Bayesian Vector Autoregressive Model Research Articles

How oil price shocks affect investor sentiment: new evidence from China

ABSTRACT This paper studies the effect of structural oil price shocks on China’s investor sentiment using the Bayesian inference structural vector autoregression (VAR) model by Baumeister and Hamilton (2019). We find that oil supply shocks followed by consumption demand shocks have positive and persistent effects on China’s investor sentiment, whereas aggregate and inventory demand shocks have only temporary effects. The effects of these shocks are transmitted mainly by affecting investor’s confidence in domestic economic fundamentals and the international economic environment. Furthermore, oil price shocks also induce different trading motivations in the stock market.

Applying Bayesian methods for macroeconomic modeling of business cycle phases

In the present research, the features of applying two models for estimating macroeconomic dynamic in the USA are investigated: Bayesian vector autoregression and Bayesian vector autoregression with Markov switching. The research goal is to identify periods, structure of fluctuations and the main directions of interaction of the variables (real US GDP and employment) using Bayesian vector autoregression models. Models with Markov chains include many equations (structures). The switching mechanisms between these structures are controlled by an unobservable variable that follows a first-order Markov process. The analyzed variables were taken from the first quarter of 1953 to the third quarter of 2015. The model parameters were estimated on the basis of a prior for the multivariate normal distribution — the inverse Wishart distribution (a generalization of the Minnesota a priori distribution). Basing on the results of the estimation of the two-dimensional model with Markov Switching the average GDP growth rate and expected duration of phases was calculated. The estimated model is acceptable for describing the US economy and with high accuracy describes the probability of being in a particular phase in different periods of time. On the basis of medium-term forecasts, root mean squared errors of the forecast are calculated and a conclusion is made about the most appropriate model. Within the framework of this paper, impulse response functions are built allowing to evaluate how variables in the model react on fluctuations, shocks.

Feasibility of very short-term forecast models for COVID-19 hospital-based surveillance.

INTRODUCTION: We evaluated the performance of Bayesian vector autoregressive (BVAR) and Holt’s models to forecast the weekly COVID-19 reported cases in six units of a large hospital. METHODS: Cases reported from epidemiologic weeks (EW) 12-37 were selected as the training period, and from EW 38-41 as the test period. RESULTS: The models performed well in forecasting cases within one or two weeks following the end of the time-series, but forecasts for a more distant period were inaccurate. CONCLUSIONS: Both models offered reasonable performance in very short-term forecasts for confirmed cases of COVID-19.

BVAR: Bayesian Vector Autoregressions with Hierarchical Prior Selection in R

Vector autoregression (VAR) models are widely used models for multivariate time series analysis, but often suffer from their dense parameterization. Bayesian methods are commonly employed as a remedy by imposing shrinkage on the model coefficients via informative priors, thereby reducing parameter uncertainty. The subjective choice of the informativeness of these priors is often criticized and can be alleviated via hierarchical modeling. This paper introduces BVAR, an R package dedicated to the estimation of Bayesian VAR models in a hierarchical fashion. It incorporates functionalities that permit addressing a wide range of research problems while retaining an easy-to-use and transparent interface. It features the most commonly used priors in the context of multivariate time series analysis as well as an extensive set of standard methods for analysis. Further functionalities include a framework for defining custom dummy-observation priors, the computation of impulse response functions, forecast error variance decompositions and forecasts.

Влияние шоков мировой деловой активности, предложения нефти и спекулятивных нефтяных шоков на экономику РФ

