Time-varying Vector Autoregressive Model Research Articles

The time-varying Multivariate Autoregressive Index model

Many economic variables are characterized by changes in their conditional mean and volatility, and time-varying Vector Autoregressive Models are often used to handle such complexity. Unfortunately, as the number of series grows, they present increasing estimation and interpretation issues. This paper tries to address this problem by proposing a Multivariate Autoregressive Index model that features time-varying mean and volatility. Technically, we develop a new estimation methodology that mixes switching algorithms with the forgetting factors strategy of Koop and Korobilis (2012). This substantially reduces the computational burden and allows one to select or weigh the number of common components, and other data features, in real-time without additional computational costs. Using US macroeconomic data, we provide a forecast exercise that shows the feasibility and usefulness of this model.

ESG practices mitigating geopolitical risks: Implications for sustainable environmental management

As climate change and geopolitical conflicts intensify, understanding how geopolitical risks affect companies prioritizing Environmental, Social, and Governance (ESG) practices is crucial. This study investigates the dynamic relationship between global geopolitical risks and the performance of Environmental, Social, and Governance (ESG) and non-ESG companies, particularly their influence on green markets. Utilizing a robust methodological framework, including the dynamic time-varying parameters vector autoregression (TVP-VAR) model, and causal impact modeling, we analyze daily financial data from 2021 to 2024. The results reveal a substantial negative impact of geopolitical risks on non-ESG companies, contrasting with the resilience of ESG-committed counterparts. This suggests that ESG-committed companies demonstrate better resilience against geopolitical risks, emphasizing the protective role of ESG practices amid uncertainties. Additionally, the inclusion of ESG companies in green markets diminishes the severity of the negative impact of geopolitical risks, underlining the transformative role of ESG commitment in shaping investor behavior towards sustainable investments. Our findings offer insights for policymakers and investors navigating geopolitical risks and ESG performance, with a focus on environmental management, and provide guidance for effective risk mitigation and investment policies to enhance environmental sustainability.

What time-varying network models based on functional analysis tell us about the course of a patient's problem

Background: Relations among psychological variables are assumed to be complex and to vary over time. Personalized networks can model multivariate complex interactions. The development of time-varying networks allows to model the variation of parameters over time. Objectives: We aimed to determine the value of time-varying networks for clinical practice. Methods: We applied time-varying mixed graphical models (TV-MGM) and time-varying vector autoregressive models (TV-VAR) to intensive longitudinal data of nine participants with depressive symptoms (n = 6) or anxiety (n = 3). Results: Most of the participants showed temporal changes in network topology within the assessment period of 30 days. Time-varying networks of participants with small, medium, and large time variability in edge parameters clearly show the different temporal evolvements of dynamic interactions between variables. The case example indicates clinical utility but also limitations to the application of time-varying networks in clinical practice. Conclusion: Time-varying network models provide a data-driven and exploratory approach that could complement current diagnostic standards by reflecting interacting, often mutually reinforcing processes of mental health problems and by accounting for variation over time. They can be used to generate hypotheses for further confirmatory and clinical testing.

Insights into the dynamics of market efficiency spillover of financial assets in different equity markets

This paper provides multidisciplinary insights into the dynamics of market efficiency spillover of financial assets, considering Bitcoin, DXY (U.S. Dollar Index), S&P 500, and crude oil in different equity markets. Given this, we employ the multifractal detrended fluctuation analysis (MF-DFA) and the time-varying parameter vector autoregressive models (TVP-VAR) to illuminate these complex interplays between these assets and other equity markets. Our findings display that Bitcoin acts as a net transmitter, whereas DXY functions as a net receiver. Additionally, Bitcoin, DXY, and S&P 500 clearly exhibit dynamics in information transmission, whereas crude oil does not. It means that the low connectedness of the oil market in terms of market efficiency spillover, suggesting that the oil market may play an effective role as a hedging instrument for other assets.

Variation in emotion dynamics over time is associated with future relationship outcomes.

Romantic relationships are defined by emotion dynamics, or how the emotions of one partner at a single timepoint can affect their own emotions and the emotions of their partner at the next timepoint. Previous research has shown that the level of these emotion dynamics plays a role in determining the state and quality of the relationship. However, this research has not examined whether the estimated emotion dynamics change over time, and how the change in these dynamics might relate to relationship outcomes, despite changes in dynamics being likely to occur. We examined whether the magnitude of variation in emotion dynamics over time was associated with relationship outcomes in a sample of 148 couples. Time-varying vector autoregressive models were used to estimate the emotion dynamics for each couple, and the average and standard deviation of the dynamics over time was related to relationship quality and relationship dissolution 1-2 years later. Our results demonstrate that certain autoregressive and cross-lagged parameters do show significant variation over time, and that this variation is associated with relationship outcomes. Overall, this study demonstrates the importance of accounting for change in emotion dynamics over time, and the relevance of this change to the prediction of future outcomes.

