Is Beta-t-EGARCH(1,1) superior to GARCH(1,1)?

Statistical performance, in-sample point forecast precision and out-of-sample density forecast precision of GARCH(1,1) and Beta-t-EGARCH(1,1) models are compared. We study the volatility of nine global industry indices for period from April 2006 to July 2010. Competing models are estimated for periods before, during and after the United States (US) financial crisis of 2008. The results provide evidence of the superior out-of-sample predictive performance of Beta-t-EGARCH compared to GARCH after the US financial crisis.     

Dynamic conditional score models: a review of their applications

ABSTRACT

In this paper, applications of dynamic conditional score (DCS) models are reviewed and those models are discussed in relation to classical time series models from the literature. DCS models are robust to outliers, which improves their statistical performance compared to classical models. Three applications are presented in order to compare the statistical performances of DCS and classical models in three very different contexts: (i) The QAR (quasi-autoregressive) plus Beta-t-EGARCH (exponential autoregressive conditional heteroscedasticity) model is presented, which is a score-driven expected return plus volatility model. This model is used for daily returns on the DAX (Deutscher Aktienindex) equity index for the period of January 1988 to December 2017. (ii) The score-driven local level and seasonality plus Beta-t-EGARCH model is presented, which is used for daily AFN/USD (Afghan Afghani/United States Dollar) currency exchange rates for the period of March 2007 to July 2017. (iii) The Seasonal-t-QVAR (quasi-vector autoregressive) model is presented, which is a score-driven multivariate dynamic model of location. For this model, monthly US inflation rate and US unemployment rate are used for the period of January 1948 to December 2017. For all applications, the statistical performance of each DCS model is superior to that of a corresponding classical alternative.     

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.     

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.     

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.     

Long range dependence in an emerging stock market’s sectors: volatility modelling and VaR forecasting

This study evaluates the sector risk of the Qatar Stock Exchange (QSE), a recently upgraded emerging stock market, using value-at-risk models for the 7 January 2007–18 October 2015 period. After providing evidence for true long memory in volatility using the log-likelihood profile test of Qu and splitting the sample and dth differentiation tests of Shimotsu, we compare the FIGARCH, HYGARCH and FIAPARCH models under normal, Student-t and skewed-t innovation distributions based on in and out-of-sample VaR forecasts. The empirical results show that the skewed Student-t FIGARCH model generates the most accurate prediction of one-day-VaR forecasts. The policy implications for portfolio managers are also discussed.     

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.     

Measuring the systemic risk transfer from the United States to the South African financial sector

The sub-prime crisis in 2008 illustrated how systemic risk in the financial sector of one country could spread to the financial sectors in other countries, and subsequently result in a global financial crisis. This direct transfer of systemic risk was made possible by phenomena such as contagion and common shocks. The way in which these elements of interconnectedness can magnify seemingly small levels of systemic risk, and subsequently transfer between financial sectors illustrate the necessity for a more in-depth analysis. This measurement is done using three approaches. A dynamic conditional correlation (DCC) model is used to investigate contagion. To analyse the volatility spillover effect from the US to SA, an exponential generalized autoregressive conditional heteroskedastic (EGARCH) model is employed. Finally, a new contribution is made where a marginal expected shortfall (MES) model is used to set the FTSE/JSE All-Share Index (ALSI) as a hypothetical bank in the financial sector of the S&P 500. All approaches show weak evidence for a direct systemic risk transfer and therefore indicate that any systemic risk transfer is more likely to take an indirect form through changes in capital flows or interest rates.     

Empirical Regularities of Financial Market Volatility and Good Modelling Process: Developing Countries’ Exchange Rate Markets Perspective

A survey of contemporary literature suggests that empirical studies on developing economies are few or almost non-existent. Engle and Patton (2001, What good is a volatility model. Quantitative Finance, 1, 237–245) as well as Poon (2005, A Practical Guide to Forecasting Financial Market Volatility. New Jersey: Wiley.) suggest that a good volatility model is one that utilizes the empirical regularities of financial market volatility (of which most were observed on industrialized economies markets). This paper uses exchange rate series from Ghana, Mozambique and Tanzania to show that;

1. they are not different from other financial markets as they exhibit most of the empirical regularities including volatility sign asymmetry, non-normal distribution and volatility clustering. It is however observed that the three exchange rate series are very volatile, with induced volatile shocks highly persistent and asymmetric, and extreme prices commonplace;

2. the ARCH technique (which has been well documented to capture these empirical regularities and produce good forecasts) generally produced a good fit to the three exchange rate series when compared with volatility forecasts generated using the EWMA technique. In the simple analysis of a day-ahead volatility forecast abilities of estimated models, it was observed that best fit does not necessarily ensure best forecast.

     

Volatility forecasting: combinations of realized volatility measures and forecasting models

This article examines financial time series volatility forecasting performance. Different from other studies which either focus on combining individual realized measures or combining forecasting models, we consider both. Specifically, we construct nine important individual realized measures and consider combinations including the mean, the median and the geometric means as well as an optimal combination. We also apply a simple AR(1) model, an SV model with contemporaneous dependence, an HAR model and three linear combinations of these models. Using the robust forecasting evaluation measures including RMSE and QLIKE, our empirical evidence from both equity market indices and exchange rates suggests that combinations of both volatility measures and forecasting models improve the forecast performance significantly.     

