Generalized Autoregressive Conditional Heteroskedasticity Model Research Articles

Bayesian inference in spatial GARCH models: an application to US house price returns

ABSTRACT In this paper we consider a high-order spatial generalized autoregressive conditional heteroskedasticity (GARCH) model to account for the volatility clustering patterns observed over space. The model consists of a log-volatility equation that includes the high-order spatial lags of the log-volatility term and the squared outcome variable. We use a transformation approach to turn the model into a mixture of normals model, and then introduce a Bayesian Markov chain Monte Carlo (MCMC) estimation approach coupled with a data-augmentation technique. Our simulation results show that the Bayesian estimator has good finite sample properties. We apply a first-order version of the spatial GARCH model to US house price returns at the metropolitan statistical area level over the period 2006Q1–2013Q4 and show that there is significant variation in the log-volatility estimates over space in each period.

Empirical Safety Stock Estimation Using GARCH Model, Historical Simulation, and Extreme Value Theory: A Comparative Study

Safety stock (SS) is an appropriate tactic to deal with demand and supply uncertainty with the aim of preventing inventory shortages. In the literature, previous work on SS estimation assumes that the forecast error distributions (FED) are independent and identically distributed (i.i.d) following the normal distribution. In order to assess violations of this assumption, there are many solution methods in the recent literature that include the following: (1) Consider the FED as other distribution models, such as gamma distribution or log-normal distribution, etc. (2) Use the Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model to consider the Heteroskedasticity phenomena, (3) Use the extreme value theory (EVT) to take into consideration the occurrence of extreme demands, etc. However, the performance of these methods is not guaranteed because there is an absence of comparative studies. Indeed, the estimation of SS is based on the approximation of quantiles of the FED. Such quantiles are related to the cycle service levels (CSL) that are important to achieve company goals. Accordingly, the aim of this research is to propose two combined empirical methods to determine the SS in a more robust fashion and compare them with traditional methods under different supply chain parameters. The first combined method, named Filtered Historical Simulation (FHS), consists of combining the GARCH model with the simulation method. The second combination named Conditional Extreme Value Theory (CEVT) is the GARCH model with EVT. To validate these proposed combined methods, the SS is also estimated using traditional methods, such as simple exponential smoothing (SES), simulation, and kernel density estimation (KDE). The methodology is illustrated with both simulation data and real case study data for different lead times. For the FED, two cases are studied: lognormal distribution and gamma distribution. The results show the superiority of the two proposed combination methods with respect to the tick loss function (TLF) for the different CSL targets and for shorter and longer lead times. Results are confirmed using the ANOVA test.

Are News Effects Necessarily Asymmetric? Evidence from Bangladesh Stock Market

The primary objective of this paper is to empirically examine the nature and statistical significance of the news effect on conditional volatility of unpredictable components of stock returns. Daily stock return data of 12 local and multinational companies on Dhaka Stock Exchange Ltd., Bangladesh, for the period 1990 to 2011 were used in this study. The likelihood of asymmetric effects of news on conditional volatility was tested using a set of diagnostics under the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) framework. The results fail to reject the null hypothesis of symmetric effects, thereby suggesting that the conditional volatility of unpredictable components of stock returns is affected equally by positive and negative news. The robustness of the results was further checked by using three widely used asymmetric models, namely exponential GARCH (EGARCH), Glosten, Jagannathan & Runkle (GJR)-GARCH, and a partially non-parametric Autoregressive Conditional Heteroscedastic (PNP-ARCH) models. Yet again, the results do not provide any evidence of significant asymmetric effects in the volatility process. In addition, the descriptive results confirm the stylized facts of unpredictable return series such as non-normal distribution, time variant conditional volatility, and persistence in return volatility. Collectively these findings, perhaps, indicate the adequacy of the GARCH (1,1) model in representing the data generating process. A number of regulatory and behavioral factors that are anticipated to be accountable for the absence of asymmetric news effects are underlined. Finally, some policy implications of the results and possible extensions of the present paper are also conveyed. JEL codes: G10, G12, G14

A general framework for spatial GARCH models

In time-series analysis, particularly in finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased risk). In contrast, it has not been considered to be of critical importance until now to model spatial dependence in the conditional second moments. Only a few models have been proposed for modelling local clusters of increased risks. In this paper, we introduce a novel spatial GARCH process in a unified spatial and spatiotemporal GARCH framework, which also covers all previously proposed spatial ARCH models, exponential spatial GARCH, and time-series GARCH models. In contrast to previous spatiotemporal and time series models, this spatial GARCH allows for instantaneous spill-overs across all spatial units. For this common modelling framework, estimators are derived based on a non-linear least-squares approach. Eventually, the use of the model is demonstrated by a Monte Carlo simulation study and by an empirical example that focuses on real estate prices from 1995 to 2014 across the postal code areas of Berlin. A spatial autoregressive model is applied to the data to illustrate how locally varying model uncertainties (e.g., due to latent regressors) can be captured by the spatial GARCH-type models.