Dynamic connectedness of inflation around the world: A time-varying approach from G7 and E7 countries

Using advanced econometric techniques of the Time-Varying Parameters Vector Autoregression model with stochastic volatility (TVP-SV-VAR) and the Quantile Vector Autoregression (QVAR) model, this research investigates the dynamics of the Consumer Price Index (CPI) across G7 and E7 countries from January 1993 to January 2023, aiming to comprehensively analyze the international transmission of inflation. The study yields several key findings. Firstly, we ascertain that approximately 64% of inflation volatility can be attributed to international transmission. Secondly, our analysis consistently identifies Turkey and Russia as net exporters of inflation over the study period, while G7 countries and Mexico emerge as persistent net importers. Thirdly, we note a gradual increase in China's inflation connectivity with developing countries following the Asian financial crisis, coupled with a diminishing impact of Chinese inflation transmission to developed nations. Fourthly, we observe a heightened complexity in the inflation transmission network during periods marked by high Total Connectivity Index (TCI) values, compared to those with low TCI values. Lastly, our study underscores that the transmission of international inflation intensifies during periods characterized by extremely high or low international inflation rates.

Business cycles in a cocoa and gold economy: Commodity price shocks do not always matter

This paper seeks to characterize the response of Ghana’s business cycle to cocoa and gold commodity price shocks using a time-varying parameter structural vector autoregressive (TVP-SVAR) model. We then provide some plausible explanations underlying the estimated effect of these price shocks on Ghana’s business cycle. In the yearly model, a significant positive effect of a cocoa price shock on Ghana’s business cycle is observed using data from 1960 to 2018. However, no significant effect of a gold price shock on Ghana’s business cycle was found. In the quarterly model, we found no significant effect of both cocoa and gold price shocks on Ghana’s quarterly business cycle under Ghana’s inflation-targeting monetary policy regime. The study concludes that the expected strong influence of cocoa and gold commodity price shocks on Ghana’s yearly and quarterly business cycles is not consistently supported by empirical data for all periods and time frequencies. We then suggest plausible explanations for the unexpectedly weak estimated effects of the two commodity price shocks on Ghana’s business cycle, particularly after the mid-1980s, including the role of a foreign-dominated gold sector, the influence of cocoa forward contracts, and the impact of cocoa smuggling. These findings call into question the incorporation of cocoa and gold commodity sectors into a business cycle model for Ghana’s economy for all business cycle episodes and time frequencies, contrary to conventional wisdom. Gold and cocoa windfalls/shortfalls in the short run are almost non-existent, which has important implications for Ghanaian policymakers and model builders.

Economic Growth and Inflation Tradeoffs within Global Stagflation: Evidence from the Vietnam Economy

The paper analyzes the interaction of economic growth and inflation rate on accounting for both sources of capital investment and global shocks. The analysis method is a time-varying coefficient Bayesian vector autoregression (TVC-BSVAR) model applied in a quarterly data sample of the Vietnam economy over Q2/2001–Q4/2022. The global factors, including the world economic growth and the inflation rate, are the most important drivers of domestic growth and inflation rate. A greater world growth rate raises the domestic growth rate while a higher world inflation rate increases the domestic inflation rate. If the world economy falls into stagflation with declining growth and a rising inflation rate, Vietnam’s economic growth reduces while the inflation surges. The monetary and fiscal policy can be employed to recover domestic economic growth but with an associated surge in the domestic inflation rate.

Depressive symptoms as a heterogeneous and constantly evolving dynamical system: Idiographic depressive symptom networks of rapid symptom changes among persons with major depressive disorder.

