A two-regime threshold model with conditional skewed Student t distributions for stock returns

This paper proposes a two-regime threshold model for the conditional distribution of stock returns in which returns follow a distinct skewed Student t distribution within each regime: the model allows capturing time variation in the conditional distribution of returns, as well as higher order moments. An application of the model to daily U.S. stock returns illustrates the advantages of the proposed model in comparison to alternative specifications: the model performs well in terms of in-sample fit; it more accurately estimates the conditional volatility; and it produces useful risk assessment as measured by the term structure of value at risk.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash

Modelling of conditional volatilities and correlations across asset returns is an integral part of portfolio decision making and risk management. Over the past three decades there has been a trend towards increased asset return correlations across markets, a trend which has been accentuated during the recent financial crisis. We shall examine the nature of asset return correlations using weekly returns on futures markets and investigate the extent to which multivariate volatility models proposed in the literature can be used to formally characterize and quantify market risk. In particular, we ask how adequate these models are for modelling market risk at times of financial crisis. In doing so we consider a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and show that the t-DCC model passes the usual diagnostic tests based on probability integral transforms, but fails the value at risk (VaR) based diagnostics when applied to the post 2007 period that includes the recent financial crisis.     

Markov regime-switching Beta-t-EGARCH

We suggest a Markov regime-switching (MS) Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model for U.S. stock returns. We compare the in-sample statistical performance of the MS Beta-t-EGARCH model with that of the single-regime Beta-t-EGARCH model. For both models we consider leverage effects for conditional volatility. We use data from the Standard Poor’s 500 (S&P 500) index and also a random sample that includes 50 components of the S&P 500. We study the outlier-discounting property of the single-regime Beta-t-EGARCH and MS Beta-t-EGARCH models. For the S&P 500, we show that for the MS Beta-t-EGARCH model extreme observations are discounted more for the low-volatility regime than for the high-volatility regime. The conditions of consistency and asymptotic normality of the maximum likelihood estimator are satisfied for both the single-regime and MS Beta-t-EGARCH models. All likelihood-based in-sample statistical performance metrics suggest that the MS Beta-t-EGARCH model is superior to the single-regime Beta-t-EGARCH model. We present an application to the out-of-sample density forecast performance of both models. The results show that the density forecast performance of the MS Beta-t-EGARCH model is superior to that of the single-regime Beta-t-EGARCH model.     

The impacts of regime-switching structures and fat-tailed characteristics on the relationship between inflation and inflation uncertainty

A great of deal of study has explored the relationship between inflation and inflation uncertainty under the assumptions of normal distribution and no regime shift. This paper attempts to investigate whether changes in the specification of distribution specification and regime shifts will affect the inflation-uncertainty relationship. Empirical results show that these two factors have a vital effect on the inflation-uncertainty relationship. A specification with four states and the Student’s t distributed error terms can successfully describe the dynamics of the inflation rate. After taking the non-normal density and independent regime shifts into account, this paper finds that inflation uncertainty has no impact on inflation, regardless of inflation pressure. Inflation has a negative impact on inflation uncertainty during periods of high inflation volatility, while the impact of inflation on inflation uncertainty is insignificant during periods of low inflation volatility.     

Modelling conditional moments and correlation with the continuous hidden-threshold-skew-normal distribution

A key issue in modelling conditional densities of returns of financial assets is the time-variation of conditional volatility. The classic econometric approach models volatility of returns with the generalized autoregressive conditional heteroscedasticity (GARCH) models where the conditional mean and the conditional volatility depend only on historical prices. We propose a new family of distributions in which the conditional distribution depends on a latent continuous factor with a continuum of states. The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. The distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. We show empirically that this distribution outperforms its main competitor, the mixed normal conditional distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.     

Value at risk estimation by threshold stochastic volatility model

This article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk (VaR) estimation. The method incorporates extreme downside shocks by modelling left-tail returns separately from other returns. Left-tail returns are generated with a t-distributional process based on the historically observed conditional excess kurtosis. This specification allows VaR estimates to be generated with extreme downside impacts, yet remains empirically widely applicable. This article applies the model to daily returns of seven major stock indices over a 22-year period and compares its forecasts to those of several other forecasting methods. Based on back-testing outcomes and likelihood ratio tests, the new model provides reliable estimates and outperforms others.     

