Conditional Variance Equation Research Articles

Modelling Mixed-Frequency Time Series with Structural Change

AbstractPredictive ability of time series models is easily compromised in the presence of structural breaks, common among financial and economic variables amidst market shocks and policy regime shifts. We address this problem by estimating a semiparametric mixed-frequency model, that incorporate high frequency data either in the conditional mean or the conditional variance equation. The inclusion of high frequency data through non-parametric smoothing functions complements the low frequency data to capture possible non-linear relationships triggered by the structural change. Simulation studies indicate that in the presence of structural change, the varying frequency in the mean model provides improved in-sample fit and superior out-of-sample predictive ability relative to low frequency time series models. These hold across a broad range of simulation settings, such as varying time series lengths, nature of structural break points, and temporal dependencies. We illustrate the relative advantage of the method in predicting stock returns and foreign exchange rates in the case of the Philippines.

The impact of the covid-19 pandemic on the stock markets of some countries in the MENA region: An assessment with GARCH modeling

This study examines the impact of the COVID-19 pandemic on stock market volatility for stock indices of a few MENA countries. The analysis consists of several elements: first, we assess the impact of this infectious disease on the standard deviations of stock market variables; second, we analyze the influence of the number of new daily cases and the number of new daily deaths on the standard deviations of these returns; and third, we assess the impact of the coronavirus on stock market volatility for these market variables using GARCH models. We find that the minimum value for most indices occurred in March 2020. Additionally, the results of the regression analysis reveal that the COVID-19 dummy variable, the number of daily new cases, and the number of new daily deaths have all had a significant negative impact on stock market volatility. Finally, the GARCH model reveals that the coefficients of COVID-19 pandemic in the conditional variance equation had a significant positive impact on the conditional variance for stock indices, further indicating that the COVID-19 outbreak increased market volatility.

Reprint of: Generalized Autoregressive Conditional Heteroskedasticity

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.

The impact of us elections on the dollar’s exchange rate

This paper explores the effect of U.S. domestic politics on the behaviour of international currency markets. Specifically, for the first time in the literature, we gauge the impact of a divided government on the exchange rate volatility of five currencies: the Japanese yen, the Canadian dollar, the British pound, the Mexican peso, and the euro. At the same time, we control for the impact of political and macroeconomic factors. A GARCH methodology has been adopted for this objective, using weekly data from 2000 to 2021. The evidence suggests that the partisan and divided government variables significantly impact the conditional variance equation, whilst the observed reduced levels of exchange rate volatility during a Democrat presidency run counter to prior studies on partisanship. In addition, exchange rate volatility seems to increase one month before an election and during periods of divided government. Given the nascent evidence, we argue that U.S. politics are instrumental in affecting global financial markets.

COVID-19 related stringencies and financial market volatility: sectoral evidence from India

PurposeThis study aims to examine the impact of the stringency of COVID-19 protocols on the volatility of sectoral indices during the period 03:2020–05:2021. Specifically, this study investigates the role of economic disturbances on sectoral volatility by applying a range of conditional volatility techniques.Design/methodology/approachFor this analysis, two approaches were adopted. The first approach considers COVID stringency as a factor in the conditional variance equation of sectoral indices. In contrast, the second approach considers the stringency indicator as a possible determinant of their estimated conditional volatility.FindingsResults show that the stringency of the protocols throughout the pandemic phase led to an instantaneous spike followed by a gradual decrease in estimated volatility of all the sectoral indices except pharma and health care. Specific sectors such as bank, FMCG, consumer durables, financial services, IT, media and private banks respond to protocols expeditiously compared to other sectors.Originality/valueThe key contribution of this study to the existing literature is the innovative approach. The inclusion of the COVID stringency index as a regressor in the variance equation of the conditional volatility techniques was a distinctive approach for assessing the volatility dynamics with the stringency of COVID protocols. Furthermore, this study also adopts an alternative approach that estimates the conditional volatility of the indices and then tests the effect of the stringencies on estimated volatility in a regression framework.

Augmenting the Realized-GARCH: the role of signed-jumps, attenuation-biases and long-memory effects

Abstract This paper extends the Realized-GARCH framework, by allowing the conditional variance equation to incorporate exogenous variables related to intra-day realized measures. The choice of these measures is motivated by the so-called heterogeneous auto-regressive (HAR) class of models. Our augmented model is found to outperform both the Realized-GARCH and the various HAR models in terms of in-sample fitting and out-of-sample forecasting accuracy. The new model specification is examined under alternative parametric density assumptions for the return innovations. Non-normality seems to be very important for filtering the return innovations to which variance responds and helps significantly upon the prediction performance of the suggested model.

