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.

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

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.

Application of Markov Regime Switching Autoregressive Model to Gold Prices in Pakistan

The goal of this study is to investigate the performance of the Markov regime switching autoregressive (MRS-AR) model to estimate and forecast the gold prices in Pakistan. Initial analysis of the data covering from January 1995 to January 2019 reveals the existence of nonstationarity, heteroscedasticity, and structural changes. The dynamics of the data are studied in two distinct regimes. The empirical analysis provides evidence that the regime shifts are mattered and MRS-AR model is found to be suitable even in the case of nonstationarity. Moreover, it is worthwhile to note that the Markov regime switching successfully captures the nonlinearities and heteroscedasticity underlying the selected data and provides efficient forecasts. Based on empirical evidence it is recommended that the applications of regime switching models should be promoted in other fields of life.

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.

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.

New trends in modeling and control of hybrid systems

New trends in modeling and control of hybrid systems

Prediction of Indonesian financial crisis using Markov regime switching autoregressive conditional heteroscedasticity models based on bank deposits and lending/deposit interest rate indicators

The financial crisis that occurred in middle of 1997 made Indonesia to become one of the countries which had the worst and the longest affected in term of its rate of recovery. This event made us aware of the importance of creating an early warning system for the financial crisis. The crisis occurred due to several macroeconomic indicators experiencing very high fluctuation and changes in the structure of the condition (regime). The combination of volatility and Markov regime switching models is a type of model that can explain the fluctuation and changes in such condition. The indicators of bank deposit and lending/deposit interest rate in January 1990 to June 2019 were used to construct the combined model. The results of this research showed that the MRS-ARCH(2,1) model for the bank deposit and lending/deposit interest rate indicators can explain the conditions of the financial crisis that occurred. The predicted value of the MRS-ARCH(2,1) model shows that from July 2019 to June 2020 there were no signs of a financial crisis in Indonesia.

On temporal aggregation of some nonlinear time-series models

Recently, economic globalisation and advances in computer technologies have accelerated the development of ‘big data’ analysis. Time-series data are routinely collected from the Internet and machine transactions at mixed frequencies. The problem of temporal aggregation arises when time-series data are observed at a lower frequency than the data generation frequency of the underlying basic model. The resulting aggregated series, which contains less information, may lead to an erroneous view of the true model and flawed decisions. Therefore, it is important to study the effects of temporal aggregation to avoid making possibly improper decisions based on distorted information from the aggregated data. Temporal aggregation of linear time-series processes has been widely studied. The effects of temporal aggregation on the first two moments of some nonlinear time-series models are assessed. More specifically, four types of nonlinear time-series models are studied: the Markov switching autoregressive (MSAR) model, the bilinear (BL) model, the mixture autoregressive (MAR) model, and the self-exciting threshold autoregressive (SETAR) model.

Modelling tourism resilience in small island states: a tale of two countries

The rising incidence and consequences of natural disasters, global economic crises, climate change, and socio-political upheavals have raised interest in resilience, particularly in small island economies. Their small size and high tourism-dependency make these small island states more vulnerable to such disruptions. Hence, understanding resilience or adaptive capacity to withstand shocks is fundamental to their sustainable development. The emerging literature uses the Adaptive Cycle Model to qualitatively analyse resilience through the evolution of tourism destinations. Nevertheless, the absence of quantitative studies using the Adaptive Cycle Model makes it a daunting task to adequately advise policymakers about the scope and scale of intervention necessary to facilitate the rebuilding of a stronger tourism industry. We, therefore, pioneer the use of Markov Switching Autoregressive Model to test the model’s applicability using four decades of data on tourist arrivals in two Caribbean destinations, Barbados and Grenada. The results reveal untapped opportunities for transformation and regeneration in both countries’ tourism industries, but highlight sharp contrast in their resilience capability. Grenada exhibits greater resilience as its adverse shocks, though deeper, are relatively transitory, while Barbados despite experiencing fewer external shocks faces prolonged repercussions from global recessions. For small islands, we conclude that the factors impacting lower resilience are the industry’s management deficiencies, inadequate cohesion among stakeholders, and lack of innovation. Overall, the findings present a modelling framework for tourism-dependent economies to determine how quickly they recover from major stress events, the associated strategies necessary to strengthen tourism resilience, and the potential to innovate in the tourism industry.