In this work we build a Bayesian vector autoregression model to estimate the impact of global economic activity shocks, supply shocks in the global oil market, as well as speculative oil shocks on key macroeconomic variables of the Russian economy: GDP, household consumption, fixed capital investment, import, export, real effective exchange rate, real wages and income, MIACR interest rate and GDP deflator. The model uses real oil prices, the index of global economic activity, oil production and oil inventories as exogenous variables. The model parameters are estimated for the period from Q1 1999 to Q4 2019. The dynamics of four exogenous variables is described using a separate external vector autoregression model, which is estimated over an extended time period from Q1 1974 to Q4 2019 in order to more accurately estimateits parameters and identify shocks. Shocks are identified based on the approach proposed in [Kilian, Murphy, 2014], which uses sign restrictions and restrictions on the price elasticities of oil demand and oil supply. According to estimates of impulse responses, such variables as real household consumption, imports, and the exchange rate respond positively and statistically significantly to all three shocks leading to an increase in oil prices. However, a shock to global economic activity has a stronger impact. With an increase in oil prices for real GDP, investment and exports a stable and statistically significant positive impact is observed only when this price increase is due to a shock to global economic activity. The work also estimates a forecast error variance decomposition and a historical decomposition of the domestic variables by shocks, which indicate the prevailing role of shocks in global economics activity in the dynamics of Russian macroeconomic variables.

MACROECONOMIC PERSPECTIVE ON CONSTRUCTING FINANCIAL VULNERABILITY INDICATOR IN CHINA

This paper attempts to develop a financial vulnerability indicator for China as a barometer for the state of financial vulnerability in the Chinese financial market, possibly for real-time application. Twelve variables from different sectors are utilised to extract a common vulnerability component using a dynamic approximate factor model. Through the implementation of a Markovswitching Bayesian vector autoregression (MSBVAR) model, the empirical results indicate that a high-vulnerability episode is associated with substantially lower economic activity, but a low-vulnerability episode does not incur substantial changes in economic activity. Notably, the constructed indicator can serve as a real-time early warning system to signify vulnerabilities in the Chinese financial market.

Sustainable Approach to the Normalization Process of the UK’s Monetary Policy

It has been more than a decade since central banks, in the face of the global financial crisis, implemented a set of unconventional initiatives that included a rapid and significant decrease in their main interest rates and an unprecedented balance sheet policy. Thus far, they still have not returned their monetary policy to the pre-crisis framework and have not implemented a normalization process. Currently, a trend of using econometric models in monetary policy for forecasting purposes has been observed. Among these models, Bayesian vector autoregression models (BVAR models) are increasingly being used by central banks. The main aim of this study was to conduct an empirical verification of the BVAR model’s usage for short-term prediction which could then be used for a sustainable (ordered) normalization process for the UK’s monetary policy. This study verifies a research hypothesis which states that the BVAR model might be a useful tool in the Bank of England’s decision-making process regarding the normalization of its monetary policy. Additionally, the cause and effect analysis, observation method, document analysis method, and synthesis method were also considered. The conducted research indicates that a large BVAR model has a significant predictive value for short-term forecasting.

The Dollar Exchange Rates in the Covid-19 Era: Evidence from 5 Currencies

Purpose: In this paper, through a novel Bayesian specification, we test whether the exchange rates are affected by the current crisis caused by the Covid-19 spread. Design/Methodology/Approach: we set out a novel Bayesian vector autoregressive model and compare it in terms of forecasting ability with the existing literature’s econometric models. Findings: Based on our findings, the novel Bayesian model proposed in the present paper, is better in terms of forecasting ability than the econometric models, and more importantly, it can unveil the impact of the Covid-19 spread on the exchange rates, while the econometric models failed to shed light on this relationship. Practical Implications: The Covid-19 has affected the overall economic system, in many ways, leading to its disorganization. Such an impact is highlighted by the present paper, examining the exchange rates. Originality/Value: The Bayesian framework proposed in the present paper has novel technical components and can unveil hidden effects of an exogenous variable on a system of endogenous variables, that the classical econometric approaches fail to unveil.

Forecasting inflation in the euro area: countries matter!

We construct a Bayesian vector autoregressive model with three layers of information: the key drivers of inflation, cross-country dynamic interactions, and country-specific variables. The model provides good forecasting accuracy with respect to the popular benchmarks used in the literature. We perform a step-by-step analysis to shed light on which layer of information is more crucial for accurately forecasting medium-run euro area inflation. Our empirical analysis reveals the importance of including the key drivers of inflation and taking into account the multi-country dimension of the euro area. The results show that the complete model performs better overall in forecasting inflation excluding energy and unprocessed food over the medium term. We use the model to establish stylized facts on the euro area and cross-country heterogeneity over the business cycle.