Pay Senedi Endeksleri ile Endeks Vadeli İşlemler Arasındaki Volatilite İlişkisi: Türkiye ve Dünya Örnekleri Arasında Karşılaştırmalı Analiz

Bu çalışmanın konusunu, pay senedi endeksleri ile bu endekslerin dayanak varlık olduğu vadeli işlemler arasındaki volatilite ilişkisinin analizi oluşturmaktadır. Bu çalışma, spot endeksler ile endeks vadeli işlemler arasındaki volatilite ilişkisinin yönünü tespit etmeyi amaçlamaktadır. Bu çalışmanın temel amacı, Türkiye örneğinde yüksek işlem hacmi göz önünde bulundurularak BIST 30 endeksi ve BIST 30 endeks vadeli işlemleri arasındaki volatilite ilişkisinin ekonometrik yöntemlerle incelenmesi, elde edilen verilerin Dünya’daki önemli endekslerle karşılaştırılması ve analiz sonuçlarının değerlendirilmesidir. Bu amaçla, BIST 30 endeksi ve BIST 30 endeks vadeli işlemleri arasında herhangi bir volatilite ilişkisi olup olmadığı hususu ekonometrik yöntemlerle analiz edilerek, Dünya örnekleri ile kıyaslamalar yapılmıştır. Dünyanın gelişmiş borsalarında işlem gören DAX 30 ve S&P 500 spot piyasa endeksleri ile DAX 30 ve S&P 500 endeks vadeli işlemleri arasındaki volatilite ilişkisine bakılarak Türkiye örneği ile karşılaştırmalar yapılmıştır. Getiri ve işlem hacimlerine ilişkin oynaklık tahminleri için Otoregresif Koşullu Değişen Varyans (ARCH) Modelleri kullanıldığından, spot endeksler ile endeks vadeli işlemler arasındaki volatilite ilişkisi GARCH, TARCH, EGARCH ve PARCH modelleri ile analiz edilmiştir. Uygulama aşamasında elde edilen bulgular, 2006-2021 yıllarını kapsayan dönemde her iki piyasa arasında çift yönlü volatilite ilişkisi olduğunu ortaya çıkarmıştır. Ancak bu çift yönlü ilişki, koşullu varyans denklemindeki açıklayıcı değişkenlerinin katsayılarının çok küçük olması nedeniyle istatistiksel olarak çok önem arz etmemektedir.

Effects of Multiple Financial News Shocks on Tourism Demand Volatility Modelling and Forecasting

Even though both symmetric and asymmetric conceptions of news impacts are well-established in the disciplines of economics and financial markets, the effects of combining multiple news shocks on the volatility of tourism demand have not yet been delved into or gauged in any tourist destination. This work hypothesises and verifies that the news impact curve (NIC), conditional heteroscedastic volatility models, and multiple news shocks are suitable for forecasting the volatility of the Malaysian tourist industry. Among them, three primarily volatility models (GARCH, EGARCH, and GJRGARCH) are used in conjunction with five financial news shocks (FFNSs), namely the Kuala Lumpur Composite Index (KLCI), the United States Dollar Index (DXY), the stock performance of 500 large companies listed on stock exchanges (S&P500), Crude Oil (CO), and Gold Price (GP). Among the most significant findings of this study are the demonstration of monthly seasonality using conditional mean equations, asymmetry effects in EGARCH-FFNSs, and GJRGARCH-FFNSs models in conditional variance equations and 50 NICs, and the GARCH-FFNSs model’s evaluation of the persistence influence of news shocks on monthly visitor arrivals in Malaysia. The GJRGARCH-FFNSs model is the best model for Malaysian tourism demand volatility forecasting accuracy. Furthermore, KLCI and Gold Price have the most substantial impact on the number of tourists to Malaysia. In addition, it should be emphasised that the methodological framework utilised in this study can be a useful tool for creating and forecasting the performance of symmetry and asymmetry impacts on tourism demand volatility.