Major depressive disorder (MDD) is conceptualized by individual symptoms occurring most of the day for at least two weeks. Despite this operationalization, MDD is highly variable with persons showing greater variation within and across days. Moreover, MDD is highly heterogeneous, varying considerably across people in both function and form. Recent efforts have examined MDD heterogeneity byinvestigating how symptoms influence one another over time across individuals in a system; however, these efforts have assumed that symptom dynamics are static and do not dynamically change over time. Nevertheless, it is possible that individual MDD system dynamics change continuously across time. Participants (N = 105) completed ratings of MDD symptoms three times a day for 90 days, and we conducted time varying vector autoregressive models to investigate the idiographic symptom networks. We then illustrated this finding with a case series of five persons with MDD. Supporting prior research, results indicate there is high heterogeneity across persons as individual network composition is unique from person to person. In addition, for most persons, individual symptom networks change dramatically across the 90 days, as evidenced by 86% of individuals experiencing at least one change in their most influential symptom and the median number of shifts being 3 over the 90 days. Additionally, most individuals had at least one symptom that acted as both the most and least influential symptom at any given point over the 90-day period. Our findings offer further insight into short-term symptom dynamics, suggesting that MDD is heterogeneous both across and within persons over time. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

The ability of energy commodities to hedge the dynamic risk of epidemic black swans

The outbreak of COVID-19 increased global financial risks and economic shocks. Although epidemic risk is on the decline, the likeliness of a similar black swan event occurring in the future cannot be ruled out. In this study, we constructed epidemic search indices using the Google Search Volume Index (SVI) to examine whether investor sentiment regarding the COVID-19 pandemic affected stocks, gold, silver, copper, crude oil, and natural gas. The results reveal that, over the entire epidemic period, energy assets (crude oil and natural gas) were the most “resistant” to epidemic panic, making them suitable for hedging the risk associated with epidemic panic risk. We employed a time-varying parameter structural vector autoregression model with stochastic volatility (TVP-SVAR-SV) to analyze the time-varying contagion effects of epidemic search indices on various asset prices at different points in time. The findings indicate that in the early stages of the COVID-19 pandemic when epidemic panic risk was highest, natural gas prices exhibited the most risk-averse characteristics. Only during the middle to later stages of the epidemic did natural gas prices begin to be positively affected by epidemic panic sentiment. However, during this period, the epidemic search indices show a stable declining trend, indicating a reduction in risk. We observe that natural gas prices only reflected panic sentiment during periods of stability. The results of this study suggest that energy commodities, especially natural gas, are suitable for hedging against unforeseen high epidemic risks. When epidemic risk decreases, profits can be realized and reinvested in assets with a higher contagion effect due to epidemic risks, further benefiting from the rebound in the prices of these assets. In addition to explaining why energy commodities are particularly suitable for mitigating epidemic-related black swan events, we provide a detailed investment strategy for hedging future epidemic risk and further elaborate on how investors should dynamically adjust their portfolios according to the severity of the epidemic and whether it is under control.

Dynamic asymmetric spillovers and connectedness between Chinese sectoral commodities and industry stock markets.

This study investigates the dynamic and asymmetric propagation of return spillovers between sectoral commodities and industry stock markets in China. Using a daily dataset from February 2007 to July 2022, we employ a time-varying vector autoregressive (TVP-VAR) model to examine the asymmetric return spillovers and dynamic connectedness across sectors. The results reveal significant time-varying spillovers among these sectors, with the industry stocks acting as the primary transmitter of information to the commodity market. Materials, energy, and industrials stock sectors contribute significantly to these spillovers due to their close ties to commodity production and processing. The study also identifies significant asymmetric spillovers with bad returns dominating, influenced by major economic and political events such as the 2008 global financial crisis, the 2015 Chinese stock market crisis, the COVID-19 pandemic, and the Russia-Ukraine war. Furthermore, our study highlights the unique dynamics within the Chinese market, where net information spillovers from the stock market to commodities drive the financialization process, which differs from the bidirectional commodity financialization observed in other markets. Finally, portfolio analysis reveals that the minimum connectedness portfolio outperforms other approaches and effectively reflects asymmetries. Understanding these dynamics and sectoral heterogeneities has important implications for risk management, policy development, and trading practices.

Impact of COVID-19 Pandemic and Russo-Ukrainian War on Tunisian Stock Exchange Performance and Volatility

The purpose of our study was to investigate the impact of COVID-19 pandemic and the Russo-Ukraine (RU) war on the return volatility and value of the Tunisian Stock Exchange proxied by TUNINDEX. We applied GARCH (1,1) to assess the impact on the index return volatility, using daily observations from January 2019 to December 2022, and a multiple linear regression to determine the effect on the index value, based on monthly observations for January 2018 to December 2022. GARCH output revealed that both exogenous shocks led to higher stock market return volatility. The regression results disclosed statistically significant though opposite impacts on the index price. The pandemic exerted a positive, though extremely mild impact on the Index value, while the war had a negative effect on its performance. As for the control variables, both inflation rate and industrial production index exhibited positive effects on the TUNINDEX values, while trade balance had a negative impact. GDP growth rate and interest rate however, showed no significant influence on the index performance during the study period. We faced some difficulty accessing data, in addition to the scarcity of data on other potentially relevant factors, along with a short study period. Incorporating new variables i.e. mortality rates, unemployment due to the lockdown, travel bans effect, trade dependence with Ukraine and Russia, and using Time-Varying Vector Auto Regressive model may add additional value to our work. The paper contributes to the literature on external shocks impacts on stock markets, specifically on the Tunisian stock exchange. In addition, it offers insights on the potential expected economic effects of unpredicted events, and may help identify appropriate strategies to mitigate their dramatic effects. Finally, this research presents the first investigation on the impact of the Russian invasion on Ukraine on the Tunisian stock exchange by probing into the impact on both volatility and performance of the market’s index.

