Time-varying Conditional Variance Research Articles

Stochastic properties of nonlinear locally-nonstationary filters

This article delivers conditions for the existence of a unique stationary, ergodic and φ-mixing invertible solution for nonlinear time-varying parameter models that are locally non-stationary or explosive. The assumptions are different from existing conditions as they do not impose Lipschitz, bounded growth or drift restrictions. Instead we require that the time series contains resetting dynamics. These dynamics are present in time series with sudden changes, such as stock prices with financial bubbles. We explain how our results can be applied to multiple models with time-varying conditional mean and time-varying conditional variance. Additionally, we show the empirical relevance of locally non-stationary models by developing a robust score-driven locally-nonstationary location model that allows us to identify price bubbles. In particular, we revisit the early warning system for Alert of Price Spikes (ALPS) developed by the World Food Programme (WFP, 2014). Our model is able to correctly identify price bubbles both in-sample and out-of-sample. We show that this information can be crucially relevant for the Global Information Early Warning System of the Food and Agriculture Organization (GIEWS) of the United Nations which identifies market bubbles in prices of grains and cereals in order to manage and prevent impending food crises in developing countries.

Understanding the Gold-Inflation Nexusi In Malaysia: Hedge and Safe Haven Perspectives

The main objective of this study is to examine the roles of gold as a hedge or a safe haven against inflation in Malaysia. We propose the standard and quantile techniques in the volatility models, with a time-varying conditional variance of regression residuals based on TGARCH specifications. We found that gold only plays a minor role as a hedge and safe haven against inflation since their returns do not evolve at the same pace as inflation. On the other hand, the rolling regression results reveal that shelter incidents against purchasing power loss only occasionally occur at different times and not consistently across holding periods. We conclude that gold does not have the ability to secure Malaysian investment during high inflationary periods and at all times. Thus, Malaysian investors should hold a well-diversified portfolio to earn sustainable returns and protection from purchasing power loss.

Does Gold Still Shelter Inflation, and, if so, When? Evidence From Four Countries

This study investigates gold as a hedge or a safe haven against inflation in four countries. We propose two standard and quantile techniques in the volatility models, with a time-varying conditional variance of regression residuals based on TGARCH specifications. Gold exhibits considerable evidence of a strong hedge in the US and China. Nevertheless, gold provides shelter at different times and not consistently across countries. With regards to be a safe haven, gold retains its status as a key investment in China. On the other hand, gold only plays a minor role in the UK and India. These findings indicate that gold can secure Chinese investment during the high inflationary periods, while gold is a profitable asset to hold over a long period of time in the US. In contrast, UK and Indian investors should hold a well-diversified portfolio for sustainable return and protection from purchasing power loss.

Data mining: Application of EGARCH dynamic model on the volatility of high-frequency exchange rate data

Dynamic model has always been the focus of data science research. The results of dynamic models with different physical backgrounds vary greatly. Considering the time-varying characteristics and heteroskedasticity of long time exchange rate series, the GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model can be used to depict the pattern of variance fluctuation and clustering over time, and the research on variance can be extended to time-varying conditional variance. In this paper, the EGARCH (Exponential GARCH) model is further adopted to analyze the high-frequency exchange rate data from 2005 to 2017, which can reduce the parameter restrictions of the GARCH model, and at the same time, the characteristics of the exponential ensure the non-negative nature of the estimated variance, so as to predict the volatility more accurately. Moreover, the different effects of positive and negative random shocks on volatility can be analyzed to fully describe the data asymmetry. Finally, we use the clustering algorithm of the EGARCH model for data mining, evaluating the influence of endogenous variables and exogenous events on the RMB exchange rate.

Impact of Macroeconomic Variability on the Stock Market Volatility of Bangladesh

This study investigates the impact of macroeconomic variability on stock market volatility in Bangladesh covering the data ranging from January 2005 to December 2018 by using three steps of analysis. Firstly, the univariate Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model is employed to estimate the time-varying conditional variance series for stock return and macroeconomic fundamentals. In the second phase, the volatility effect of macroeconomic forces on stock return is estimated by using the most recent standardized squared residuals of macroeconomic fundamentals as exogenous variables in the conditional variance equation of stock returns. Finally, Vector Auto Regression (VAR) model is used to examine the possible interaction between macroeconomic forces and stock price. The findings of the study evidence that increased volatility in Consumer Price Index, Treasury Bill Rates, and inflow in Foreign Remittance increases the stock return volatility whilst fluctuations in IP leads to a decrease in stock return volatility. Therefore, the implication of these findings documents that both the stock market and macroeconomic forces becoming interdependent in Bangladesh.