Forecasting electricity prices with expert, linear, and nonlinear models

This paper compares several models for forecasting regional hourly day-ahead electricity prices, while accounting for fundamental drivers. Forecasts of demand, in-feed from renewable energy sources, fossil fuel prices, and physical flows are all included in linear and nonlinear specifications, ranging in the class of ARFIMA-GARCH models—hence including parsimonious autoregressive specifications (known as expert-type models). The results support the adoption of a simple structure that is able to adapt to market conditions. Indeed, we include forecasted demand, wind and solar power, actual generation from hydro, biomass, and waste, weighted imports, and traditional fossil fuels. The inclusion of these exogenous regressors, in both the conditional mean and variance equations, outperforms in point and, especially, in density forecasting when the superior set of models is considered. Indeed, using the model confidence set and considering northern Italian prices, predictions indicate the strong predictive power of regressors, in particular in an expert model augmented for GARCH-type time-varying volatility. Finally, we find that using professional and more timely predictions of consumption and renewable energy sources improves the forecast accuracy of electricity prices more than using predictions publicly available to researchers.

Effects of Conditional Oil Volatility on Exchange Rate and Stock Markets Returns

The underlying volatility at a given time is called conditional volatility at this particular time and is modeled by various ARMA-GARCH conditional variance equations (GARCH, EGARCH, GJR, APARCH, IGARCH). How important are oil price fluctuations and oil price volatility in foreign exchange markets and stock markets? What is the nature of the relationship between these three markets? What are the political implications if volatility, using appropriate models to determine, turns out to be important? We evaluate these questions empirically, using the specification of Narayan and Narayan (2010). This specification, in our paper, deals with the determination of volatility appropriate models, based on information criteria, of the ARMA-ARCH family conditional volatility of oil returns using daily data for each country independently (i), and revolve around an analysis of the effect of the volatility of black gold price on the returns of the other two markets in Oil Importing Developed Countries category (ii). The selection of appropriate models of oil returns according to the period of the chosen data gives the ARMA(2,2)- GJR(1,2) model for the Germany and the ARMA(2,2)-GJR(2,2) model for the Japan and the USA. The results that the conditional variances of oil returns, foreign exchange market returns and stock market returns are contested and they have a long-term relationship in different countries. In addition, the results of the granger causality tests and the study of impulse response functions have shown that it has a sending effect of the volatility of oil prices on most foreign exchange markets and stock markets, highlighting the strong explanatory power of market volatility, but bidirectional causality is not always present. Our empirical results involved in the prevention of shocks are important for policymakers, for portfolio managers seeking optimal portfolio allocation, for monetary authorities who are studying changes in the exchange rate of the national currency against currencies, for oil-importing countries seeking to minimize their spending on crude oil, and for oil-exporting countries seeking the sound management of oil reserves. They also show that the volatility of crude oil prices on the world market is generally more significant for foreign exchange and stock markets than the volatility of oil price in the local market. This main conclusion gives political implications to policymakers.

An Empirical Analysis of the Price Volatility Characteristics of China’s Soybean Futures Market Based on ARIMA-GJR-GARCH Model

As the main force in the futures market, agricultural product futures occupy an important position in the China’s market. Taking the representative soybean futures in Dalian Commodity Futures Market of China as the research object, the relationship between price fluctuation characteristics and trading volume and open position was studied. The empirical results show that the price volatility of China’s soybean futures market has a “leverage effect.” The trading volume and open interest are divided into expected parts and unexpected parts, which are added to the conditional variance equation. The expected trading volume coefficient is estimated. Also, the estimated value of the expected open interest coefficient is, respectively, smaller than the estimated value of the unexpected trading volume coefficient and the estimated value of the unexpected open interest coefficient. Therefore, the impact of expected trading volume on the price fluctuation of China’s soybean futures market is less than that of unexpected trading volume on the price of soybean futures market. This paper adds transaction volume as an information flow to the variance of the conditional equation innovatively and also observes transaction volume as the relationship between conditional variance and price fluctuations.

Modeling Asymmetric Effects and Long Memory in Conditional Volatility of Dhaka Stock Exchange: New Evidence from Family of FIGARCH Models

This paper investigates modeling the conditional volatility of the Bangladesh equity market, namely the Dhaka Stock Exchange benchmark index (DSEX) and the Shariah Index (DSES), to explore the presence of leverage effects and long memory behavior covering the period from July 01, 2004 to December 31, 2020. We employ a family of Fractionally Integrated GARCH models FIFARCH BBM, FIGARCH CHUNG, FIEGARCH, FIAPARCH BBM, FIAPARCH CHUNG, and HYGARCH to capture both asymmetric effects and long memory behavior in conditional variance, a unique study in volatility literature. We detect strong evidence in favor of asymmetric effects and long memory behavior in the conditional volatility of DSEX and DSES returns, which repudiates the weak-form efficient market hypothesis. The study reveals FIEGARCH and FIAPRACH CHUNG outperform the other fractionally integrated GARCH specifications in modeling conditional volatility of equity returns. The paper further examines the diagnostic test of misspecification of the conditional variance equation based on the news impact curve, and results ensure that all models are fairly specified. This study also looks into the risk-return tradeoff in time-varying volatility and finds no evidence of the positive relationship between equity returns and volatility dynamics. The findings have pragmatic implications for retail and wholesale investors and other market players to initiate the investments and hedging strategies before investing in an emerging equity market like Bangladesh.

