properties considered. Deterministic nonlinear models are not reviewed. The use of nonlinear vector autoregressive models in macroeconometrics seems to be increasing, and because this may be viewed as a rather recent development, they receive somewhat more attention than their univariate counterparts. Vector threshold autoregressive, smooth transition autoregressive, Markov-switching, and random coefficient autoregressive models are covered along with nonlinear generalizations of vector autoregressive models with cointegrated variables. Two nonlinear panel models, although they cannot be argued to be typically macroeconometric models, have, however, been frequently applied to macroeconomic data as well. The use of all these models in macroeconomics is highlighted with applications in which model selection, an often difficult issue in nonlinear models, has received due attention. Given the large amount of nonlinear time series models, no unique best method of choosing between them seems to be available.

The ice core time series from Vostok Station in Antarctica and the North Greenland Ice Core Project have seasonal variation corresponding to the Milankovitch cycles. After removing these cycles, and interpolating to equal time intervals, stationary time series models are fitted. The series show clear directionality and this feature is modelled by either non-Gaussian errors or non-linear time series models. Threshold autoregressive models are fitted by penalized least squares and compared with non-threshold autoregressive models. Since both ice core time series are reasonably modelled as first order autoregressive series with parameters close to one, directionality will arise from non-symmetric error distributions. However, two regime threshold autoregressive models, of order one and two for Greenland and Vostok, respectively, give an improved match to the observed directionality and a reduced sum of squared residuals. Realizations from the threshold autoregressive models are noticeably different from the non-threshold models. Since the non-threshold models are a restricted case of the threshold models, and the threshold models are a better fit to the observed time series, threshold models should provide more realistic realizations. References C. Chatfield. The Analysis of Time Series: An Introduction . CRC Press, 2004. https://www.crcpress.com/The-Analysis-of-Time-Series-An-Introduction-Sixth-Edition/Chatfield/p/book/9781584883173 A. J. Lawrance. Directionality and reversibility in time series. Int. Stat. Rev. 59(1):67–79, 1991. doi:10.2307/1403575 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Threshold autoregressive models for directional time series. In I. Rojas and H. Pomares (Eds.), Time Series Analysis and Forecasting Selected Contributions from the ITISE Conference (ITISE 2015) . pp. 13–25, 2016. doi:10.1007/978-3-319-28725-6 M. M. Mansor, M. E. Glonek, D. A. Green and A. V. Metcalfe. Modelling directionality in stationary geophysical time series. International work-conference on Time Series (ITISE 2015) . http://www.researchgate.net/publication/281835075 M. M. Mansor, D. A. Green and A. V. Metcalfe. Modelling and simulation of directional financial time series. Proceedings of the 21st International Congress on Modelling and Simulation (MODSIM 2015) , pp. 1022–1028, 2015. http://www.mssanz.org.au/modsim2015/E4/mansor.pdf M. M. Mansor, D. A. Green and A. V. Metcalfe. Directionality and volatility in electroencephalogram time series. Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS 2016), AIP Conf. Proc. 1739:020080, 2016. doi:10.1063/1.4952560 North Greenland Ice Core Project members. High-resolution record of Northern Hemisphere climate extending into the last interglacial period. Nature , 431:147–151, 2004. doi:10.1038/nature02805 J. R. Petit, J. Jouzel, D. Raynaud, N. I. Barkov, J.-M. Barnola, I. Basile, M. Bender, J. Chappellaz, M. Davis, G. Delaygue, M. Delmotte, V. M. Kotlyakov, M. Legrand, V. Y. Lipenkov, C. Lorius, L. Pepin, C. Ritz, E. Saltzman and M. Stievenard. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature , 399:429–436, 1999. doi:10.1038/20859 S. Soubeyrand, C. E. Morris and E. K. Bigg. Analysis of fragmented time directionality in time series to elucidate feedbacks in climate data. Environ. Modell. Softw. 61:78–86, 2014. doi:10.1016/j.envsoft.2014.07.003

