Markov-switching Autoregressive Model Research Articles

Time-Varying Autoregressive Models for Economic Forecasting

This research introduces a time-varying autoregressive (TVAR) model, developed to improve the precision of forecasting in economic time series data. The model advances the conventional TVAR framework by incorporating potential mean adjustments and utilizing the Kalman Filter within a Maximum Likelihood Estimation (MLE) framework, with further optimization through the NelderMead method. Applied to the real gross national product (GNP) data of the United States (U.S.), the model effectively captures dynamic patterns and structural changes that traditional models often overlook. The model’s performance is rigorously compared with the widely used Markov switching autoregressive (MSAR) model, demonstrating superior results in both training and testing forecasts. The TVAR model consistently achieves lower error metrics, underscoring its robustness and flexibility in capturing dynamic economic trends and providing reliable forecasts. This research emphasizes the TVAR models potential for broader applications in economic policy analysis, strategic planning, and decision-making processes, particularly in understanding and predicting economic growth. The models adaptability and precision make it a valuable tool for economists and policymakers aiming to navigate complex economic fluctuations with greater confidence as well as accuracy.

Identifying crucial financial markets in the flows of cross-border capital – evidence from China's financial risk network

With the increasing openness of China's financial markets, it is important to address cross-border capital risks. This paper first calculates the stress indicators of financial markets by 24 variables, and then utilizes the Diebold-Yilmaz connectedness approach to examine the spillover effects among the volatility of cross-border capital and the stress indicators of various financial markets. We show both the real estate and stock market are crucial for cross-border capital flow. Using the rolling window method, we find significant time-varying spillovers between cross-border capital and financial markets, which peak during the periods with significant events such as the global financial crisis, the COVID-19 epidemic, and the shift in currency regime. This paper further applies the Markov-switching autoregressive model to identify three different states for the synthetic financial stress. After re-analyzing the subsample data, we observe that stock and real estate markets play significant roles in the low-stress state, foreign exchange and real estate markets in the medium-stress state, and stock and money markets in the high-stress state.

Conditional seasonal markov-switching autoregressive model to simulate extreme events: Application to river flow

Extreme events have the potential to significantly impact transportation infrastructure performance. For example, in the case of bridges, climate change impacts the river discharge, hence scouring patterns, which in turn, affects the bridge foundation stability. Therefore, extreme events (river flow) forecasting is mandatory in bridge reliability analysis. This paper approaches this river flow forecasting problem by developing a Markov-Switching Autoregressive model coupled with a conditional hidden seasonal Markov component. In addition, the proposed model is also combined with the deep machine learning neural networks method to forecast river flow from a dataset or from simulations. The proposed method is illustrated by using realistic data: historic river flow values of the Thames River. The results indicate that the proposed model well represented the extreme events within the dataset. In terms of river flow forecasting, the results indicate that the forecasts improve when the training period changes from 20 years to 40 years.

A Markov-Switching model of public debt in South Africa

This research aimed to explore the sustainability of public debt with changes in the South African regime from 1960 to 2020. Annual data was obtained from the South Africa Reserve Bank, and the Markov-switching autoregressive (MS-AR) model was employed to describe the public debt process in South Africa. Compared to traditional endogenous modelling, the process explicitly allows for the possibility of regime changes. Regime 1 defines the stages of high public debt, and regime 2 describes periods of a downward trend in public debt. The results reveal that in regime 1, there is a 98% likelihood of remaining in high public debt and a lower probability of 1.76% switching to a lower public debt regime. Also, when the system is in a lower debt regime, there is a 98.2% likelihood of remaining in a lower public debt state and a lower probability of 1.74% switching to a higher public debt state. The expected average duration of a period of higher public debt is 56 years, while the average duration of a lower public debt regime is 57 years. This implies that it is only in an extreme event that public debt can switch from a high-debt regime to a low-debt regime and vice versa. Hence, it is suggested that the government implement policies knowing that public debt will not decline suddenly.

