CBOE Volatility Index Forecasting under COVID-19: An Integrated BiLSTM-ARIMA-GARCH Model

After the outbreak of COVID-19, the global economy entered a deep freeze. This observation is supported by the Volatility Index (VIX), which reflects the market risk expected by investors. In the current study, we predicted the VIX using variables obtained from the sentiment analysis of data on Twitter posts related to the keyword “COVID-19,” using a model integrating the bidirectional long-term memory (BiLSTM), autoregressive integrated moving average (ARIMA) algorithm, and generalized autoregressive conditional heteroskedasticity (GARCH) model. The Linguistic Inquiry and Word Count (LIWC) program and Valence Aware Dictionary for Sentiment Reasoning (VADER) model were utilized as sentiment analysis methods. The results revealed that during COVID-19, the proposed integrated model, which trained both the Twitter sentiment values and historical VIX values, presented better results in forecasting the VIX in time-series regression and direction prediction than those of the other existing models.     

A generalized Dynamic Conditional Correlation model for portfolio risk evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle [R.F. Engle, Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal of Business and Economic Statistics 20 (2002) 339–350] and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al.[L. Cappiello, R.F. Engle, K. Sheppard, Asymmetric dynamics in the correlations of global equity and bond returns, Journal of Financial Econometrics 25 (2006) 537–572]. The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. [M. Billio, M. Caporin, M. Gobbo, Flexible dynamic conditional correlation multivariate GARCH for asset allocation, Applied Financial Economics Letters 2 (2006) 123–130] and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation.     

Testing the martingale difference hypothesis using integrated regression functions

An omnibus test for testing a generalized version of the martingale difference hypothesis (MDH) is proposed. This generalized hypothesis includes the usual MDH, testing for conditional moments constancy such as conditional homoscedasticity (ARCH effects) or testing for directional predictability. A unified approach for dealing with all of these testing problems is proposed. These hypotheses are long standing problems in econometric time series analysis, and typically have been tested using the sample autocorrelations or in the spectral domain using the periodogram. Since these hypotheses cover also nonlinear predictability, tests based on those second order statistics are inconsistent against uncorrelated processes in the alternative hypothesis. In order to circumvent this problem pairwise integrated regression functions are introduced as measures of linear and nonlinear dependence. The proposed test does not require to chose a lag order depending on sample size, to smooth the data or to formulate a parametric alternative model. Moreover, the test is robust to higher order dependence, in particular to conditional heteroskedasticity. Under general dependence the asymptotic null distribution depends on the data generating process, so a bootstrap procedure is considered and a Monte Carlo study examines its finite sample performance. Then, the martingale and conditional heteroskedasticity properties of the Pound/Dollar exchange rate are investigated.     

On pseudo maximum likelihood estimation for multivariate time series models with conditional heteroskedasticity

We consider a general multivariate conditional heteroskedastic model under a conditional distribution that is not necessarily normal. This model contains autoregressive conditional heteroskedastic (ARCH) models as a special class. We use the pseudo maximum likelihood estimation method and derive a new estimator of the asymptotic variance matrix for the pseudo maximum likelihood estimator. We also study four special cases in this class, which are conditional heteroskedastic autoregressive moving-average models, regression models with ARCH errors, models with constant conditional correlations, and ARCH in mean models.     

Volatility dynamics of the US business cycle: A multivariate asymmetric GARCH approach

Most empirical investigations of the business cycles in the United States have excluded the dimension of asymmetric conditional volatility. This paper analyses the volatility dynamics of the US business cycle by comparing the performance of various multivariate generalised autoregressive conditional heteroskedasticity (GARCH) models. In particular, we propose two bivariate GARCH models to examine the evidence of volatility asymmetry and time-varying correlations concurrently, and then apply the proposed models to five sectors of Industrial Production of the United States. Our findings provide strong evidence of asymmetric conditional volatility in all sectors, and some support of time-varying correlations in various sectoral pairs. This has important policy implications for government to consider the effective countercyclical measures during recessions.     