Evidence for Financial Contagion in Endogenous Volatile Periods

The objective of this study is to analyze cross‐border contagious dynamics in both foreign exchange markets and stock exchange markets. Propagation is analyzed with respect to the transmission of excessive volatility that is endogenously determined. The contagion process is discussed in the context of financial systems, foreign direct investments and trade. Implementing a vector autoregressive‐multivariate generalized autoregressive conditional heteroskedasticity (VAR‐MGARCH) model, we show that country‐specific turbulence in financial markets is able to create unanticipated financial contagion across countries. Diversified trade and financial relations decrease the risk of exposure to contagion from external markets. The world's largest economies, however, play a price‐setter role, and diversification is of secondary importance. Asymmetric transmission of the empirically predicted contagion prevails in the latter case.     

Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

We suggest a Monte Carlo simulation-based unit root test of the purchasing power parity theory for Latin American countries. Under the null hypothesis, we use a Markov regime-switching (MS) model with unit root in the conditional location and MS volatility dynamics. Under the alternative hypothesis, the proposed test incorporates Markov regime-switching autoregressive moving average (MS-ARMA) plus MS volatility dynamics. Under both the null and alternative hypotheses, one of the volatility models estimated is Beta-t-EGARCH, which is a recent dynamic conditional score volatility model. We use data on real effective exchange rate time series for 14 Latin American countries. For each country, we estimate by Monte Carlo simulation the critical values of the unit root test. We provide an economic discussion of the unit root test results and also study the robustness of MS-ARMA plus MS volatility with respect to smooth transition autoregressive models with Fourier function.     

Financial contagion and volatility spillover: An exploration into Indian commodity derivative market

This study measures the extent of financial contagion in the Indian asset markets. In specific it shows the contagion in Indian commodity derivative market vis-à-vis bond, foreign exchange, gold, and stock markets. Subsequently, directional volatility spillover among these asset markets, have been examined. Applying DCC-MGARCH method on daily return of commodity future price index and other asset markets for the period 2006–16, time varying correlation between commodity and other assets are estimated. The degree of financial contagion in commodity derivative market is found to be the largest with stock market and least with the gold market. A generalized VAR based volatility spillover estimation shows that commodity and stock markets are net transmitters of volatility while bond, foreign exchange and gold markets are the net receivers of volatility. Volatility is transmitted to commodity market only from the stock market. Such volatility spillover is found to have time varying nature, showing higher volatility spillover during the Global Financial Crisis and during the period of large rupee depreciation in 2013–14. These results have significant implication for optimal portfolio choice.     

Interest-rate volatility and volatility spillovers in emerging Europe

While many transition economies – particularly those that hope to join the Euro – have seen their economies converge to Europe’s, this process is by no means complete. Considerable macroeconomic volatility persists. This study examines the variability of the short-term nominal interest rates of ten transition economies, finding that eight of them exhibit time-varying volatility that can be modeled as a GARCH or Exponential GARCH process. Incorporating various measures of external volatility into the models, we find that those economies with fixed or managed exchange rates tend to experience more volatility spillovers, particularly from the Eurozone, regardless of the degree of transition. Only Estonia has a fixed exchange rate and remains free of international contagion.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

Volatility and VaR forecasting in the Madrid Stock Exchange

This paper provides an empirical study to assess the forecasting performance of a wide range of models for predicting volatility and VaR in the Madrid Stock Exchange. The models performance was measured by using different loss functions and criteria. The results show that FIAPARCH processes capture and forecast more accurately the dynamics of IBEX-35 returns volatility. It is also observed that assuming a heavy-tailed distribution does not improve models ability for predicting volatility. However, when the aim is forecasting VaR, we find evidence of that the Student’s t FIAPARCH outperforms the models it nests the lower the target quantile.      

Which way does water flow? An econometric analysis of the global price integration of water stocks

Around US$600 billion of investment is desperately needed to address forecasted huge shortages in water supply globally. A number of worldwide investors – so-called water funds – have started to take up this challenge. For these global water investors, knowledge about the extent of integration between the water sectors of financial markets is highly important. According to international portfolio diversification theory, the less (more) integrated markets are, the more (less) benefits there are from international diversification. In this study, we investigate the extent and manner of interdependence among the US, European and Asian water sector of the equity markets based on Vector Autoregression (VAR), Granger causality and impulse response analyses. We find that world water stock market prices are indeed significantly interdependent although this interdependence varies across time periods. Each market quickly responds to shocks from each other and completes its response within 3 days. Hence, for water investors, international diversification that is undertaken just within the water sector will not be beneficial. The result also implies that there is the risk of crossmarket contagion – that is, price volatility spill over across water sectors of different financial markets, and therefore, water authorities in one market should take cognisance of events in other markets.     

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.     

Dynamic conditional score models of degrees of freedom: filtering with score-driven heavy tails

This article extends the quasi-autoregressive (QAR) plus Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) dynamic conditional score (DCS) model. For the new DCS model, the degrees of freedom parameter is time varying and tail thickness of the error term is updated by the conditional score. We compare the performance of QAR plus Beta-t-EGARCH with constant degrees of freedom (benchmark model) and QAR plus Beta-t-EGARCH with time-varying degrees of freedom (extended model). We use data from the Standard and Poor’s 500 (S&P 500) index, and a random sample of its 150 components that are from different industries of the United States (US) economy. For the S&P 500, all likelihood-based model selection criteria support the extended model, which identifies extreme events with significant impact on the US stock market. We find that for 59% of the 150 firms, the extended model has a superior statistical performance. The results suggest that the extended model is superior for those industries, which produce products that people usually are unwilling to cut out of their budgets, regardless of their financial situation. We perform an application to compare the density forecast performance of both DCS models. We perform an application to Monte Carlo value-at-risk for both DCS models.