Bayesian analysis of high-frequency water temperature time series through Markov switching autoregressive models

Bayesian analysis of high-frequency water temperature time series through Markov switching autoregressive models

Conditional Seasonal Markov-Switching Autoregressive Model to Simulate Extreme Events: Application to River Flow

Conditional Seasonal Markov-Switching Autoregressive Model to Simulate Extreme Events: Application to River Flow

Modeling the hourly consumption of electricity during period of power crisis

<abstract><p>In this paper, we capture the dynamic behavior of hourly consumption of electricity during the period of power crisis ("dumsor'' period) in Ghana using two-state Markov switching autoregressive (MS-AR) and autoregressive (AR) models. Hourly data between the periods of January 1, 2014 and December 31, 2014 was obtained from the Ghana Grid company and used for the study. Using different information criteria, the MS(2)-AR(4) is selected as the optimal model to describe the dynamic behavior of electricity consumption during periods of power crisis in Ghana. The parameters of the MS(2)-AR(4) model are then estimated using the expectation-maximization algorithm. From the results, the likelihood of staying under a low electricity consumption regime is estimated to be 87%. The expected duration for a low electricity consumption regime is 7.8 hours, and the high electricity consumption regime is expected to last 2.3 hours before switching to the low demand regime. The proposed model is robust as compared to the autoregressive model because it effectively captures the dynamics of electricity demand over time through the peaks and significant fluctuations in consumption patterns. Similarly, the model can identify distinct regime changes linked to electricity consumption during periods of power crises.</p></abstract>

Partially Hidden Markov Chain Multivariate Linear Autoregressive model: inference and forecasting—application to machine health prognostics

Time series subject to regime shifts have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, models such as the popular Hidden Markov Chain (HMC) describe time series whose state process is unknown at all time-steps. Sometimes, time series are annotated. Thus, another category of models handles the case with regimes observed at all time-steps. We present a novel model which addresses the intermediate case: (i) state processes associated to such time series are modelled by Partially Hidden Markov Chains (PHMCs); (ii) a multivariate linear autoregressive (MLAR) model drives the dynamics of the time series, within each regime. We describe a variant of the expectation maximization (EM) algorithm devoted to PHMC-MLAR model learning. We propose a hidden state inference procedure and a forecasting function adapted to the semi-supervised framework. We first assess inference and prediction performances, and analyze EM convergence times for PHMC-MLAR, using simulated data. We show the benefits of using partially observed states as well as a fully labelled scheme with unreliable labels, to decrease EM convergence times. We highlight the robustness of PHMC-MLAR to labelling errors in inference and prediction tasks. Finally, using turbofan engine data from a NASA repository, we show that PHMC-MLAR outperforms or largely outperforms other models: PHMC and MSAR (Markov Switching AutoRegressive model) for the feature prediction task, PHMC and five out of six recent state-of-the-art methods for the prediction of machine useful remaining life.

The transition of the global financial markets' connectedness during the COVID-19 pandemic

This study contributes to the literature on financial research under the presence of the COVID-19 pandemic. Fresh evidence emerges from using two novel approaches, namely network analysis and wavelet coherence, to examine the connectedness and comovement of financial markets consisting of stock, commodity, gold, real estate investment trust, US exchange, oil, and Cryptocurrency before and during the COVID-19 onset. Moreover, unlike the previous studies, we seek to fill a gap in the literature regarding the ex-post detection of COVID-19 crises and propose the Markov-switching autoregressive model to detect structural breaks in financial market returns. The first result shows that most financial markets entered the downtrend after January 30, 2020, coinciding with the date the World Health Organization (WHO) declared the COVID-19 pandemic as a Public Health Emergency of International Concern. Thus, it is reasonable to use this date as the break date due to COVID-19. The empirical result from network analysis indicates a similar connectedness, or the network structure, in other words, among global financial markets in both the pre-and during COVID-19 pandemic periods. Moreover, we find evidence of market differences as the MSCI stock market plays a central role while Cryptocurrency presents a weak role in the global financial markets. The findings from the wavelet coherence analysis are quite mixed and illustrate that the comovement of the financial markets varies over time across different frequencies. We also find the main and most significant period of coherence and comovement among financial markets to be between December 2019 and August 2020 at the low-frequency scale (>32 days) (middle and long terms). Among all market pairs, the oil and commodity market pair has the strongest comovement in both pre-and during the COVID-19 pandemic phases at all investment horizons.