Improving prediction of exchange rates using Differential EMD

Volatility is a key parameter when measuring the size of errors made in modelling returns and other financial variables such as exchanged rates. The autoregressive moving-average (ARMA) model is a linear process in time series; whilst in the nonlinear system, the generalised autoregressive conditional heteroskedasticity (GARCH) and Markov switching GARCH (MS-GARCH) have been widely applied. In statistical learning theory, support vector regression (SVR) plays an important role in predicting nonlinear and nonstationary time series variables. In this paper, we propose a new algorithm, differential Empirical Mode Decomposition (EMD) for improving prediction of exchange rates under support vector regression (SVR). The new algorithm of Differential EMD has the capability of smoothing and reducing the noise, whereas the SVR model with the filtered dataset improves predicting the exchange rates. Simulations results consisting of the Differential EMD and SVR model show that our model outperforms simulations by a state-of-the-art MS-GARCH and Markov switching regression (MSR) models.     

A consistent nonparametric Bayesian procedure for estimating autoregressive conditional densities

This article proposes a Bayesian infinite mixture model for the estimation of the conditional density of an ergodic time series. A nonparametric prior on the conditional density is described through the Dirichlet process. In the mixture model, a kernel is used leading to a dynamic nonlinear autoregressive model. This model can approximate any linear autoregressive model arbitrarily closely while imposing no constraint on parameters to ensure stationarity. We establish sufficient conditions for posterior consistency in two different topologies. The proposed method is compared with the mixture of autoregressive model [Wong and Li, 2000. On a mixture autoregressive model. J. Roy. Statist. Soc. Ser. B 62(1), 91-115] and the double-kernel local linear approach [Fan et al., 1996. Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika 83, 189-206] by simulations and real examples. Our method shows excellent performances in these studies.     

Analysing the performance of bootstrap neural tests for conditional heteroskedasticity in ARCH-M models

The robustness against strongly non-linear forms for the conditional variance of tests for detecting conditional heteroskedasticity using both artificial neural network techniques and bootstrap methods combined, is analysed in the context of ARCH-M models. The size and the power properties in small samples of these tests are examined by using out Monte-Carlo experiments with various standard and non-standard models of conditional heteroskedasticity. The P value functions are explored in order to select particularly problematic cases. Graphical presentations, based on the principle of size correction, are used for presenting the true power of the tests, rather than a spurious nominal power as it is usually made in the literature. In addition, graphics linking the process dynamics with the heteroskedasticity forms are shown for analysing in which circumstances the neural networks are effective.     

The influence of ARIMA-GARCH parameters in feed forward neural networks prediction

The objective of this article is to find out the influence of the parameters of the ARIMA-GARCH models in the prediction of artificial neural networks (ANN) of the feed forward type, trained with the Levenberg–Marquardt algorithm, through Monte Carlo simulations. The paper presents a study of the relationship between ANN performance and ARIMA-GARCH model parameters, i.e. the fact that depending on the stationarity and other parameters of the time series, the ANN structure should be selected differently. Neural networks have been widely used to predict time series and their capacity for dealing with non-linearities is a normally outstanding advantage. However, the values of the parameters of the models of generalized autoregressive conditional heteroscedasticity have an influence on ANN prediction performance. The combination of the values of the GARCH parameters with the ARIMA autoregressive terms also implies in ANN performance variation. Combining the parameters of the ARIMA-GARCH models and changing the ANN’s topologies, we used the Theil inequality coefficient to measure the prediction of the feed forward ANN.     

Bayesian estimation of the Gaussian mixture GARCH model

Bayesian inference and prediction for a generalized autoregressive conditional heteroskedastic (GARCH) model where the innovations are assumed to follow a mixture of two Gaussian distributions is performed. The mixture GARCH model can capture the patterns usually exhibited by many financial time series such as volatility clustering, large kurtosis and extreme observations. A Griddy-Gibbs sampler implementation is proposed for parameter estimation and volatility prediction. Bayesian prediction of the Value at Risk is also addressed providing point estimates and predictive intervals. The method is illustrated using the Swiss Market Index.     

On Asymmetric Market Model with Heteroskedasticity and Quantile Regression

The capital asset pricing model is widely used in financial risk management due to its simplicity and utility in a variety of situations. Many of the constructs of this market model are widely used in investment, but the simple assumptions of a constant beta coefficient and variance in the original market model are not convincing from the empirical viewpoint. In this paper we propose a general asymmetric market model embedding both the leverage effect of market news and the previous return to express the instability of beta and the error with heteroskedasticity to capture the time-varying conditional variance. Because extreme values occur quite frequently in financial markets, the quantile regression is employed to explore the different behaviors in the market beta and lagged autoregressive effect for different quantile levels. We analyze fifteen stocks, which are heavily traded in the Dow Jones Industrial Average, to demonstrate the empirical performance of our methodology. The evidence indicates that each market beta and impact of negative news vary with different quantile levels, capturing different states of market conditions.     