Value for Equity Index Options: Expected—Not Realized—Volatility and the Distribution of Forecasts

Models of option returns neglect the distribution of expected asset volatility, unfortunately for not only derivatives traders but also investors who monitor options as <i>fear gauges</i>. Six common GARCH (generalized autoregressive conditional heteroskedasticity) models afford estimates of the physical, rather than the risk-neutral, distribution of anticipated—instead of historical—volatility, as well as of volatility disagreement. This value specification covering nine global equity indexes and five expiries from 1 to 12 months fits implied volatilities closely, with sizeable and robust error-correction speeds out of sample, all else equal. Exploratory backtests of delta-neutral trading rules produce high Sharpe ratios and alphas, with modest drawdowns and skew.

Forecasting Exchange Rate of Pakistan Using Time Series Analysis

Exchange rates are crucial in regulating the foreign exchange market's dynamics. Because of the unpredictability and volatility of currency rates, the exchange rate prediction has become one of the most challenging applications of financial time series forecasting. This study aims to build and compare the accuracy of various methods. The time series model Auto-Regressive Integrated Moving Average (ARIMA) and Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) are utilized to forecast the daily US dollar to Pakistan rupee currency exchange rates (USD/PKR). Lagged observations of the data series and moving average technical analysis are used in both models. Explanatory factors were used as indicators, and the prediction performance was assessed using a variety of commonly known statistical metrics. These statistical metrics suggested the presence of conditional heteroscedasticity. Thus, the process turns to capture the volatility effect of conditional heteroscedasticity through GARCH modeling. It may be inferred based on the results of tentative models; that the ARCH model outperforms the GARCH model in terms of predicting the USD/PKR exchange rate.

Capturing the month of the year effect in the Indian stock market using GARCH models

Purpose In the research of stock market efficiency, it is argued that the stock market moves randomly and absorbs all the available information. As a result, it is quite impossible to make predictions about the possible future movement by the investors. But literatures have detected certain calendar anomalies where a day(s) in a week or month(s) in a year or a particular event in a year becomes conducive for investors to earn more than the normal. Hence, the purpose of this study is to find out the month of the year effect in the Indian stock market. Design/methodology/approach In this study, daily time series data of Sensex and Nifty from 1996 to 2021 is used. The study uses month dummies to capture the effect. Different variants of generalised autoregressive conditional heteroskedasticity (GARCH) models, both symmetric and asymmetric, are used in the study to model the conditional volatility in the presence month effect. Findings This study found the September effect in the return series of both the stock market. Apart from that, asymmetric GARCH models are found to be the best fit model to estimate conditional volatility. Originality/value This study is an endeavour to study month of the year effect in the Indian context. This research will provide valuable insight for studying the different calendar anomalies.

Forecasting Crude Oil Future Volatilities with a Threshold Zero-Drift GARCH Model

The recent price crash of the New York Mercantile Exchange (NYMEX) crude oil futures contract, which occurred on 20 April 2020, has caused history-writing movements of relative prices. For instance, the West Texas Intermediate (WTI) experienced a negative price. Explosive heteroskedasticity is also evidenced in associated products, such as the Intercontinental Exchange Brent (BRE) and Shanghai International Energy Exchange (INE) crude oil futures. Those movements indicate potential non-stationarity in the conditional volatility with an asymmetric influence of negative shocks. To incorporate those features, which cannot be accommodated by the existing generalized autoregressive conditional heteroskedasticity (GARCH) models, we propose a threshold zero-drift GARCH (TZD-GARCH) model. Our empirical studies of the daily INE returns from March 2018 to April 2020 demonstrate the usefulness of the TZD-GARCH model in understanding the empirical features and in precisely forecasting the volatility of INE. Robust checks based on BRE and WTI over various periods further lead to highly consistent results. Applications of news impact curves and Value-at-Risk (VaR) analyses indicate the usefulness of the proposed TZD-GARCH model in practice. Implications include more effectively hedging risks of crude oil futures for policymakers and market participants, as well as the potential market inefficiency of INE relative to WTI and BRE.