Analysis of the impact of central bank digital currency on stock markets: Dynamics and implications

The purpose of the study is to explore the influence of central bank digital currency on stock markets. To realize the purpose, the TVP-VAR model was built, which determines the impact of volatility of the CBDC attention index (CBDCAI) on the volatility of stock market indices. The study uses a time-varying vector autoregressive model that analyzes weekly data from the first week of January 2015 to the first week of July 2023. The endogenous vector to be assessed by VAR contains CBDCAI and stock market indices of different countries (France: CAC 40, The United States of America: S&P 500, Germany: DAX 40, United Kingdom: FTSE 100, China: SSEC, The Netherlands AEX 25, Switzerland: SMI 20, Japan: Nikkei 225, India: NIFTY 50, Brazil: BVSP, South Korea: KOSPI). The results of the TVP-VAR model show that compared to stock market indices, CBDCAI appeared to be relatively independent and isolated. Interdependence and mutual influence between the digital currency market of central banks and stock markets were also revealed. In addition, CBDC functions primarily as a volatility absorber rather than a source of volatility. Despite the overall ability of the CBDC market to absorb fluctuations in volatility, it may also change its function with the widespread adoption of central bank digital currencies in many countries.

Dynamic connectedness across energy and metal futures markets during the COVID-19 pandemic: New evidence from a time-varying spillover index

The COVID-19 outbreak has greatly increased economic uncertainty worldwide and significantly impacted the markets for energy and metal futures. In order to capture the dynamic connectedness between the energy and metal futures markets for the period of January 3, 2013, to June 30, 2022, and to validate the mechanism by which COVID-19 affects spillover effects, this study combines a time-varying parametric vector autoregressive model with spillover effects. It is clear that there is a clear spillover effect in the energy and metal futures markets, showing time-varying characteristics, with fluctuations in the range of 35%–65%. The findings demonstrate that there are considerable spillover effects in the energy and metal futures markets, which fluctuate between 35% and 65% over time and are subject to unexpected events. Especially, the spillover network and dynamic spillover results indicate that during the COVID-19 outbreak, the spillover effect between the energy futures market and the metal futures market significantly increased. The mechanism analysis results indicate that COVID-19 influences the spillover effects between the energy and metal futures markets mostly through uncertainty and financial channel. Further research found that compared to normal market conditions, bullish and bearish market conditions had a greater impact on spillovers in the energy and metal futures markets.

DeepTVAR: Deep learning for a time-varying VAR model with extension to integrated VAR

This paper proposes a new approach called DeepTVAR that employs a deep learning methodology for vector autoregressive (VAR) modeling and prediction with time-varying parameters. By optimizing the VAR parameters with a long short-term memory (LSTM) network, we retain the Markovian dependence for prediction purposes and make full use of the recurrent structure and powerful learning ability of the LSTM. To ensure the stability of the model, we enforce the causality condition on the autoregressive coefficients using the Ansley–Kohn transform. We provide a simulation study of the estimation ability using realistic curves generated from data. The model is extended to integrated VAR with time-varying parameters, and we compare its forecasting performance with existing methods when applied to energy price data.

Are the systemic risk spillovers of good and bad volatility in oil and global equity markets alike?

This paper explores the asymmetric connectedness of systemic risk between the oil and global stock markets in both the time and frequency domains. To do so, we introduce time-varying parametric vector autoregressive (TVP-VAR) spillover index models and implied volatility indices to examine risk spillover under bad and good volatility changes. The results reveal that the oil market and global stock markets are highly risk-connected. The risk spillover from increases in oil-stock volatility is greater than that from decreases in volatility, showing an apparent asymmetric phenomenon. Additionally, asymmetric risk spillovers are caused by volatility in the oil market. In particular, the ability to predict systemic risk driven by bad and good volatility changes is enhanced during extreme market periods. Furthermore, we observe that the risk spillovers between the oil and global stock markets under bad and good volatility changes are more pronounced in the short term and that risk spillovers are still dominated by bad volatility in each period. The oil market has a significant risk spillover effect under bad volatility changes in all periods, while it only plays a strong risk spillover role under good volatility changes in the medium and long term. Finally, trading strategies based on minimum connectedness portfolios significantly reduce asset volatility. These findings can aid investors in optimizing their portfolios according to market conditions and provide recommendations to relevant policymakers.