Conditional moment closure method with tabulated chemistry in adiabatic turbulent nonpremixed jet flames

The conditional moment closure (CMC) method with tabulated chemistry is proposed to reduce the computational load for integration of stiff reaction steps in the conventional CMC methods. It is based on the assumption that temperature and all species except CO and CO2 adjust fast enough so that they can be uniquely determined by the single reaction progress variable given as the sum of CO and CO2 mass fractions. The CMC equations are solved for the conditional reaction progress variable, Qpv, whereas the other species mass fractions and the reaction rates including that for Qpv are retrieved from lookup tables. A steady homogeneous form of the conditional variance and covariance equations are solved to construct the second-order closure table to be consistent with Steady Laminar Flamelet Model (SLFM)-based first-order closure. Good agreement is shown between the results by integrated and tabulated chemistry in both the first-order and the second-order CMC for Sandia Flames D, E and F. The overall computational time is reduced to about 0.5% of that by the conventional CMC method involving integration of the detailed reaction mechanism for all species and temperature.

Macroeconomic sensitivity and firm level volatility: the case of New York Stock Exchange

Purpose – This paper investigates whether the macroeconomic factors affect the firm stock returns volatility differently depending on their location in different sectors. For this purpose, daily financial time-series data for 683 firms located in nine US sectors for the period of 2000 to 2017 are employed. Research methodology – The GARCH (1,1) model was applied to each firm located in nine US sectors. The four macroeconomic factors, namely, exchange rate, treasury yield spread, oil prices, and market return, are included in both mean and variance equations of GARCH (1,1) model to estimate the effect. Research limitations – This research study is limited to the New York Stock Exchange; therefore, it can be extended to the other economies as well. Further, this study uses one firm feature that is the sectoral location of the firm; it is recommended that some other firm features should be studied to explore the volatility behaviour of firms. In the methodological part, this study does not include the lag effect, since it is recognised in the literature that the investors underreact to public information, so future research can be extended to test the underreaction hypothesis. Practical implications – This study has implications for the investors and policymakers. Since it has emerged from the findings that some sectors are more sensitive than others to macroeconomic changes, so this knowledge will help the investors to diversify their portfolio and policymakers to maintain macroeconomic discipline. Originality/Value – The main contribution of this study is that it undertakes the assumption of heterogeneous nature of firms and conducts a detailed firm level analysis by sector covering a more extended period of time to investigate the impact of four macroeconomic factors, namely, exchange rate, treasury yield spread, oil prices, and market return on firm stock returns, volatility using daily data. Further, this study contributes by including all the macroeconomic factors together as an exogenous variable in mean and conditional variance equations of the GARCH (1,1) model to investigate the effect simultaneously.

The Influence of the Economic Variables on the Chinese B-Share Markets

This paper analyzed how economic variables affect the Chinese B-share market. For this purpose, we investigated the monthly data of major economic variables (consumer price index, imports and exports volume, money supply, real estate index and retail sales volume) and B-share price index of Shanghai and Shenzhen Exchange of China from 2009 to 2019 by employing the multivariate VAR-GARCH-BEKK model. We measured the return spillover effect between Chinese major economic variables and B-share market index from the estimation results of VAR conditional mean equation, and volatility spillover effect between the economic variables and B-share index from the estimation results of GARCH-BEKK conditional variance equation. From these results, we investigated whether there is any difference between the Shanghai and Shenzhen Exchange markets. The main findings are as follows. First, the return spillover effect does not exist in both markets except the Consumer Price Index (CPI). Second, there is the volatility spillover effect between economic variables and Shenzhen B-share market, implying that the volatility spillover effect is more important than the return spillover effect in the Chinese B-share market. Third, compared with Shanghai, the change of the Shenzhen stock market is more affected by the change of economic variables. These findings have some important policy implications. First, investors in Chinese stock market need to make good use of the information inherent in China’s economic changes to increase returns and reduce investment risks. Second, the investors should pay close attention to the overall trends of the Chinese economy and the global economy, not just to the trends of the Chinese market.