Stand Still and Do Nothing: COVID-19 and Stock Returns and Volatility

We examine the intraday returns and volatility in the US equity market amid the COVID-19 pandemic crisis. Our empirical results suggest an increase in volatility over time with mostly negative returns and higher volatility in the last trading session of the day. Our Univariate analysis reveals structural break(s) since the first trading halt in March 2020 and that failure to account for this may lead to biased and unstable conditional estimates. Allowing for time-varying conditional variance and conditional correlation, our dynamic conditional correlation tests suggest that COVID-19 cases and deaths are jointly related to stock returns and realised volatility.

Bayesian analysis of static and dynamic Hurst parameters under stochastic volatility

Despite the fact that the use of Hurst exponent is well-established, few attempts have been made to embed this parameter in a wider framework to account for stylized facts in stock returns. For example, fat tails and volatility clustering are well known to exist in financial time series, yet a comprehensive model involving the Hurst exponent is unavailable. In this paper, we generalize standard fractional Brownian motion to account for time-varying conditional heteroskedasticity when the Hurst parameter is static or, alternatively, when it also evolves over time, in which case we use a multi-fractional Brownian motion. The generalized model delivers persistence parameters for both time-varying volatility as well as time-varying Hurst exponents. In an application to Eurostoxx-50 (daily data for 1990–2018) we find that once we allow for time variation in the Hurst parameter, the persistence of conditional variances is substantially smaller. Model comparison shows that there are aspects introduced by the Hurst exponent that are not captured by stochastic volatility or other models with time-varying conditional variances. Log-predictive densities are used to compare different models out-of-sample.

Stochastic frontier models with time-varying conditional variances

In this paper we introduce stochastic frontier models in which either the inefficiency or the noise component or both the components follow Generalized AutoRegressive Conditional Heteroskedasticity GARCH(1,1) process. Bayesian estimation of the technology parameters are proposed using a half-normal (exponential) distribution for the inefficiency component, and a normal distribution for the noise component. We show, in simulations, that predictions of inefficiency ignoring the GARCH(1,1) process are not aligned with their true values. We use real panel data on electricity distribution and show how to estimate our proposed model, and predict inefficiency. Moreover, we examine the effect of ignoring GARCH specification on economic measures like input elasticities, technical change and returns to scale. We also provide test for GARCH vs no GARCH models using Bayes factors. Finally, we examine variants of the GARCH family such as the ARCH and EGARCH models and we compared GARCH models of different orders.

The volatility of tourism demand and real effective exchange rates: a disaggregated analysis

Purpose One of the main factors that can impact the cost of holidays to a particular destination is the exchange rate; exchange rate fluctuations impact the overall price of the holiday and should be expected to effect tourism demand. This paper aims to scrutinize the volatility of the real effective exchange rate between the source market relative to the holiday destination and tourism demand volatility, where the influence of disaggregated data is noted. Design/methodology/approach The study uses multivariate conditional volatility regressions to simulate the time-varying conditional variances of international visitor demand and exchange rates for the relatively mature Caribbean tourist destination of Barbados. Data on the country’s main source markets, the UK, the USA and Canada is used, where the decision to disaggregate the analysis by market allows the authors to contribute to policymaking, particularly the future of tourism marketing. Findings The volatility models used in the paper suggests that shocks to total arrivals, as well as the USA and UK markets tend to die out relatively quickly. Asymmetric effects were observed for total arrivals, mainly due to the combination of the different source markets and potential evidence of Butler’s (1980) concept of a tourist area’s cycle of growth. The results also highlight the significance of using disaggregated tourism demand models to simulate volatility, as aggregated models do not adequately capture source market specific shocks, due to the potential model misspecification. Exchange rate volatility is postulated to have resulted in the greater utilization of packaged tours in some markets, while the effects of the market’s online presence moderates the impact of exchange rate volatility on tourist arrivals. Markets should also explore the potential of attracting higher numbers of older tourist, as this group may have higher disposable incomes, thereby mitigating the influence of exchange rate volatility. Research limitations/implications Some of the explanatory variables were not available on a high enough frequency and proxies had to be used. However, the approach used was consistent with other papers in the literature. Practical implications The results from the paper suggest that the effects of exchange rate volatility in key source markets were offset by non-price factors in some markets and the existence of the exchange rate peg in others. In particular, the online presence of the destination was one of those non-price factors highlighted as being important. Originality/value In most theoretical models of tourism demand, disaggregation is not normally considered a significant aspect of the model. This paper contributes to the literature by investigating the impact real effective exchange rate volatility has on tourism demand at a disaggregated source country level. The approach highlights the importance of modeling tourism demand at a disaggregated level and provides important perspective from a mature small island destination.