Co-movement and causal relationships between conventional and Islamic stock market returns under regime-switching framework

PurposeThis paper aims at examining the co-movement dependent regime and causality relationships between conventional and Islamic returns for emerging, frontier and developed markets from November 2008 to August 2020.Design/methodology/approachFirst, the authors used the Markov-switching autoregression (MS–AR) model to capture the regime-switching behavior in the stock market returns. Second, the authors applied the Markov-switching regression and vector autoregression (MS-VAR) models in order to study, respectively, the co-movement and causality relationship between returns of conventional and Islamic indexes across market states.FindingsResults show the presence of two different regimes for the three studied markets, namely, stability and crisis periods. Also, the authors found evidence of a co-movement relationship between the conventional and Islamic indexes for the three studied markets whatever the regime. For the Granger causality, it is proved only for emerging and developed markets and only during the stability regime. Finally, the authors conclude that Islamic indexes can act as diversifiers, or safe-haven assets are not strongly supported.Originality/valueThis paper is the first study that examines the co-movement and the causal relationship between conventional and Islamic indexes not only across different financial markets' regimes but also during the COVID-19 period. The findings may help investors in making educated decisions about whether or not to add Islamic indexes to their portfolios especially during the recent outbreak.

Several explorations on how to construct an early warning system for local government debt risk in China.

This paper aims to explore several ways to construct a scientific and comprehensive early warning system (EWS) for local government debt risk in China. In order to achieve this goal, this paper studies the local government debt risk from multiple perspectives, i.e., individual risk, contagion risk, static risk and dynamic risk. Firstly, taking China's 30 provinces over the period of 2010~ 2018 as a sample, this paper establishes early warning indicators for individual risk of local government debt, and uses the network model to establish early warning indicators for contagion risk of local government debt. Then, this paper applies the criteria importance though intercrieria correlation (CRITIC) method and coefficient of variation method to obtain the proxy variable Ⅰ, which combines the above two risks. Secondly, based on the proxy variable Ⅰ, both the Markov-switching autoregressive (MS-AR) model and coefficient of variation method are used to obtain the proxy variable Ⅱ, which comprehensively considers the individual risk, contagion risk, static risk and dynamic risk of local government debt. Finally, machine learning algorithms are adopted to generalize the EWS designed in this paper. The results show that: (1) From different perspectives of local government debt risk, the list of provinces that require early warning is different; (2) The support vector machines can well generalize our EWS.

An evolutionary Monte Carlo method for the analysis of turbidity high‐frequency time series through Markov switching autoregressive models

AbstractA turbidity time series, recorded every 15 min in a first‐order Scottish stream for more than a year, along with two covariates (stage height and rainfall), is considered. Turbidity time series have complex dynamics because they are nonlinear, nonnormal, nonstationary, with a long memory, and present missing values. Given these issues the turbidity process is analyzed by Markov switching autoregressive models under the Bayesian paradigm. Since the multimodality of the posterior density novel evolutionary Monte Carlo (EMC) algorithms incorporating a few original features are developed to better traverse the posterior surface and escape from local basins of attraction. This because a population of chains are processed in parallel exchanging information one another and with different temperatures attached to each chain. These advanced EMC algorithms allow performing both Bayesian inference and model choice. Hence, it is possible to efficiently fit the actual data, reconstruct the sequence of hidden states, restore the missing values, and classify the observations into a few regimes, providing new insight on turbidity dynamics. A comparison with different nonlinear time series models is also proposed. Finally, a simulation study on the selection of the tuning factors of the EMC algorithm is presented.