Demand, supply, monetary policy, and oil price shocks in the Russian economy (Analysis based on the BVAR model with sign restrictions)

This paper considers a simple Bayesian vector autoregressive model for the Russian economy based on data for real GDP, GDP deflator and oil price as an exogenous variable that acts as a proxy variable for the terms of trade. Along with the impact of oil price shocks, the model estimates the impact of supply and demand shocks, the identification of which is based on the approach of sign restrictions. According to the results obtained, at the end of 2014 and in 2015, demand shocks had a positive impact on GDP growth, which can be interpreted as a positive effect of the ruble devaluation at the end of 2014. In the next years, demand shocks led mainly to a slowdown in economic growth. The paper also attempts to identify monetary policy shocks and assesses their impact on GDP, household consumption and investment. According to the results, the effect of monetary shocks in 2015—2019 on all endogenous variables was negative. However, an increase in the interest rate at the end of 2014 is identified mostly as an endogenous reaction to other shocks, and the effect of the monetary shock on GDP in 2015 is nearly zero. In 2017, monetary shocks slowed down GDP by 0.92 percentage points.

The impact of foreign capital shifts on economic activities and asset prices: a threshold VAR approach

Purpose The purpose of this paper is to investigate the impact of foreign capital shifts on economic activities and asset prices in South Korea. Design/methodology/approach The authors in this paper apply the Bayesian threshold vector autoregressive (TVAR) model to estimate the regimes of large and low inflows of foreign capital. Then, structural impulse-response analysis is used to check whether the responses of the variables differ across the estimated regimes. The model is estimated using quarterly data of foreign capital inflows, gross domestic product (GDP), consumer price index, credit to the private non-financial sector, real effective exchange rate (REER), stock returns and house prices. Findings The main findings suggest that large inflows of gross foreign capital, foreign direct investments (FDI) and foreign portfolio investments (FPI) are ineffective to boost economic growth, but large inflows of other foreign investments (OFIs) significantly contribute to GDP. The decreases in the foreign capital inflows are associated with larger depreciation of REER. The large inflows of gross foreign capital, FDI and OFIs are associated with further expansion of credit supply to private non-financial sectors. Research limitations/implications The policy implications of foreign capital inflows are of particular importance to all the emerging markets alike. However, the empirical analysis is limited to the case of South Korea due to various reasons. The experience with international capital inflows among emerging markets is heterogeneous. Therefore, it would be better to take each case of emerging market individually. In addition, TVAR analysis requires a long data sample, which unfortunately is not available for most of the emerging markets. Originality/value The foreign capital inflows are shown to be procyclical and notoriously volatile in many studies. Nevertheless, this topic has commonly been studied using linear VAR models, which do not properly deal with the cyclical characteristics of foreign capital inflows. This study attempts to resolve these methodological limitations by examining a non-linear VAR model that is capable of capturing the structural breaks associated with the cyclical behaviors of foreign capital inflows.

Macroeconomic transmission of Eurozone shocks to India—A mean-adjusted Bayesian VAR approach

This paper analyzes the macroeconomic transmission of Eurozone shocks to an emerging economy — India using the mean-adjusted Bayesian Vector Autoregressive (BVAR) model. In its quantitative exploration, the study answers two key issues: (i) is there any evidence of decoupling from advanced economy business cycles? And (ii) what was the impact of the Eurozone recession on the growth performance of India? The findings suggest that Eurozone idiosyncratic shocks, on average, had large effects on economic activity in India. The variation explained by the innovations generated by the BVAR model range from 1.8 percent to 3.6 percent in the 1–12 quarter horizon. The main results are supported by the empirical estimations of the Wavelet analysis. The estimated output elasticities suggest that the Eurozone recession had a significant negative impact on India. The implication is that well-balanced diversity in the productive structure of emerging economies, particularly India, can diffuse the transmission of macroeconomic shocks from the advanced economies.

