Time-varying Parameter Regression Research Articles

Herding behaviour surrounding the Russo–Ukraine war and COVID-19 pandemic: evidence from energy, metal, livestock and grain commodities

PurposeThis study examines herding behaviour in commodity markets amid two major global upheavals: the Russo–Ukraine conflict and the COVID-19 pandemic.Design/methodology/approachBy analysing 18 commodity futures worldwide, the study examines herding trends in metals, livestock, energy and grains sectors. The applied methodology combines static and dynamic approaches by incorporating cross-sectional absolute deviations (CSAD) and a time-varying parameter (TVP) regression model extended by Markov Chain Monte Carlo (MCMC) sampling to adequately reflect the complexity of herding behaviour in different market scenarios.FindingsOur results show clear differences in herd behaviour during these crises. The Russia–Ukraine war led to relatively subdued herding behaviour in commodities, suggesting a limited impact of geopolitical turmoil on collective market behaviour. In stark contrast, the outbreak of the COVID-19 pandemic significantly amplified herding behaviour, particularly in the energy and livestock sectors.Originality/valueThis discrepancy emphasises the different impact of a health crisis versus a geopolitical conflict on market dynamics. This study makes an important contribution to the existing literature as it is one of the first studies to contrast herding behaviour in commodity markets during these two crises. Our results show that not all crises produce comparable market reactions, which underlines the importance of the crisis context when analysing financial market behaviour.

Locally time-varying parameter regression

. I discuss a framework to allow dynamic sparsity in time-varying parameter regression models. The conditional variances of the innovations of time-varying parameters are time varying and equal to zero adaptively via thresholding. The resulting model allows the dynamics of the time-varying parameters to mix over different frequencies of parameter changes in a data driven way and permits great flexibility while achieving model parsimony. A convenient strategy is discussed to infer if each coefficient is static or dynamic and, if dynamic, how frequent the parameter change is. An MCMC scheme is developed for model estimation. The performance of the proposed approach is illustrated in studies of both simulated and real economic data.

The impact of the Russo-Ukraine conflicts on price discovery on the financial markets

ABSTRACT This paper investigates the response of financial markets to two significant events within the Russo-Ukraine conflicts: the November 2013 Euromaidan protest and the February 2022 Russian invasion of Ukraine. Employing diverse methods, including event studies, price discovery models, and time-varying parameter regression, we analyse abnormal returns, price discovery, time-varying herding behaviour, and market dynamics across various financial instruments, such as stock indices, currencies, and commodities. Overall, the Russian invasion of Ukraine had a more pronounced impact on financial markets compared to the Euromaidan protest. Moreover, during both events, the US dollar and yen consistently functioned as safe-haven assets. The findings also reveal variations in the responses of different assets to the conflicts, indicating potential effects on market efficiency, investor perceptions, and expectations.

Dynamic Shrinkage Priors for Large Time-Varying Parameter Regressions Using Scalable Markov Chain Monte Carlo Methods.

Time-varying parameter (TVP) regression models can involve a huge number of coefficients. Careful prior elicitation is required to yield sensible posterior and predictive inferences. In addition, the computational demands of Markov Chain Monte Carlo (MCMC) methods mean their use is limited to the case where the number of predictors is not too large. In light of these two concerns, this paper proposes a new dynamic shrinkage prior which reflects the empirical regularity that TVPs are typically sparse (i.e. time variation may occur only episodically and only for some of the coefficients). A scalable MCMC algorithm is developed which is capable of handling very high dimensional TVP regressions or TVP Vector Autoregressions. In an exercise using artificial data we demonstrate the accuracy and computational efficiency of our methods. In an application involving the term structure of interest rates in the eurozone, we find our dynamic shrinkage prior to effectively pick out small amounts of parameter change and our methods to forecast well.

Time-dependent shrinkage of time-varying parameter regression models

This article studies the time-varying parameter (TVP) regression model in which the regression coefficients are random walk latent states with time-dependent conditional variances. This TVP model is flexible to accommodate a wide variety of time variation patterns but requires effective shrinkage on the state variances to avoid over-fitting. A Bayesian shrinkage prior is proposed based on reparameterization that translates the variance shrinkage problem into a variable shrinkage one in a conditionally linear regression with fixed coefficients. The proposed prior allows strong shrinkage for the state variances while maintaining the flexibility to accommodate local signals. A Bayesian estimation method is developed that employs the ancilarity-sufficiency interweaving strategy to boost sampling efficiency. Simulation study and an empirical application to forecast inflation rate illustrate the benefits of the proposed approach.