Regime shifts in the COVID-19 case fatality rate dynamics: A Markov-switching autoregressive model analysis

The 2019 novel coronavirus disease (COVID-19) has spread rapidly to many countries around the world from Wuhan, the capital of China’s Hubei province since December 2019. It has now a huge effect on the global economy. As of 13 September 2020, more than 28, 802, 775, and 920, 931 people are infected and dead, respectively. The mortality of COVID-19 infections is increasing as the number of infections increase. Many countries published control measures to contain its spread. Even though there are many drugs and vaccines under trial by pharmaceutical companies and research groups, no specific vaccine or drug has yet been found. Therefore, it is necessary to explain the behaviour of the case fatality rate (CFR) of COVID-19 using the most updated COVID-19 epidemiological data before 13 September 2020. The dynamics in the CFR were analyzed using the Markov-switching autoregressive (MSAR) models. Results showed that the two-regime and three-regime MSAR approach better captured the non-linear dynamics in the CFR time series data for each of the top heavily infected countries including the world. The results also showed that rises in CFRs are more volatile than drops. We believe that this information can be useful for the government to establish appropriate policies in a timely manner.

Who raised from the abyss? A comparison between cryptocurrency and stock market dynamics during the COVID-19 pandemic

This research examines the behaviour of cryptocurrencies and stock markets during the COVID-19 pandemic through the wavelet coherence approach and Markov switching autoregressive model. Our results show a financial contagion in March, since both cryptocurrency and stock prices fell steeply. Despite this turn-down, cryptocurrencies promptly rebounded, while stock markets are trapped in the bear phase. In other words, we observe that the price dynamics during the pandemic depends on the type of the market. These findings are relevant for investors since some hedging properties can be found in the cryptocurrency response to such a drastic event.

Unilateral 2D Markov-switching autoregressive model

For nonlinear two-dimensional spatial data, a 2D Markov-switching unilateral autoregressive model is defined. Strict stationarity is studied and parameter estimation via the variational expectation maximisation (VEM) algorithm is performed. First, a 2D Markov random field (MRF) is constructed for which an imposed causality allows to establish an analogy between this 2D MRF and the Markov chain representation. Based on the proposed 2D MRF, the 2D MS-AR model is defined under some necessary assumptions and useful notations. Finally, parameter estimation of the model is discussed paving the way to broad exploitation perspectives of the proposed 2D MS-AR processes to efficiently model several phenomena exhibiting a structural break in spatial data.

Can We Reckon Bitcoin as a Hedge, a Safe Haven or a Diversifier for US Dollars?

This article aims to analyse the hedging, diversifier and safe-haven properties of Bitcoin for the US Dollar Index (USDI). We explore the long-term relationship between USDI and Bitcoin by estimating a Markov-switching autoregressive (MS-AR) model with two regimes. Thus, the data used cover the period from 18 January 2010 to 30 June 2017 for both USDI and Bitcoin. The empirical findings based on the analysis of the MS-AR model report that investing in Bitcoin involves more benefits than USDI even if the economy is in a recession. However, by examining Bitcoin and USDI volatility, the research findings underline positive dependency between the two. Such results denote that Bitcoin does not act as a hedge, and not even as a safe haven, against USDI. We found that Bitcoin is merely a diversifier for USDI. Accordingly, the outcomes will help investors and portfolio risk managers to make more up-to-date investment analyses and decisions.

Inflation Expectations Modeling: The Application of Markov Switching Autoregression