The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying lengths (T = 25, 50, 75, 100, 125) using Statistical Analysis System (SAS) version 9.2. Autoregressive components for the 5 series vectors included coefficients of .80, .70, .65, .50 and .40. Error variance components included values of .20, .20, .10, .15, and .15, with cross-lagged coefficients of .10, .10, .15, .10, and .10. A Monte Carlo study revealed that in comparison to frequentist methods, the Bayesian approach provided increased sensitivity for hypothesis testing and detecting Type I error.

Researcher every so often model economic relationship using linear models. Even when non-linear models are used, they hardly consider the possibility of regimes, the transmission from one regime to another and also the duration of stay in a particular regime. These are not captured by linear models. To address this, we applied the Markov-Switching Mean Vector Autoregressive Model to model and estimate the interdependence between macroeconomic variables (International Trade and Macroeconomic Stability) within the context of the Nigerian economy. Specifically, the study analyzed the trends of total export, total import, exchange rate, and inflation rate in Nigeria within the study period, Estimated MSM-VAR models on the study variables and selected the best model using information criteria. The study empirically investigated the interdependence existing among the study variables, determined the probabilities of transition from one regime to another and the duration of stay in a regime. The study ascertained the relative significance of each random innovation in affecting the study variables. Monthly time series data 246 months spanning through January 2000 to June 2020 was collected form the Central Bank of Nigeria Statistical Bulletin. The study used the Markov-Switching Mean Vector Autoression in the Analysis. The results showed that all variables were stationary at first difference. The study chose 2 regimes and the model selection criteria selected [MS(2)-MVAR(2)]. The variables were largely self-explanatory and very strongly exogenous.

The damage identification of a reticulated shell is a challenging task, facing various difficulties, such as the large number of degrees of freedom (DOFs), the phenomenon of modal localization and transition, and low modeling accuracy. Based on structural vibration responses, the damage identification of a reticulated shell was studied. At first, the auto-regressive (AR) time series model was established based on the acceleration responses of the reticulated shell. According to the changes in the coefficients of the AR model between the damaged conditions and the undamaged condition, the damage of the reticulated shell can be detected. In addition, the damage sensitive factors were determined based on the coefficients of the AR model. With the damage sensitive factors as the inputs and the damage positions as the outputs, back-propagation neural networks (BPNNs) were then established and were trained using the Levenberg–Marquardt algorithm (L–M algorithm). The locations of the damages can be predicted by the back-propagation neural networks. At last, according to the experimental scheme of single-point excitation and multi-point responses, the impact experiments on a K6 shell model with a scale of 1/10 were conducted. The experimental results verified the efficiency of the proposed damage identification method based on the AR time series model and back-propagation neural networks. The proposed damage identification method can ensure the safety of the practical engineering to some extent.

This study examines the interconnectedness and spillover dynamics among green bonds (GBs), oil, and stock markets in the US and Europe under varying volatility regimes. Using a Markov-switching vector autoregressive (MS-VAR) model with daily data from January 2, 2018, to June 28, 2024, we find that S&P500 returns are largely driven by their own lagged returns, especially in high-volatility periods, with limited effects from GBs and oil. Similarly, the STOXX600 is mainly influenced by its lagged returns in low-volatility regimes. Spillovers between oil and the S&P500 intensify during high volatility. Portfolio analysis suggests allocating more to GBs and oil than stocks, with oil becoming the preferred hedge in volatile markets. GBs provide stability but are less effective for hedging under stress. Robustness checks using wavelet quantile correlation and cross-quantilogram confirm asymmetric, regime-dependent connectedness, emphasizing the importance of dynamic portfolio strategies for risk management.

The Nonlinear Dynamics of Corporate Bond Spreads: Regime-Dependent Effects of Their Determinants

Defence date: 18 December 2012