Stock Market Efficiency in Asia: Evidence from the Narayan–Liu–Westerlund's GARCH‐based unit root test

AbstractStock market integration with efficiency is important in finance. This study therefore analyses the stock market efficiency in Vietnam and other Asian countries by using the recently developed Generalized Autoregressive Conditional Heteroscedasticity (GARCH)‐based unit root test of Narayan et al. to examine the stock market efficiency of Vietnam and other 18 Asian countries, using daily prices. Particularly, we examine weather stock market prices in these countries reflects all available information. The model flexibly accounts for heteroskedasticity and two structural breaks, the presence of which can lead to inaccurate results if neglected. Our results disclose the stock markets of 14 countries as inefficient following the rejection of the unit root null hypothesis. However, the stock markets of China, Hong Kong, Japan, and the Korea Republic are adjudged efficient. We further extend the model to accommodate a maximum of five breaks to check the robustness of our results to higher breaks. We observe that the results are largely consistent except for Lebanon and Singapore. For completeness, we compare the results with those of conventional GARCH models that do not account for structural breaks and discover differing results for some countries. Hence, the role of structural breaks is not negligible in assessing market efficiency. Future studies should also incorporate heteroskedasticity and structural breaks in their modelling framework to obtain accurate results.

Modeling Volatility of Daily Stock Return Using Generalized Autoregressive Conditional Heteroscadatic with Skewed Error Distribution and Stochastic Volatility Models

The problem of how best to model volatility of stock prices returns have continued to occupy the minds of researchers in this area. This study therefore compares the performance of two competitive volatility models: The Stochastic Volatility (SV) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) based on skewed error distributions models using daily stock returns of Fourteen Nigerian banks. The daily stock closing price of the selected banks were collected for the period 4/1/2007 to 31/12/2021 and the stationarity, normality and ARCH effect of the series were tested. The parameter of SV and different types of GARCH models based on skewed normal, skewed student t and skewed generalized error distribution were estimated and selection of the best model was done using Akaike Information Criterion (AIC). Post estimation and evaluation were carried out using the Mean Square Error (MSE) and Root Mean Square Error (RMSE). Results of analysis revealed a stationary but asymmetrically distributed return series with ARCH effect. The model forecasting performance proved APARCH (1,1) based on student t-distribution as the best among the competing GARCH models with the record of the least AIC value in ten of the fourteen daily bank stocks returns. Although, APARCH (1,1) and SV models were found to be comparable. SV model was however recommended as the best since it recorded the least RMSE value in 11 (79%) of the 14 bank stocks against 3 (21%) bank stock in favour of APARCH (1,1). This implies that SV model was found to be adequate in modeling volatility of the daily stock returns of ECO Bank, First City Monument bank, Fidelity bank, first bank, Guaranty Trust bank, Stanbic IBTC bank, Sterling bank, United Bank for Africa, Union bank, WEMA bank and Zenith bank; while APARCH (1,1) base on Skewed student ‘t’ distribution was preferred in modeling volatility of Access bank, Skye Bank and Unity bank. Results also showed the presence of volatility persistence, suggesting uncertainties and the risk of losses by investors. Therefore, it can be deduced that the application of a stochastic volatility model to the selected stock returns would drastically minimize the losses by investors.

The five-factor model, stock returns and idiosyncratic volatility: evidence from Sri Lanka

Traditionally, the success of asset pricing models is assessed in the absence of idiosyncratic volatility, as it is believed that the role of idiosyncratic volatility is irrelevant. Nevertheless, the existing literature shows that idiosyncratic volatility matters in asset pricing decisions. Hence, this study aims to test the performance of the five-factor asset pricing model of Fama and French (2015) in the presence of idiosyncratic volatility. This study utilizes a sample of 214 companies listed on the Colombo Stock Exchange (CSE) except for those listed under the banks, finance, and insurance sectors over 163 months from September 2004 to March 2018. Nelson’s (1991) Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) models are used to estimate the idiosyncratic volatility of individual stocks. The empirical findings of the study confirm that the five-factor asset pricing model of Fama and French (2015) is less successful and failed to explain the stock returns in the presence of unsystematic risk in the Sri Lankan context. This finding yields striking evidence of the success of the five-factor asset pricing model in the presence of idiosyncratic volatility while it casts doubts on the applicability of such factor models in estimating the cost of equity of firms in the real world. Although the impact of idiosyncratic volatility on stock returns is well-researched in the finance literature, there is little structured research on how idiosyncratic volatility affects the performance of asset pricing models in the Sri Lankan context. This study fills this gap by investigating the performance of the five-factor asset pricing model of Fama and French (2015) using the firms listed on the CSE. The research findings should help academia develop more pronounced asset pricing models while tackling the idiosyncratic volatility of stocks.