Analysis of electricity prices for Central American countries using dynamic conditional score models

In this paper, we compare the performance of dynamic conditional score (DCS) and standard financial time-series models for Central American energy prices. We extend the Student’s t and the exponential generalised beta distribution of the second kind stochastic location and stochastic seasonal DCS models. We consider the generalised t distribution as an alternative for the error term and also consider dynamic specifications of volatility. We use a unique dataset of spot electricity prices for El Salvador, Guatemala and Panama. We consider two data windows for each country, which are defined with respect to the liberalisation and development process of the energy market in Central America. We study the identification of a wide range of DCS specifications, likelihood-based model performance, time-series components of energy prices, maximum likelihood parameter estimates, the discounting property of conditional score, and out-of-sample forecast performance. Our main results are the following. (i) We determine the most robust models of energy prices, with respect to parameter identification, from a wide range of DCS specifications. (ii) For most of the cases, the in-sample statistical performance of DCS is superior to that of the standard model. (iii) For El Salvador and Panama, the standard model provides better point forecasts than DCS, and for Guatemala the point forecast precision of standard and DCS models does not differ significantly. (iv) For El Salvador, the standard model provides better density forecasts than DCS, and for Guatemala and Panama, the density forecast precision of standard and DCS models does not differ significantly.     

Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries

Income distribution remains a crucial topic in economic analysis, among other reasons, due to the increase in inequality in recent years, as one of the effects of the Great Recession. In this context, proposing parametric models that represent the full distribution through a small number of parameters arouses great interest as an instrument for economic analysis. This paper studies the ability of log Student’s t distribution to model the size distribution of income due to its potential to reproduce the effect of a mode around low-incomes as well as its precision in capturing the degree of kurtosis of empirical distributions. These characteristics make the log-t an ideal analysis tool, for instance, for exploring the effects of anti-poverty policies. The model has been fitted to income data for the EU25 and for several years. The conclusion is that the log Student’s t distribution offers the best fit in the vast majority of cases.     

BAYESIAN ANALYSIS OF GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY AND STOCHASTIC VOLATILITY: MODELING LEVERAGE,JUMPS AND HEAVY‐TAILS FOR FINANCIAL TIME SERIES*

This paper develops a Bayesian model comparison of two broad major classes of varying volatility model, the generalized autoregressive conditional heteroskedasticity and stochastic volatility models, on financial time series. The leverage effect, jumps and heavy‐tailed errors are incorporated into the two models. For estimation, the efficient Markov chain Monte Carlo methods are developed and the model comparisons are examined based on the marginal likelihood. The empirical analyses are illustrated using the daily return data of US stock indices, individual securities and exchange rates of UK sterling and Japanese yen against the US dollar. The estimation results indicate that the stochastic volatility model with leverage and Student‐t errors yield the best performance among the competing models.     

Spillover effects and conditional dependence

A better understanding of cross-market linkages and interactions would help to better manage international financial exposure. So far, no attempt has been made to investigate the degree of price and volatility spillovers in a non-Gaussian conditional framework. We present a new model for these transmission mechanisms that relies on asymmetric-t marginal distributions and a copula function to characterize the conditional dependence. Rendering the dependence parameter time varying, we investigate how the dependence structure is affected by stock return innovations.     

The linkages,persistence, asymmetry in the volatility,the price discovery and efficiency,and the effect of the US subprime mortgage financial crisis on the spot and the futures market’s returns: the case of India

This article examines the effects of persistence, asymmetry and the US subprime mortgage crisis on the volatility of the returns and also the price discovery, efficiency and the linkages and causality between the spot and futures volatility by using various classes of the ARCH and GARCH models, and through the Granger’s causality. We have used two indices: one for spot and the other for futures, for the daily data from 12 June 2000 to 30 September 2013 from Nifty stock indices. We have then tested for ARCH effects, and subsequently employed various models of the ARCH and GARCH conditional volatility. The GARCH(1,1) model is found to be significant, and it implies that the returns are not autocorrelated and have ‘short memory’. It supports the hypothesis of the efficiency of the markets. The negative ‘news’ has more significant effect on volatility, corroborating the ‘leverage impact’ in finance on market volatility. We have also tested the volatility spillover effects. The two methods we employed support the spillover effects and the causality is bidirectional. We also have used the dummy variable for the US subprime mortgage financial crisis and found that they are statistically significant. Indian stock market is thus integrated to the world stock markets.     

Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.     

Conditional price volatility,speculation, and excessive speculation in commodity markets: sheep or shepherd behaviour?

The present study aims to investigate the dynamics of primary commodity spot prices and the role of speculation for the period 1995–2012. Using a linear and nonlinear Granger causality analysis, the relationship between speculation and GARCH conditional price volatility on the one side, and the linkage between excessive speculation and GARCH conditional price volatility on the other side, is carefully examined with the scope to establish whether volatility drives speculation or speculation drives price volatility, or whether there are no linkages between the two variables. The results show that excessive speculation leads conditional price volatility, and that bilateral relationships often exist between price volatility and speculation. In addition, the lead-lag relationships are not found for the entire sample period, but rather when small sub-periods are taken into account. It turns out, in fact, that excessive speculation has driven price volatility for maize, rice, soybeans, and wheat in particular time frames, but the relationships are not always overlapping for all considered commodities. Generally, the results under linear causality tests are in agreement with those obtained under nonlinear counterparts.     

Can volume predict Bitcoin returns and volatility? A quantiles-based approach

Prior studies on the price formation in the Bitcoin market consider the role of Bitcoin transactions at the conditional mean of the returns distribution. This study employs in contrast a non-parametric causality-in-quantiles test to analyse the causal relation between trading volume and Bitcoin returns and volatility, over the whole of their respective conditional distributions. The nonparametric characteristics of our test control for misspecification due to nonlinearity and structural breaks, two features of our data that cover 19th December 2011 to 25th April 2016. The causality-in-quantiles test reveals that volume can predict returns – except in Bitcoin bear and bull market regimes. This result highlights the importance of modelling nonlinearity and accounting for the tail behaviour when analysing causal relationships between Bitcoin returns and trading volume. We show, however, that volume cannot help predict the volatility of Bitcoin returns at any point of the conditional distribution.     

Correlation dynamics of crude oil with agricultural commodities: A comparison between energy and food crops

This study elucidates plausible correlation between crude oil and agricultural commodities. We assess whether the conditional correlation of crude oil with energy crops (e.g., corn and soybeans) is different from that of food crops (e.g., oats and wheat). We find a stronger correlation of about 20 percent between returns of crude oil and energy crops. However, the correlation coefficient value for oil-oats and oil-wheat is as low as eight percent. We add to the literature by exploring correlation in a dynamic context using three different GARCH models and found that conditional correlation between crude oil and energy corps is relatively high. In order to reduce risk associated with crude oil price fluctuations, this study also examined hedging possibilities against crude oil by investment in agricultural commodities. Although hedging effectiveness is low with all underlying agricultural commodities, soybeans provide relatively better hedging possibilities compared to other agricultural crops.     

Bayesian model comparison by Markov chain simulation: Illustration using stock market data

The paper illustrates the computation of marginal likelihoods and Bayes factors when Markov Chain Monte Carlo has been used to produce draws from a model’s posterior distribution. The method is based on Raftery (1996) and does not require that Gibbs sampling is used or conditional posterior distributions are available in closed form. Models used include a normal finite mixture, a GARCH and a Student t -model as alternative models for the Standard and Poor’s stock returns.     

German stock market dynamics

This article estimates generalized ARCH (GARCH) models for German stock market indices returns, using weekly and monthly data, various GARCH specifications and (non)normal error densities, and a variety of diagnostic checks. German stock return series exhibit significant levels of second-order dependence. Our results clearly demonstrate that for both weekly as well as monthly return series the Student-t distribution is superior to the standard normal distribution. In particular, the estimated GARCH-t models appear to be reasonably successful in accounting for both observed leptokurtosis and conditional heteroskedasticity from German stock return movements.     

我国粮食市场价格波动特征——基于ARCH类模型的实证分析

基于1998年1月9日至2012年12月14日全国小麦、玉米和大豆的批发价格指数周数据,利用ARCH类模型对我国小麦、玉米和大豆的市场价格波动特征进行实证分析。研究结果表明:在5%的显著性水平下,小麦、玉米和大豆的市场价格波动具有明显的时变性和集簇性;玉米市场具有高风险、高回报的特征;小麦的市场价格波动具有非对称性;玉米市场与大豆市场之间存在显著的双向价格波动溢出效应。