Do birds of a feather flock together? Evidence from time-varying herding behaviour of bitcoin and foreign exchange majors during Covid-19

This paper analyses herding behaviour within bitcoin and foreign exchange majors before and during the Covid-19 pandemic. We utilise both static and time-varying parameter regression herding measures to assess herding intensity based on hourly and daily frequencies, covering the period from 1 March 2018 to 28 February 2022. Our hourly static and time-varying model results indicate the absence of herding (hence, the presence of anti-herding behaviour) within bitcoin and the foreign exchange majors before and during Covid-19. In daily herding analyses, however, while we do not find evidence of herding within bitcoin or the foreign exchange majors, we do observe strong time-varying herding within the foreign exchange majors after excluding bitcoin both before and during Covid-19, and during both up- and down-market days. We conclude that herding behaviour between foreign exchange majors tends to be time-varying and horizon-dependent. Our results could be useful for bitcoin and foreign exchange investors, traders, researchers and regulators, helping them to strengthen their understanding of herding behaviour before and during periods of market stress such as the period of Covid-19.

Globalization Versus Slowbalization: A Perspective on the Indian Economy

The crisis and ensuing recession have led the global leaders to focus inwards. While the trend had taken off with countries having to face rising inequality and a focus towards self-development, there is little evidence besides newspaper articles to support this hypothesis from the Indian perspective. The results, using dynamic hierarchical factor model analysis, over a subset of 21 economies which account for 66% of India’s trade, reveal that India’s globalization has been withering away over time. Using time-varying parameter regression estimation on the domestic and factors loading, it is observed that the portion of growth explained by domestic factors is increasing over time and that of foreign factors is degrading. The study provides evidence of slowbalization in Indian economy. As the government looks forward to an era of self-reliance and Make in India, the results hold significance for the future growth trajectory of the Indian economy.

Fast and Flexible Bayesian Inference in Time-varying Parameter Regression Models

In this article, we write the time-varying parameter (TVP) regression model involving K explanatory variables and T observations as a constant coefficient regression model with KT explanatory variables. In contrast with much of the existing literature which assumes coefficients to evolve according to a random walk, a hierarchical mixture model on the TVPs is introduced. The resulting model closely mimics a random coefficients specification which groups the TVPs into several regimes. These flexible mixtures allow for TVPs that feature a small, moderate or large number of structural breaks. We develop computationally efficient Bayesian econometric methods based on the singular value decomposition of the KT regressors. In artificial data, we find our methods to be accurate and much faster than standard approaches in terms of computation time. In an empirical exercise involving inflation forecasting using a large number of predictors, we find our models to forecast better than alternative approaches and document different patterns of parameter change than are found with approaches which assume random walk evolution of parameters.

Forecasting selected energy commodities prices with Bayesian dynamic finite mixtures

In this paper selected energy commodities spot prices are forecasted with the help of Bayesian dynamic finite mixtures. In particular, crude oil, natural gas, and coal spot prices are analyzed. Due to the availability of data, crude oil is analyzed between 1988 and 2019, natural gas between 1990 and 2019, and coal between 1987 and 2019. Monthly data are used. The dynamic mixtures used herein are a novel methodological tool in forecasting. Their first important feature is that regression coefficients are estimated in a recursive on-line way, allowing for real-time performance. Secondly, the switching between mixture components is also allowed to vary in time. Thirdly, the algorithms used herein are based on explicit solutions, allowing for the fully Bayesian inference approach, whereas approximations are only on the numerical level of the pdfs (probability density functions) statistics. In other words, the evolution of prior to posterior pdfs has fixed functional form; only the numerical statistics of those pdfs are evolving in time. Both normal regression components and state-space models are considered as mixture components, which makes this study a generalization of previous research with Bayesian approaches to model averaging techniques. Indeed, those mixtures are compared with other benchmark models, such as Dynamic Model Averaging, Time-Varying Parameter regression, ARIMA, and the naïve method, with the Diebold-Mariano test, and are found to generate significantly more accurate forecasts. Additionally, the Giacomini-Rossi fluctuation test and Model Confidence Set are applied for more thorough examination of forecasting performances.

Time varying dynamics of globalization effect in India

The link between globalization and economic growth is getting complex as the propagators of globalization are opting protectionism. The paper attempts to identify the time-varying dimension of globalization in India from Q2 1996 to Q3 2019. The aim is to capture the portion of growth explained by domestic and foreign factors suggesting the pace of globalization. The factor-induced domestic and foreign loadings are used in Time-Varying Parameter Regression and Time-Varying Parameter Autoregressive approach to indicate the evidence for slowbalization in India. The models combined with stochastic volatility, aid in capturing the structural changes in the economy in a robust manner.