Pemodelan Harga Saham Menggunakan Arma-Garch

Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models were used for modeling with heteroscedasticity data. This study aims to determine the time series model on the stock price data of PT Triputra Agro Persada Tbk. (TAPG) with modeling ARMA, ARCH and GARCH. Based on the smallest Akaike Information Criterion (AIC) and Schwarz Criterion (SC), it shows that the ARMA(1,0)-GARCH(2,1) model is the best model for predicting the value of TAPG stock prices.

Cryptocurrencies Intraday High-Frequency Volatility Spillover Effects Using Univariate and Multivariate GARCH Models

Over the past years, cryptocurrencies have drawn substantial attention from the media while attracting many investors. Since then, cryptocurrency prices have experienced high fluctuations. In this paper, we forecast the high-frequency 1 min volatility of four widely traded cryptocurrencies, i.e., Bitcoin, Ethereum, Litecoin, and Ripple, by modeling volatility to select the best model. We propose various generalized autoregressive conditional heteroscedasticity (GARCH) family models, including an sGARCH(1,1), GJR-GARCH(1,1), TGARCH(1,1), EGARCH(1,1), which we compare to a multivariate DCC-GARCH(1,1) model to forecast the intraday price volatility. We evaluate the results under the MSE and MAE loss functions. Statistical analyses demonstrate that the univariate GJR-GARCH model (1,1) shows a superior predictive accuracy at all horizons, followed closely by the TGARCH(1,1), which are the best models for modeling the volatility process on out-of-sample data and have more accurately indicated the asymmetric incidence of shocks in the cryptocurrency market. The study determines evidence of bidirectional shock transmission effects between the cryptocurrency pairs. Hence, the multivariate DCC-GARCH model can identify the cryptocurrency market’s cross-market volatility shocks and volatility transmissions. In addition, we introduce a comparison of the models using the improvement rate (IR) metric for comparing models. As a result, we compare the different forecasting models to the chosen benchmarking model to confirm the improvement trends for the model’s predictions.

Modelling and forecasting Nifty 50 using hybrid ARIMA-GARCH Model

This study proposes an estimation technique for developing the best Öt ARIMA- GARCH model to predict the closing values of Nifty 50. The study put forward di§erent methods to resolve the issue of non-stationarity in mean as well as variance of the series before starting the estimation process. This study has applied autoregressive integrated moving- average (ARIMA), generalized autoregressive conditional heteroscedasticity (GARCH), ex- ponential GARCH (EGARCH) and threshold GARCH (TGARCH) model along with other estimation procedures on the daily closing prices of Nifty 50 from Jan 1, 2009 to Dec 30, 2019. Finally, the study identiÖes ARIMA(2,1,2)-EGARCH(1,1,1) as best model to predict the closing prices of Nifty 50. The Öndings indicate that the static forecast provides better results as compared to the dynamic forecast. These research Öndings will add to the tool kit of domestic as well as international portfolio managers and investors to frame suitable NIFTY trade strategies with least possible risks.

Linear time-varying regression with copula–DCC–asymmetric–GARCH models for volatility: the co-movement between industrial electricity demand and financial factors

ABSTRACT This paper examines the dependence structure of industrial electricity demand and financial indicators (the Korea Composite Stock Price Index [KOSPI], Korean Securities Dealers Automated Quotations [KOSDAQ], exchange rate, government bonds and exports) using the copula dynamic conditional correlation with symmetric and asymmetric generalized autoregressive conditional heteroscedasticity (GARCH) models to forecast volatility. We investigated symmetric and asymmetric GARCH types, such as the standard, exponential, Glosten–Jagannathan–Runkle and asymmetric power models to fit the marginal distribution. The two types of elliptical copula, Gaussian and Student’s t-distributions, were also considered to investigate the tail dependence between financial and electricity time series. We analysed the monthly log returns for January 2002 to April 2020. The empirical results reveal that the best-fit models for the Akaike information criteria are the asymmetric GARCH models, specifically the exponential-GARCH (E-GARCH). Moreover, the asymmetric GARCH model is superior to the symmetric GARCH in terms of forecast volatility. Extreme tail dependence exists for the KOSDAQ and exports indicators with the electricity demand. The KOSPI, Korea’s primary stock market, is the best-fit financial variable and presents the highest forecasting accuracy.