Statistical Analysis of Price Volatility of Agricultural Commodities Traded at the Ethiopian Commodity Exchange (ECX) Using Multiplicative GARCH-MIDAS Two-component Model

We applied multiplicative GARCH-MIDAS two component models for price return volatility of selected commodities traded at the Ethiopian commodity exchange (ECX). Unlike the ‘traditional’ generalized autoregressive conditional heteroscedasticity (GARCH) family models, GARCH-MIDAS component model can capture the time-varying conditional as well as unconditional volatilities, and accommodates macroeconomic variables observed at different frequencies through mixed interval data sampling (MIDAS) specification. The results of our specification tests revealed the existence of both time-varying conditional and unconditional variance. The fitted GARCH-MIDAS component models showed that realized volatility, inflation rate and fuel oil price have had an increasing effect on the price volatility of the commodities under consideration, while real effective exchange rate (REER) had the opposite effect. Furthermore, mean square error (MSE), mean absolute error (MAE) and Diebold and Mariano (DM) test were used for evaluating and comparing the forecasting ability of GARCH-MIDAS component models against standard GARCH models. The results revealed that GARCH-MIDAS component models outperformed the standard GARCH model for high-frequency data.

DOES GOLD INVESTMENT OFFER PROTECTION AGAINST STOCK MARKET LOSSES? EVIDENCE FROM FIVE COUNTRIES

This study aims to analyze the characteristics of gold as a diversifier, a hedge or a safe haven against the stock market collapse in five countries. We propose the standard and quantile techniques in the volatility models, with the time-varying conditional variance of the regression residuals based on the TGARCH specifications. Gold exhibits considerable evidence of the strong hedge in India and the US and diversified role in China. With regards to its role as a safe haven, gold retains its status as a key investment particularly in a country where gold has a preeminent cultural role, i.e., India, as well as in the US and the UK. On the contrary, gold only plays a minor role in emerging markets like in Malaysia. Therefore, investors in India and the US can use gold to protect against losses in the stock market at all times, whereas in the UK, gold is only viewed as a profitable asset to own during the stock market collapse. Contrariwise, Chinese investors should hold a well-diversified portfolio to earn sustainable returns and offer protection against the stock market collapse. We conclude that the recent worldwide financial crises have increased the investment demand for gold over the last 17 years at least.

Option Pricing with Arima-Garch Models of Underlying Asset Returns

ARIMA-GARCH models are used in the analysis of financial series with time-varying conditional variance. A calibrated model of underlying asset returns allows computing all derivatives of the original money flow. The article describes an ARIMA-GARCH model of the underlying asset returns, the forms of ARIMA- and GARCH-components, and the corresponding stationarity conditions. A survey of the results on option pricing by ARIMA-GARCH and GARCH models of underlying asset returns is presented.

Mutual information identifies spurious Hurst phenomena in resting state EEG and fMRI data.

Long-range memory in time series is often quantified by the Hurst exponent H, a measure of the signal's variance across several time scales. We analyze neurophysiological time series from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) resting state experiments with two standard Hurst exponent estimators and with the time-lagged mutual information function applied to discretized versions of the signals. A confidence interval for the mutual information function is obtained from surrogate Markov processes with equilibrium distribution and transition matrix identical to the underlying signal. For EEG signals, we construct an additional mutual information confidence interval from a short-range correlated, tenth-order autoregressive model. We reproduce the previously described Hurst phenomenon (H>0.5) in the analytical amplitude of alpha frequency band oscillations, in EEG microstate sequences, and in fMRI signals, but we show that the Hurst phenomenon occurs without long-range memory in the information-theoretical sense. We find that the mutual information function of neurophysiological data behaves differently from fractional Gaussian noise (fGn), for which the Hurst phenomenon is a sufficient condition to prove long-range memory. Two other well-characterized, short-range correlated stochastic processes (Ornstein-Uhlenbeck, Cox-Ingersoll-Ross) also yield H>0.5, whereas their mutual information functions lie within the Markovian confidence intervals, similar to neural signals. In these processes, which do not have long-range memory by construction, a spurious Hurst phenomenon occurs due to slow relaxation times and heteroscedasticity (time-varying conditional variance). In summary, we find that mutual information correctly distinguishes long-range from short-range dependence in the theoretical and experimental cases discussed. Our results also suggest that the stationary fGn process is not sufficient to describe neural data, which seem to belong to a more general class of stochastic processes, in which multiscale variance effects produce Hurst phenomena without long-range dependence. In our experimental data, the Hurst phenomenon and long-range memory appear as different system properties that should be estimated and interpreted independently.