Forecasting the production side of GDP

AbstractWe evaluate the forecasting performance of time series models for the production side of gross domestic product (GDP)—that is, for the sectoral real value‐added series summing up to aggregate output. We focus on two strategies to model a large number of interdependent time series simultaneously: a Bayesian vector autoregressive model (BVAR) and a factor model structure; and compare them to simple aggregate and disaggregate benchmarks. We evaluate point and density forecasts for aggregate GDP and the cross‐sectional distribution of sectoral real value‐added growth in the euro area and Switzerland. We find that the factor model structure outperforms the benchmarks in most tests, and in many cases also the BVAR. An analysis of the covariance matrix of the sectoral forecast errors suggests that the superiority can be traced back to the ability to capture sectoral comovement more accurately.

Forecasting the implications of foreign exchange reserve accumulation with a microsimulation model

ABSTRACT We develop a stock-flow-consistent microsimulation model that comprises all relevant mechanisms of money creation and parametrise it to fit actual data. The model is used to make out-of-sample projections of broad money and credit developments under the commencement/termination of foreign reserve accumulation by the Bank of Russia. We use direct forecasts from the miscrosimulation model as well as the two-step approach, which implies the use of artificial data to pre-train the Bayesian vector autoregression model. We conclude that the suggested approach is competitive in forecasting and yields promising results.

The impact of non-banking financial institutions on monetary policy transmission in Euro area

The structure of financial intermediation has been subject to significant changes in last decades. The share of banks in the financial system is declining while non-banks are increasing, and this trend is especially evident in Euro area. The changing structure of financial intermediation has been subject of increasing attention of monetary authorities, as it may generate significant changes in the way monetary policy is transmitted to the economy. The goal of this research is to study the impact of non-banking financial institutions on monetary policy transmission in Euro area. This analysis applies a Bayesian vector autoregression model and identifies monetary policy shock in Euro area using three identification strategies—recursive identification, sign restriction and external instruments in the form of surprise changes in market rates in a short time-frame around ECB monetary policy meetings and announcements. The results show that non-banking financial institutions do not dampen transmission of monetary policy in Euro area—in response to monetary contraction they contract their balance sheets for the most part, while banks have more dampening effect or contract their assets less.

Stress Testing in Statistical Modeling of Business Activity in Conditions of Market Shocks

The authors proposed an original method of stress testing in statistical modeling of business activity based on the results of business tendency surveys to study possible scenarios for the development triggered by external unforeseen supply and demand shocks, as in the case of the COVID-19 pandemic. The article also provides an overview of existing approaches in the field of stress testing and the construction of stress indices with an emphasis on methods based on vector autoregressive models and their various modifications. Thus, the article aims to adapt existing methods of macro-level stress testing for their use based on the results of business tendency surveys.The basis for empirical calculations was the data from business tendency surveys of the leaders of Russian manufacturing enterprises, reflecting their combined estimates of the current state of business activity. The methods used in the article included: firstly, the formation of four composite indices based on the results of business tendency surveys from 2008 to March 2020, reflecting various aspects of business activity of enterprises (demand index, production index, financial index and employment index); secondly, the construction of the BVAR (Bayesian vector autoregression) model and its application for studying and comparing various forecast scenarios of index reactions to market shocks.The results of the study, forecasts of the dynamics of indices were obtained as a reaction to four possible shock scenarios: short-term, V-, W-, and U-shaped. Moreover, for each of the scenarios, cases of shocks from the side of demand, production and their simultaneous impact are presented.The conclusions based on the results of this study point to the key role of demand in the dynamics of all the considered indices and to the relatively greater sensitivity of the employment index in relation to the demand index and the finance index in relation to the production index. W-shaped shock was the worst of the four scenarios considered.Conclusions based on the study results indicate the vital role of demand in the dynamics of all the indices under consideration, the Wshaped shock, as the worst of the considered scenarios, as well as the relatively higher sensitivity of the employment index to the demand index and the finance index to the production index.