The Dynamic Effect of Pandemics on Industrial Production Growth

Using a time-varying parameter-structural vector autoregressive (TVP-SVAR) model, this study investigates the dynamic impact of uncertainty caused by worldwide pandemics on industrial productivity growth. We discover that the coronavirus has a negative influence on industrial production growth rates across economic blocs (i.e., United States, Developed, and Emerging nations). We also discover that, since 2016, there has been a considerable rise in the comovement of industrial production growth rates. We also employ the dynamic volatility connectedness methodology and find that the industrial productivity growth of Emerging nations economic bloc, and DPUI is observed to be net transmitters of volatility, whereas the industrial productivity growth of United States and other developed nations economic blocs are found to be net recipients of volatility throughout the sample periods. Furthermore, we find that the dynamic total connectedness among the variables under study is observed to be very strong and time-varying. JEL Codes: C15, C58, G15

The time-varying effects of economic policy uncertainty and low-carbon economic transition on enterprise innovation in China

With the increasing concern of all sectors of society about climate change, enterprises have become an important subject to undertake environmental protection. At the same time, enterprises have to seek survival and development under the background of economic policy uncertainty. Therefore, companies need to not only fulfill their environmental responsibilities but also find ways to respond to changes in economic policies through innovation. In the study, a three-variable time-varying vector autoregressive (TVP-VAR) model with stochastic volatility was used to investigate the nonlinear dynamic effects of economic policy uncertainty and low-carbon economic transition on enterprise innovation in China. It is found that the influence of economic policy uncertainty on enterprise innovation is time-varying and asymmetrical, especially with the 2008 financial crisis as the turning point. After the financial crisis, the positive impact of economic policy uncertainty on enterprises has been weakening, and in 2015, the positive impact turned into a negative impact. In general, economic policy uncertainty is not conducive to the transition to low-carbon economic transition, and with the outbreak of the financial crisis in 2008, the negative impact reached a negative peak. The low-carbon economic transition has a significant crowding-out effect on enterprise innovation, while enterprise innovation has a significant spillover effect on low-carbon economic transition. The conclusion can provide the scientific basis for enterprises to adapt to the change in the economic environment to complete low-carbon economic transition and formulate innovation strategies, which is conducive to the sustainable development of the ecological environment and economic society.

International and Chinese energy markets: Dynamic spillover effects

On the basis of a time-varying parametric vector autoregressive model (TVP-VAR) with spillover index model and wavelet coherence analysis, we study spillover effects of price fluctuations in global and Chinese energy markets. The empirical results indicate that the price trends of coal, crude oil, and natural gas in China and the world are closely interlinked. Extreme events have significantly amplified energy market fluctuations' spillover effect. Additionally, international energy market is a net exporter of fluctuations and spillovers, especially crude oil, and natural gas, which is consistent with China's energy import structure. There are time-varying characteristics and cross-effects between spillover effects in different energy markets. Finally, rising shipping costs, increased stock market volatility, and geopolitical risks are more likely to exacerbate cross-market risk spillovers, while exchange rate depreciation and economic policy uncertainty can dampen risk spillovers to some extent. Based on our findings, we recommend the following actions: build a comprehensive energy price warning mechanism, establish and improve the natural gas futures market, set up a more diversified investment portfolio and dynamically adjust investment strategies, and more flexible and precise policy combinations.

Evaluating Fiscal Policy Under Cyclical Balance in Developed Countries

Abstract This study investigates the cyclical patterns of fiscal policy rules using various policy variables that respond to the macroeconomic performance of developed countries over the past few decades. The study reveals that regardless of whether the economy is in a recession or a boom, fiscal policy basically displays counter-cyclical behavior. However, the degree of cyclicality varies depending on the output gap measurements chosen and the countries analyzed. Additionally, the estimates using various fiscal policy indicators demonstrate a strong time variation in fiscal cyclical behavior, resulting in a significant increase in the counter-cyclicality of the fiscal balance. The article also applies the time-varying coefficients vector autoregression model to assess the effects of fiscal policy on output and finds that a boost in the cyclically adjusted primary balance positively impacts production in the short run.