Blind Source Separation Using Temporal Correlation, Non-Gaussianity and Conditional Heteroscedasticity

Independent component analysis separates latent sources from a linear mixture by assuming sources are statistically independent. In real world applications, hidden sources are usually non-Gaussian and have dependence among samples. In such case, both attributes should be considered jointly to obtain a successful separation. To capture sample dependence, a latent source is sometimes modeled by autoregressive or moving average models with an independent and identically distributed error or residual. However, these models are limited by assuming only linear dependence among a source’s samples. This paper proposes a new blind source separation algorithm based on an autoregressive-autoregressive conditional heteroscedasticity (AR-ARCH) model, which captures linear correlations, non-Gaussianity, and squared residuals’ dependence. The AR part of the AR-ARCH model captures the correlation among samples. The ARCH part of the model captures the non-Gaussianity and nonlinear dependence among samples. The ARCH model also assumes the time-varying conditional variances for sources. We derive the Cramer Rao lower bound (CRLB) for the mixing matrix based on the AR-ARCH model. We perform simulations on both synthetic and real data. The results show that the proposed method outperforms the baseline algorithms especially for a small number of samples and approaches the CRLB.

Within and Cross Volatility Contagion Effects among Stock, Crude and Forex Returns: Empirical Evidence from Five Emerging Economies

The paper examines the spillover effects of return volatility among stock market index, foreign exchange market and WTI crude oil market across five emerging nations. Here a Trivariate Diagonal BEKK-GARCH model is used to estimate the time-varying conditional variance and to test the own-volatility spillover effects of returns among the three underlying variables. We find that significant own volatility spillover exists in the WTI returns followed by that of stock returns and forex returns. Further, fluctuations in WTI returns exert considerable influence over the stock market volatilities. The lagged variance of the variables as well as their lagged squared residuals from the mean equation has a positive and significant impact on the current volatility in most cases. The findings of the study are of pertinent importance to financiers, economists, investors and policymakers.

Modeling volatility in heat rate variability.

Modeling Heart Rate Variability (HRV) data has become important for clinical applications and as a research tool. These data exhibit long memory and time-varying conditional variance (volatility). In HRV, volatility is traditionally estimated by recursive least squares combined with short memory AutoRegressive (AR) models. This work considers a parametric approach based on long memory Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with heteroscedastic errors. To model the heteroscedasticity nonlinear Generalized Autoregressive Conditionally Heteroscedastic (GARCH) and Exponential Generalized Autoregressive Conditionally Heteroscedastic (EGARCH) models are considered. The latter are necessary to model empirical characteristics of conditional volatility such as clustering and asymmetry in the response, usually called leverage in time series literature. The ARFIMA-EGARCH models are used to capture and remove long memory and characterize conditional volatility in 24 hour HRV recordings from the Noltisalis database.

Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances

We develop a finite-sample procedure to test the mean-variance efficiency and spanning hypotheses, without imposing any parametric assumptions on the distribution of model disturbances. In so doing, we provide an exact distribution-free method to test uniform linear restrictions in multivariate linear regression models. The framework allows for unknown forms of nonnormalities as well as time-varying conditional variances and covariances among the model disturbances. We derive exact bounds on the null distribution of joint F statistics to deal with the presence of nuisance parameters, and we show how to implement the resulting generalized nonparametric bounds tests with Monte Carlo resampling techniques. In sharp contrast to the usual tests that are not even computable when the number of test assets is too large, the power of the proposed test procedure potentially increases along both the time and cross-sectional dimensions.

Dynamic conditional correlation multiplicative error processes

We introduce a dynamic model for multivariate processes of (non-negative) high-frequency trading variables revealing time-varying conditional variances and correlations. Modeling the variables' conditional mean processes using a multiplicative error model, we map the resulting residuals into a Gaussian domain using a copula-type transformation. Based on high-frequency volatility, cumulative trading volumes, trade counts and market depth of various stocks traded at the NYSE, we show that the proposed transformation is supported by the data and allows capturing (multivariate) dynamics in higher order moments. The latter are modeled using a DCC-GARCH specification. We suggest estimating the model by composite maximum likelihood which is sufficiently flexible to be applicable in high dimensions. Strong empirical evidence for time-varying conditional (co-)variances in trading processes supports the usefulness of the approach. Taking these higher-order dynamics explicitly into account significantly improves the goodness-of-fit and out-of-sample forecasts of the multiplicative error model.

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.

The role of uncertainty in the term structure of interest rates: A GARCH-ATSM approach

This article examines the roles of uncertainties regarding various macro-variables in determining risk premiums of bond yields. We develop a multivariate GARCH-VAR to quantify uncertainties regarding inflation, real activities and monetary policy as time-varying conditional variances. We jointly estimate the multivariate GARCH and no-arbitrage bond pricing equations using a maximum likelihood method. The results indicate that the inflation uncertainty is the largest contributor to the dynamics of long-term yields since the 1980s, while the monetary policy uncertainty also plays noticeable roles.