The foreign capital inflows and the boom in house prices: time-varying evidence from emerging markets

ABSTRACT This study applies time-varying parameter methods to investigate the association of foreign capital inflows with the occurrence of house price booms in a sample of emerging markets. The time-varying causality tests show evidence of unidirectional as well as bi-directional causality between gross foreign capital inflows and house prices. Furthermore, the upward evolution of the time-varying impact of foreign capital inflows on house prices appears to be mostly related to the distinct episodes of the housing booms as shown by the results of time-varying parameter regression. However, there are instances where the time-varying impact of foreign capital inflows abruptly shifts upward without causing price booms in the housing market. We also find evidence that some components of foreign capital inflows are negatively affecting house prices during the boom episodes.

Time-varying monetary policy reaction function under asymmetric preferences: revisiting the Brazilian inflation targeting experience

PurposeThis paper analyzes the potential presence of time-varying asymmetries in the preference parameters of the Central Bank of Brazil during the inflation targeting regime.Design/methodology/approachGiven the econometric issues inherent to classical time-varying parameter (TVP) regressions, a Bayesian estimation procedure is implemented in order to provide more robust parameter estimates. A stochastic volatility specification is also included to take into account the potential presence of conditional heteroskedasticity.FindingsThe obtained results show that the reduced form and structural parameters were not constant during the period considered. Moreover, the subsequent analysis of the preference parameters provided evidences of short periods in which asymmetry was an important feature to the conduction of monetary policy in Brazil. Yet, during most of the sample period, the loss function was considered to be symmetrical.Originality/valueThis paper aims to contribute to the rather scarce monetary debate on time-varying central bank preferences. The study of Lopes and Aragón (2014) is, to the best of the authors’ knowledge, the only study for Brazil considering specifically TVPs. The authors applied Kalman filter estimation to data from 2000:M1 to 2011:M12. Despite the similar structure of TVPs, the present paper extends the latter study by controlling for stochastic volatility. Ignoring conditional heteroskedasticity might lead to spurious movements in time-varying variables and inaccurate inference (Hamilton, 2010). Thus, the stochastic volatility specification is included to take this issue into account. The authors follow the theoretical scheme put forward by Surico (2007) and Aragón and Portugal (2010), in which the economy is modeled from a New Keynesian perspective and the central bank loss function is assumed to be asymmetric regarding the responses to inflation and output deviations from their targets. On the empirical side, the authors propose a TVP univariate regression with stochastic volatility for the Brazilian reduced-form reaction function, following closely the Bayesian econometric procedure developed by Nakajima (2011). Given the nonlinear non-Gaussian nature of the TVP regression with stochastic volatility, the choice of a nonlinear Bayesian approach using the Markov chain Monte Carlo (MCMC) method is justified due to the intractability of the associated likelihood function (Primiceri, 2005). Finally, based on the theoretical model specification, the authors intend to recover the central bank preference parameters as to further evaluate the degree of asymmetry and its potential time-variation under the inflation targeting regime.

Statistical methods for forecasting daily snow depths and assessing trends in inter-annual snow depth dynamics

This paper introduces a time-varying parameter regression model for modeling, forecasting, and assessing inter-annual trends in daily snow depths. The time-varying parameter regression is written in a simple state-space representation and forecasted using a Kalman filter. The recursive Kalman filter algorithm updates the time-varying parameter sequentially when a new data point becomes available and is a flexible forecasting technique. The proposed method is applied to a time series of daily snow depth observations recorded over a 103 year period at a station in Napoleon, North Dakota. The forecasts of the final ten years of data perform well when compared to the actual daily snow depths. Inter-annual snow depth trends indicate an increase in mid-winter snow depths followed by an earlier spring ablation.