A Markov Regime Switching Approach of Estimating Volatility Using Nigerian Stock Market

Understanding and forecasting the behavior of volatility in stock market has received significant attention among researchers and analysts in the last few decades due to its crucial roles in financial markets. Portfolios managers, option traders, and market makers are all interested in the possibility of forecasting, with a reasonable level of accuracy. This study examined the volatility on the Nigeria stock market by comparing two Markov regime switching Autoregressive (MS-AR) Models estimated at different lagged values using the Nigeria stock exchange monthly All Share Index data from 1988 to 2018 in the Central Bank of Nigeria (CBN) Statistical Bulletin. It was found that factors like financial crisis, information flow, trading volume, economical aspects and investor’s behavior are the causes of volatility in the stock market. The results and forecasts obtained from the statistical analysis in this research showed that the stock market will experience a steady growth in 2020 and beyond. Also, the stock market is experiencing fluctuations in the price indices which show that over the years, investors have been exposed to some certain risks in the time past. We therefore recommended that researchers should focus more attention in developing robust statistical model that will reflect and continue to monitor future trends and realities.

European unemployment nonlinear dynamics over the business cycles: Markov switching approach

The dynamics of European unemployment showed considerable fluctuations and asymmetric behaviour during business cycles over the past decade. The dynamic pattern of unemployment rate demonstrated the significant differences for different countries during its growth and decline periods. To describe the differences in dynamic properties of unemployment rate in different countries and economic situation, we developed the Markov switching autoregressive models with time-varying probabilities of transition between behaviour regimes. The results revealed that the unemployment rate in EU countries during 2000-2016 behaved asymmetrically over the business cycle. Therefore, we got different processes for describing unemployment dynamics in each phase of the economy.

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.

European unemployment nonlinear dynamics over the business cycles: Markov switching approach

The dynamics of European unemployment showed considerable fluctuations and asymmetric behaviour during business cycles over the past decade. The dynamic pattern of unemployment rate demonstrated the significant differences for different countries during its growth and decline periods. To describe the differences in dynamic properties of unemployment rate in different countries and economic situation, we developed the Markov switching autoregressive models with time-varying probabilities of transition between behaviour regimes. The results revealed that the unemployment rate in EU countries during 2000-2016 behaved asymmetrically over the business cycle. Therefore, we got different processes for describing unemployment dynamics in each phase of the economy.

Attention Matters: An Exploration of Relationship Between Google Search Behaviors and Crude Oil Prices

Extant studies have suggested that Google search volume data can serve as a new and direct measure of investor attention in various research fields such as economy, financial and energy markets. However, it is not clear that whether investor attention influences prices in the same direction in different market states (prices increase or decrease). In this paper, the authors propose a measure of speculative attention, demonstrate its advantages by comparing it with several existing ones, and then adopt a Markov switching autoregressive model and an EGARCH model to examine its influences on crude oil prices in two market states. It is argued that the responses of crude oil prices to investor attention are asymmetrical in the two states of crude oil prices. The empirical study shows that one increase in searches causes a significant positive increase in crude oil prices during oil price surges, and a more significant reduction of prices during oil price collapses. The authors also conduct robustness checks by limiting the sample periods and using other measures, and the results support the asymmetric effect of web search behaviors on crude oil prices.