Chaotic analysis of predictability versus knowledge discovery techniques: case study of the Polish stock market

Increasing evidence over the past decade indicates that financial markets exhibit nonlinear dynamics in the form of chaotic behavior. Traditionally, the prediction of stock markets has relied on statistical methods including multivariate statistical methods, autoregressive integrated moving average models and autoregressive conditional heteroskedasticity models. In recent years, neural networks and other knowledge techniques have been applied extensively to the task of predicting financial variables.
This paper examines the relationship between chaotic models and learning techniques. In particular, chaotic analysis indicates the upper limits of predictability for a time series. The learning techniques involve neural networks and case–based reasoning. The chaotic models take the form of R/S analysis to measure persistence in a time series, the correlation dimension to encapsulate system complexity, and Lyapunov exponents to indicate predictive horizons. The concepts are illustrated in the context of a major emerging market, namely the Polish stock market.     

Exchange rate prediction using hybrid neural networks and trading indicators

This paper describes a hybrid model formed by a mixture of various regressive neural network models, such as temporal self-organising maps and support vector regressions, for modelling and prediction of foreign exchange rate time series. A selected set of influential trading indicators, including the moving average convergence/divergence and relative strength index, are also utilised in the proposed method. A genetic algorithm is applied to fuse all the information from the mixture regression models and the economical indicators. Experimental results and comparisons show that the proposed method outperforms the global modelling techniques such as generalised autoregressive conditional heteroscedasticity in terms of profit returns. A virtual trading system is built to examine the performance of the methods under study.     

Dual multivariate auto-regressive modeling in state space for temporal signal separation

Many existing independent component analysis (ICA) approaches result in deteriorated performance in temporal source separation because they have not taken into consideration of the underlying temporal structure of sources. In this paper, we model temporal sources as a general multivariate auto-regressive (AR) process whereby an underlying multivariate AR process in observation space is obtained. In this dual AR modeling, the mixing process from temporal sources to observations is the same as the mixture from the nontemporal residuals of the source AR (SAR) process to that of the observation AR (OAR) process. We can therefore avoid the source temporal effects in performing ICA by learning the demixing system on the independently distributed OAR residuals rather than the time-correlated observations. Particularly, we implement this approach by modeling each source signal as a finite mixture of generalized autoregressive conditional heteroskedastic (GARCH) process. The adaptive algorithms are proposed to extract the OAR residuals appropriately online, together with learning the demixing system via a nontemporal ICA algorithm. The experiments have shown its superior performance on temporal source separation.     

A combined Independent Component Analysis–Neural Network model for forecasting exchange rate variation

The currency market is one of the most efficient markets, making it very difficult to predict future prices. Several studies have sought to develop more accurate models to predict the future exchange rate by analyzing econometric models, developing artificial intelligence models and combining both through the creation of hybrid models. This paper proposes a hybrid model for forecasting the variations of five exchange rates related to the US Dollar: Euro, British Pound, Japanese Yen, Swiss Franc and Canadian Dollar. The proposed model uses Independent Component Analysis (ICA) to deconstruct the series into independent components as well as neural networks (NN) to predict each component. This method differentiates this study from previous works where ICA has been used to extract the noise of time series or used to obtain explanatory variables that are then used in forecasting. The proposed model is then compared to random walk, autoregressive and conditional variance models, neural networks, recurrent neural networks and long–short term memory neural networks. The hypothesis of this study supposes that first deconstructing the exchange rate series and then predicting it separately would produce better forecasts than traditional models. By using the mean squared error and mean absolute percentage error as a measures of performance and Model Confidence Sets to statistically test the superiority of the proposed model, our results showed that this model outperformed the other models examined and significantly improved the accuracy of forecasts. These findings support this model’s use in future research and in decision-making related to investments.     