The shift of the monetary policy framework in Ukraine has led to the transformation of the power of the key transmission channels. Inflation targeting (IT) assumes the interest rates channel as the main one; besides that, since the exchange rate is floating, the influence from the key policy rate change on it is stronger and more effective. Implementation of the IT at the end of 2016 significantly affected the prices; in particular, the inflation has slowed down from almost 60 % in the corresponding month of the previous year to 2.3 % in 2020. Specifically, the interaction between the key policy rate, which is the main monetary policy instrument under the IT, consumer prices, and economic growth has changed. One of the important channels is the inflation expectations channel that became influential after IT has started. Consequently, the article is aimed to investigate how inflation expectations are dependent on the inflation dynamics, the key policy rate changes, and the index of the real wage fluctuations applying Markov switching autoregression model with two regimes, which is widely used to estimate the effects of economic crisis, break of the trend, and instability. The developed model consists of two equations, one of which defines a regime with the high volatility, and the other with the low. The obtained results show the dominance of the high volatility regime during almost all the research period because of essential inflation uncertainty and the overall unstable situation in the country caused by the crisis. Additionally, probability to stay in the first regime is much higher than in the second and is equal to 91 %. Outcomes from the modelling allow to judge about the future inflation and inflation expectations dynamics based on discovered new features. The further steps in the evaluation of effects of monetary policy regimes shift are expansion of the model to three- or four-regime switch (high, low, moderate volatility, etc.), the use of additional independent variables, experiments with the key policy rate, and inflation as dependent variables. JEL classification: E42, E58, C34 Manuscript received 10.04.2020

Assessing marine operations with a Markov-switching autoregressive metocean model

This article presents a metocean modelling methodology using a Markov-switching autoregressive model to produce stochastic wind speed and wave height time series, for inclusion in marine risk planning software tools. By generating a large number of stochastic weather series that resemble the variability in key metocean parameters, probabilistic outcomes can be obtained to predict the occurrence of weather windows, delays and subsequent operational durations for specific tasks or offshore construction phases. To cope with the variation in the offshore weather conditions at each project, it is vital that a stochastic weather model is adaptable to seasonal and inter-monthly fluctuations at each site, generating realistic time series to support weather risk assessments. A model selection process is presented for both weather parameters across three locations, and a personnel transfer task is used to contextualise a realistic weather window analysis. Summarising plots demonstrate the validity of the presented methodology and that a small extension improves the adaptability of the approach for sites with strong correlations between wind speed and wave height. It is concluded that the overall methodology can produce suitable wind speed and wave time series for the assessment of marine operations, yet it is recommended that the methodology is applied to other sites and operations, to determine the method’s adaptability to a wide range of offshore locations.

Consistent estimation of the number of regimes in Markov-switching autoregressive models

Markov-switching models have become a popular tool in areas ranging from finance to electrical engineering. Determining the number of hidden regimes in such models is a key problem in applications. This paper proposes a strongly consistent estimator of the number of regimes for Markov-switching autoregressive models. By using subadditive ergodic theorem, law of iterated logarithm for martingales, together with results from information theory, we derive sufficient conditions to avoid underestimation as well as overestimation. In particular, we propose a modified information criterion, regime-switching information criterion (RSIC) which generates a simple and consistent model selection procedure. Finally, we conduct a Monte Carlo study to evaluate the efficacy of our procedure in finite sample and also compare the performance of RSIC with popular information criteria including AIC, BIC and HQC.

Stochastic weather generator for the design and reliability evaluation of desalination systems with Renewable Energy Sources

Abstract The operation of Renewable Energy Sources (RES) systems is highly affected by the continuously changing meteorological conditions and the design of a RES system has to be robust to the unknown weather conditions that it will encounter during its lifetime. In this paper, the use of Stochastic Weather Generators (SWGENs) is introduced for the optimal design and reliability evaluation of hybrid Photovoltaic/Wind-Generator systems providing energy to desalination plants. A SWGEN is proposed, which is based on parametric Markov-Switching Auto-Regressive (MSAR) models and is capable to simulate realistic hourly multivariate time series of solar irradiance, temperature and wind speed of the target installation site. Numerical results are presented, demonstrating that: (i) SWGENs enable to evaluate the reliability of RES-based desalination plants during their operation over a 20 years lifetime period and (ii) using an appropriate time series simulated with a SWGEN as input to the design optimization process results in a RES-based desalination plant configuration with higher reliability compared to the configurations derived when the other types of meteorological datasets are used as input to the design optimization process.