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.

The Impact of COVID-19 on Gold Price Volatility

Purpose: This article investigates the implications of the spread of COVID-19 on gold spot prices. Design/Methodology/Approach: We use GARCH and GJR-GARCH models based on daily gold returns over the period 2012-2020 to analyze the impact of the coronavirus on the volatility of gold returns. Findings: We find a positive correlation between the increasing number of global coronavirus cases and increases in gold price. Using GARCH and GJR-GARCH models, we find a significant positive impact of COVID-19 on the conditional variance equation, indicating that the coronavirus may indeed increase the volatility of gold returns. This relates to the fact that the spread of the virus increases uncertainty with regard to the future of economic and financial markets, causing the demand for gold to increase and in turn pushing prices upwards, a trend which may be likely to continue until a vaccine or other treatments begin to stabilize the global economic outlook. Practical Implications: The issue of volatility is of significant concern to both investors and policymakers who base decisions on the relative stability of both individual financial markets and the world economy. Furthermore, volatility estimation is an essential factor in many models and has broad application to the market risk management practices of firms. Finally, understanding the volatility of the gold market is crucial for any analysis of current and future expectations regarding the risks associated with coronavirus which apply to global markets. Originality/Value: The lockdown restrictions which have been widely implemented across the globe to curb the spread of the virus have included travel prohibitions and border closures, stay-at-home and work-from-home orders, and extensive business closures, all causing immense fallout for the global economy. In the current study, we analyze for the first time the impact of the coronavirus on gold spot prices by examining their correlation with the number of cumulative global cases and daily new cases.

Linkages among energy price, exchange rates and stock markets: Evidence from emerging African economies

ABSTRACTThis study examines the dynamic links among oil prices, foreign exchange rates and stock markets in emerging Africa using recent 10 years data and VAR-BEKK-GARCH forecasting framework. We find evidence of significant return and volatility interactions in oil return, exchange rates and stock markets. The non-existence of long-term cointegration equilibrium implies potential diversification benefit in the long run. Autoregressive characteristics for most African foreign currencies and stock markets indicate markets’ own predictability. We see that high oil return leads to an appreciation of Botswana pula, Nigerian dollar and Zambian kwacha, depreciation of Egyptian pound and boost the stock markets of Egypt, Kenya, Nigeria and Tunisia. From the conditional variance equation, we observe significant statistical evidence of local spillover effects from oil to financial markets. Strong bi-directional shock and volatility spillovers between oil and most African exchange rates are reported. Significant shock and volatility spillovers between oil and stock markets are found in some of the African countries. We conduct portfolio optimization analyses as part of the financial risk management and risk mitigation strategies. Policy wise, leaders should promote the development of financial derivative instruments since foreign exchange rates are used as a tool to absorb oil and other external shocks.

Forecasting of the Nigeria Stock Returns Volatility Using GARCH Models with Structural Breaks

This study examines the stock returns series using Symmetric and Asymmetric GARCH models with structural breaks in the presence of some varying distribution assumptions. Volatility models of Symmetric GARCH (1,1), Asymmetric Power GARCH (1,1) and GJR-GARCH(1,1) models were considered in estimating and measuring shock persistence, leverage effects and mean reversion rate with structural breaks considering dummy variable for these structural changes and varying distributions . The skewed student-t distribution is considered best distribution for the models; moreover findings showed the high persistence of shock in returns series for the estimated models. However, when structural breaks were incorporated in the estimated models by including dummy variable in the conditional variance equations of all the models, there was significant reduction of shock persistence parameter and mean reversion rate. The study found the GJR-GARCH (1,1) with skewed student-t distribution best fit the series. The volatility was forecasted for 12 months period using GJR-GARCH (1,1) model and the values are compared with the actual values and the results indicates a continuous increase in unconditional variance.

Investment Certainty and Demonetization: Evidence from India

This article analyzes the impact of demonetization on the volatility of the Indian stock market and assesses the investment certainty in India after demonetization. A symmetric generalized autoregressive conditional heteroskedasticity (1, 1) model has been applied by incorporating a dummy variable for the event of demonetization in the conditional variance equation. This article also looks for percentage change in unconditional variance after demonetization. The results show that after demonetization, the risk related to market price decreased and the certainty of investment increased in the Indian stock market. In addition, the degree of volatility shocks declined in the post-demonetization period in comparison to the pre-demonetization period. TOPICS:Security analysis and valuation, statistical methods, emerging markets, risk management