Computational intelligence approaches and linear models in case studies of forecasting exchange rates

Artificial neural networks and fuzzy systems, have gradually established themselves as a popular tool in approximating complicated nonlinear systems and time series forecasting. This paper investigates the hypothesis that the nonlinear mathematical models of multilayer perceptron and radial basis function neural networks and the Takagi–Sugeno (TS) fuzzy system are able to provide a more accurate out-of-sample forecast than the traditional auto regressive moving average (ARMA) and ARMA generalized auto regressive conditional heteroskedasticity (ARMA-GARCH) linear models. Using series of Brazilian exchange rate (R$/US$) returns with 15 min, 60 min and 120 min, daily and weekly basis, the one-step-ahead forecast performance is compared. Results indicate that forecast performance is strongly related to the series’ frequency and the forecasting evaluation shows that nonlinear models perform better than their linear counterparts. In the trade strategy based on forecasts, nonlinear models achieve higher returns when compared to a buy-and-hold strategy and to the linear models.     

SEMIFARMA-HYGARCH Modeling of Dow Jones Return Persistence

This paper analyzes the cyclical behavior of Dow Jones by testing the existence of long memory through a new class of semiparametric ARFIMA models with HYGARCH errors (SEMIFARMA-HYGARCH); this class includes nonparametric deterministic trend, stochastic trend, short-range and long-range dependence and long memory heteroscedastic errors. We study the daily returns of the Dow Jones from 1896 to 2006. We estimate several models and we find that the coefficients of the SEMIFARMA-HYGARCH model, including long memory coefficients for the equations of the mean and the conditional variance, are highly significant. The forecasting results show that the informational shocks have permanent effects on volatility and the SEMIFARMA-HYGARCH model has better performance over some other models for long and/or short horizons. The predictions from this model are also better than the predictions of the random walk model; accordingly, the weak efficiency assumption of financial markets seems violated for Dow Jones returns studied over a long period.     

Computational Tools for the Analysis of Market Risk

The estimation and management of risk is an important and complex task faced by market regulators and financial institutions. Accurate and reliable quantitative measures of risk are needed to minimize undesirable effects on a given portfolio fromlarge fluctuations in market conditions. To accomplish this, a series of computational tools has beendesigned, implemented, and incorporated into MatRisk, an integratedenvironment for risk assessment developed in MATLAB. Besides standard measures, such as Value at Risk(VaR), the application includes other more sophisticated risk measures that address the inability of VaRproperly to characterize the structure of risk. Conditionalrisk measures can also be estimated for autoregressive models with heteroskedasticity, including some novel mixture models. These tools are illustrated with a comprehensive risk analysis of the Spanish IBEX35 stock index.     

Modeling Hong Kong’s stock index with the Student t-mixture autoregressive model

It is well known that financial returns are usually not normally distributed, but rather exhibit excess kurtosis. This implies that there is greater probability mass at the tails of the marginal or conditional distribution. Mixture-type time series models are potentially useful for modeling financial returns. However, most of these models make the assumption that the return series in each component is conditionally Gaussian, which may result in underestimates of the occurrence of extreme financial events, such as market crashes. In this paper, we apply the class of Student t-mixture autoregressive (TMAR) models to the return series of the Hong Kong Hang Seng Index. A TMAR model consists of a mixture of g autoregressive components with Student t-error distributions. Several interesting properties make the TMAR process a promising candidate for financial time series modeling. These models are able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time-varied from short- to long-tailed or from unimodal to multi-modal. The use of Student t-distributed errors in each component of the model allows for conditional leptokurtic distribution, which can account for the commonly observed unconditional kurtosis in financial data.     

Bayesian Unit Root Test in Double Threshold Heteroskedastic Models

This paper aims to detect the presence of local non-stationarity of nonlinear autoregressive processes with heteroskedastic errors. A Bayesian test is developed to test for the unit root in multi-regime threshold autoregression with heteroskedasticity. To implement a test, a posterior odds analysis is proposed. Particularly, a mixture prior for the autoregressive coefficient is used to alleviate the identifiability problem that occurs when time series has unit roots. The proposed method achieves a reliable inference despite of the non-integrability problem in the likelihood function. A simulation study and two real data analysis are conducted for illustration. This paper successfully proves the proposed model can accommodate different threshold values to cope with local non-stationarity and in addition, captures discrete time-varying properties.