Dynamic Regression Models for Time-Ordered Functional Data

For time-ordered functional data, an important yet challenging task is to forecast functional observations with uncertainty quantification. Scalar predictors are often observed concurrently with functional data and provide valuable information about the dynamics of the functional time series. We develop a fully Bayesian framework for dynamic functional regression, which employs scalar predictors to model the time-evolution of functional data. Functional within-curve dependence is modeled using unknown basis functions, which are learned from the data. The unknown basis provides substantial dimension reduction, which is essential for scalable computing, and may incorporate prior knowledge such as smoothness or periodicity. The dynamics of the time-ordered functional data are specified using a time-varying parameter regression model in which the effects of the scalar predictors evolve over time. To guard against overfitting, we design shrinkage priors that regularize irrelevant predictors and shrink toward time-invariance. Simulation studies decisively confirm the utility of these modeling and prior choices. Posterior inference is available via a customized Gibbs sampler, which offers unrivaled scalability for Bayesian dynamic functional regression. The methodology is applied to model and forecast yield curves using macroeconomic predictors, and demonstrates exceptional forecasting accuracy and uncertainty quantification over the span of four decades.

Time-varying effect of oil price shocks on the stock market returns: Evidence from oil-importing and oil-exporting countries

This paper performs a two-stage methodology based on the Structural VAR and time-varying parameter regression models to examine the dynamic reaction of a set of oil-related countries’ stock markets to oil price shocks. Oil prices are studied by disentangling demand and supply shocks. Based on monthly data from the 1999–2018 period, the results report evidence of a time-varying reaction of all stock market returns to different oil shocks. Moreover, the stock returns react to the demand shocks more than to the supply shocks. Besides, the effect of supply shocks on stock returns is generally limited and negative, while the aggregate demand shocks exert a positive effect on almost all stock returns. Oil-specific demand shocks have positive effects on the oil-exporting stock returns and negative effects in the case of oil-importing countries, except for the Chinese market. These findings have important policy implications for policymakers and investors.

Dynamic Shrinkage Processes

SummaryWe propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute-by-minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods.

Forecasting India’s economic growth: a time-varying parameter regression approach

ABSTRACTForecasting GDP growth is essential for effective and timely implementation of macroeconomic policies. This paper uses a principal component augmented Time Varying Parameter Regression (TVPR) approach to forecast real aggregate and sectoral growth rates for India. We estimate the model using a mix of fiscal, monetary, trade and production side-specific variables. To assess the importance of different growth drivers, three variants of the model are tried, namely, Demand-side, Supply-side and Combined models. We also find that TVPR model consistently outperforms constant parameter principal component augmented regression model and Dynamic Factor Model in terms of forecasting performance for all the three specifications.

A New Structural Analysis of Inflation and Economic Activity

We theoretically investigate the role of expectations in modelling economic activity and the evolution of inflation rates. The New Keynesian Phillips-IS model is extended in our study by having two types of firms with a fraction of firms that uses ‘limited’ information to develop their expectations. The remaining firms, which are referred to as forward-looking, would use all information available to set prices and make manufacturing budgets. Then we use UK data to examine the robustness of our extension. To estimate our augmented model, we employ the Uhlig (2005) priori restrictions and the Nakajima (2011a) time-varying parameter regression. Our results suggest that the expectations of each type of firms play an important role in explaining the inflation rate and real economic growth in the UK.

A NEW STRUCTURAL ANALYSIS OF INFLATION AND ECONOMIC ACTIVITY

We theoretically investigate the role of expectations in modelling economic activity and the evolution of inflation rates. The New Keynesian Phillips-IS model is extended in our study by having two types of firms with a fraction of firms that uses ?limited? information to develop their expectations. The remaining firms, which are referred to as forward-looking, would use all information available to set prices and make manufacturing budgets. Then we use UK data to examine the robustness of our extension. To estimate our augmented model, we employ the Uhlig (2005) priori restrictions and the Nakajima (2011a) time-varying parameter regression. Our results suggest that the expectations of each type of firms play an important role in explaining the inflation rate and real economic growth in the UK.

On-line peak detection in medical time series with adaptive regression methods

Sequential analysis of medical time series has important implications when data concern vital functions of the human body. Traditional monitoring of vital signs is performed by comparing the level of time series with predetermined target bands. As in industrial control charts, alarm signals start when the series level goes beyond the bands. Many physiological time series, however, are non-stationary with stochastic cycles and are characterized by turning points, i.e. periods where the slope of the series changes sign and determines the beginning of rise and fall phases. Turning points are useful indicators of the effect of drugs and medications and must be timely detected in order to calibrate the drug dosage or perform interventions. Sequential and recursive filters are suitable methods for change and turning points; they are mainly given by double exponential smoothing, time-varying parameter regression and prediction error statistics. Their tuning coefficients can be selected in a data-driven way, by optimizing score functions based on the series’ oscillation. Extensive application to real and simulated data shows that adaptive techniques represent effective solutions to on-line monitoring and surveillance in medicine.11Data and Matlab software are provided in the supplementary material.