Pemodelan Deteksi Krisis Keuangan di Indonesia Berdasarkan Indikator M2/Cadangan Devisa

The banking crisis reflects the liquidity crisis and bankruptcy of banks in the financial system. The financial crisis that occurred in mid-1997 resulted in a financial crisis that had a severe impact on the Indonesian economy. This made it aware of the importance of building a financial crisis early detection system to prepare for a crisis. The crisis occurs due to several macroeconomic indicators undergoing structural changes (regimes) and contain very high fluctuations. Combined volatility models and Markov regime switching are very suitable for explaining crises. The M2/international reserves indicator from 1990 to 2018 was used to build a crisis model. The results showed that the Markov regime switching autoregressive conditional heteroscedasticity model MRS-ARCH(2,1) could explain the crisis that occurred in mid-1997. Based on this model, in the future the crisis might occur if the M2/international reserves indicator decreased minimum of 13%

A Markov-Switching Model Approach to Heart Sound Segmentation and Classification

We consider challenges in accurate segmentation of heart sound signals recorded under noisy clinical environments for subsequent classification of pathological events. Existing state-of-the-art solutions to heart sound segmentation use probabilistic models such as hidden Markov models (HMMs), which, however, are limited by its observation independence assumption and rely on pre-extraction of noise-robust features. We propose a Markov-switching autoregressive (MSAR) process to model the raw heart sound signals directly, which allows efficient segmentation of the cyclical heart sound states according to the distinct dependence structure in each state. To enhance robustness, we extend the MSAR model to a switching linear dynamic system (SLDS) that jointly model both the switching AR dynamics of underlying heart sound signals and the noise effects. We introduce a novel algorithm via fusion of switching Kalman filter and the duration-dependent Viterbi algorithm, which incorporates the duration of heart sound states to improve state decoding. Evaluated on Physionet/CinC Challenge 2016 dataset, the proposed MSAR-SLDS approach significantly outperforms the hidden semi-Markov model (HSMM) in heart sound segmentation based on raw signals and comparable to a feature-based HSMM. The segmented labels were then used to train Gaussian-mixture HMM classifier for identification of abnormal beats, achieving high average precision of 86.1% on the same dataset including very noisy recordings. The proposed approach shows noticeable performance in heart sound segmentation and classification on a large noisy dataset. It is potentially useful in developing automated heart monitoring systems for pre-screening of heart pathologies.

Oil prices, Gold Prices and Exchange Rate in Algeria: A Non-Linear Analysis Prix du pétrole, prix de l'or et taux de change en Algérie: une analyse non linéaire

This analytical review explores the nonlinear links between crude oil prices,gold prices and Algeria Dinar real effective exchange rate for the period January 1990 toDecember 2016, we use in this paper a Markov Switching Auto-Regressive model(MSVAR) developed by Hamilton (1989), the empirical results show that there are twosignificant regimes, and the transitions between the two regimes followed the discounts ofthe Algerian Dinar value by the Central Bank (1991 and 1994), the results show also thatoil prices affect the exchange rate by the limited manner especially in the first regime.

Uncertainty and energy-sector equity returns in Iran: a Bayesian and quasi-Monte Carlo time-varying analysis

This study investigates whether the implied crude oil volatility and the historical OPEC price volatility can impact the return to and volatility of the energy-sector equity indices in Iran. The analysis specifically considers the refining, drilling, and petrochemical equity sectors of the Tehran Stock Exchange. The parameter estimation uses the quasi-Monte Carlo and Bayesian optimization methods in the framework of a generalized autoregressive conditional heteroskedasticity model, and a complementary Bayesian network analysis is also conducted. The analysis takes into account geopolitical risk and economic policy uncertainty data as other proxies for uncertainty. This study also aims to detect different price regimes for each equity index in a novel way using homogeneous/non-homogeneous Markov switching autoregressive models. Although these methods provide improvements by restricting the analysis to a specific price-regime period, they produce conflicting results, rendering it impossible to draw general conclusions regarding the contagion effect on returns or the volatility transmission between markets. Nevertheless, the results indicate that the OPEC (historical) price volatility has a stronger effect on the energy sectors than the implied volatility has. These types of oil price shocks are found to have no effect on the drilling sector price pattern, whereas the refining and petrochemical equity sectors do seem to undergo changes in their price patterns nearly concurrently with future demand shocks and oil supply shocks, respectively, gaining dominance in the oil market.