Multi-response online parameter design based on Bayesian vector autoregression model

With the rapid development of the Internet of Things and sensor technology, some noise factors can be measured or estimated during operation and production. This paper develops a new multi-response optimization method that facilitates online parameter design by using the extra information available about observable noise factors. Bayesian multivariate regression model and Bayesian vector autoregressive model are used to consider the uncertainty of both the response model and the noise model. The Monte Carlo procedure is employed to obtain the predictions of multiple correlated noise factors from their posterior predictive distribution. The proposed method provides a convenient way to continuously update process settings during the production, which helps to further reduce the influence of the variability in the noise factor on product or process quality. Two examples are used to illustrate the effectiveness of the proposed method. The results show that the proposed method outperformance the offline parameter design and another online parameter design that does not consider model parameter uncertainty.

Bitcoin Network Mechanics: Forecasting the BTC Closing Price Using Vector Auto-Regression Models Based on Endogenous and Exogenous Feature Variables

The Bitcoin (BTC) market presents itself as a new unique medium currency, and it is often hailed as the “currency of the future”. Simulating the BTC market in the price discovery process presents a unique set of market mechanics. The supply of BTC is determined by the number of miners and available BTC and by scripting algorithms for blockchain hashing, while both speculators and investors determine demand. One major question then is to understand how BTC is valued and how different factors influence it. In this paper, the BTC market mechanics are broken down using vector autoregression (VAR) and Bayesian vector autoregression (BVAR) prediction models. The models proved to be very useful in simulating past BTC prices using a feature set of exogenous variables. The VAR model allows the analysis of individual factors of influence. This analysis contributes to an in-depth understanding of what drives BTC, and it can be useful to numerous stakeholders. This paper’s primary motivation is to capitalize on market movement and identify the significant price drivers, including stakeholders impacted, effects of time, as well as supply, demand, and other characteristics. The two VAR and BVAR models are compared with some state-of-the-art forecasting models over two time periods. Experimental results show that the vector-autoregression-based models achieved better performance compared to the traditional autoregression models and the Bayesian regression models.

A Flexible Mixed-Frequency Vector Autoregression with a Steady-State Prior

Abstract We propose a Bayesian vector autoregressive (VAR) model for mixed-frequency data. Our model is based on the mean-adjusted parametrization of the VAR and allows for an explicit prior on the “steady states” (unconditional means) of the included variables. Based on recent developments in the literature, we discuss extensions of the model that improve the flexibility of the modeling approach. These extensions include a hierarchical shrinkage prior for the steady-state parameters, and the use of stochastic volatility to model heteroskedasticity. We put the proposed model to use in a forecast evaluation using US data consisting of 10 monthly and three quarterly variables. The results show that the predictive ability typically benefits from using mixed-frequency data, and that improvement can be obtained for both monthly and quarterly variables. We also find that the steady-state prior generally enhances the accuracy of the forecasts, and that accounting for heteroskedasticity by means of stochastic volatility usually provides additional improvements, although not for all variables.

Modeling mortality with a Bayesian vector autoregression

Parametric mortality models capture the cross section of mortality rates. These models fit the older ages better, because of the more complex cross section of mortality at younger and middle ages. Dynamic parametric mortality models fit a time series to the parameters, such as a Vector-auto-regression (VAR), in order to capture trends and uncertainty in mortality improvements. We consider the full age range using the Heligman and Pollard (1980) model, a cross-sectional mortality model with parameters that capture specific features of different age ranges. We make the Heligman–Pollard model dynamic using a Bayesian Vector Autoregressive (BVAR) model for the parameters and compare with more commonly used VAR models. We fit the models using Australian data, a country with similar mortality experience to many developed countries. We show how the Bayesian Vector Autoregressive (BVAR) models improve forecast accuracy compared to VAR models and quantify parameter risk which is shown to be significant.