Oil Price Uncertainty and Industrial Output in Nigeria

Concerned by the dismal performance of Nigeria’s industrial sector as evidenced by the sector’s inauspicious and uneven contributions to the country’s aggregate output and total government earnings, this study has been embarked upon to examine the impact of crude oil price volatility on industrial output in Nigeria. The Ordinary Least Square (OLS) technique was employed in estimating the time series data used in the study which spans from 1981–2019. The Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model was estimated to capture crude oil price fluctuations and government oil revenue fluctuations by obtaining the conditional variances from the estimated results. The study found that crude oil price fluctuation has negative impact on industrial output, while an increase in government oil revenue fluctuation results in a significant decrease in industrial output. It was also found that an increase in unearned government oil revenue leads to an insignificant decrease in industrial output, while government recurrent expenditure exerts positive but insignificant impact on industrial output. Domestic investment was found to have a positive and significant impact on industrial output while population growth has a positive and significant impact on industrial output. The study concludes that it is government’s financial imprudence that allows oil price volatility to be hazardous to Nigeria’s industrial output. It recommends more effective export diversification policies and a pro-development government financial structure that takes erratic oil revenue and inimical effects of high unproductive expenditures into account.

Parameter Estimation of GARCH Model with Bootstrap Approximation

This study aims to estimate the parameters of the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model using a bootstrap approach. In the heteroscedasticity data model, it is determined how much the residual value of the sample used is. The bootstrap approach is a non-parametric and resampling technique used to estimate the parameter. From the sample data implemented, the residual estimation using the Maximum Likelihood Estimation method is - 0.065851304. Furthermore, the residual estimation value using the bootstrap approach is -1.769129241. Thus, the use of the bootstrap approach in the GARCH model results in a smaller residual value than MLE.

Performance of Generalized Autoregressive Conditional Heteroscedasticity (GARCH) Models in Modeling Volatility of Brent Crude Oil Price

Fluctuations in the price of crude oil determines the economic state of many nations especially the oil producing ones, it becomes important to examine these fluctuations, hence the GARCH models were applied to model the volatility in the price of brent crude oil to determine the best model suitable for predicting future volatility. Descriptive statistics of the stock price and its returns were obtained, some inferential tests were employed to examine the stationarity and the goodness of fit of the daily price and the return under different distributions – the Gaussian, the Student t and the Generalized Error Distributions. Results showed that the price of crude oil dropped between 2014 and 2016 and drastically dropped in 2020. Among the competing models, Exponential GARCH(1,1) with Student t distribution was the best model with the least values of AIC, SBIC and HQIC respectively. The result showed negative significant value in the coefficient of its asymmetric parameter, suggesting that bad news or vital event such as COVID19 has larger effect on the volatility in the price of the Brent crude oil. This study therefore recommended the use of Exponential GARCH model in modelling or predicting volatility in the stock price of crude oils.

Did the Islamic Stock Index Provide Shelter for Investors during the COVID-19 Crisis? Evidence from an Emerging Stock Market

The economic and financial chaos caused by COVID-19 has been a discussion topic since the beginning of 2020. This study intends to provide a parallel comparison of volatility change and external shock persistence of the Islamic and conventional stock indexes of the Pakistan Stock Exchange. The daily stock index was extracted from Eikon Thomson Reuters for the conventional and Islamic stock index from Jan 2018 to April 2021, which was further divided in three periods, i.e., full, pre-, and post-pandemic period. The data have been analyzed using generalized autoregressive conditional heteroscedasticity (GARCH). An optimally parameterized GARCH (1,1) model is used to measure volatility change for both the pre- to post-pandemic periods. The results suggest that the magnitude of risk in a conventional index is significantly higher than that of the Islamic stock index for the period of study. However, the level of COVID shock persistence is longer in the KSE (conventional) index compared to the KMI (Islamic) index.

Asymmetric Shocks In Oil Price: An Exponential Generalized Autoregressive Conditional Heteroskedasticity Approach

This study empirically examined the asymmetric oil price shocks in Nigeria from 1981q1-2019q4 using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model. The EGARCH model was employed to investigate the asymmetric oil price shocks by obtaining the conditional variance from the estimated results. Empirical results revealed a weak indication for leverage effect and a strong indication for asymmetric effect. The positive egarch (L2) coefficient means that unanticipated increases in the price crude Oil are more profitable than unanticipated decreases in the price of crude Oil. Also, the results revealed strong asymmetry of oil price shocks in Nigeria. In specific terms, the positive asymmetric coefficient (1.8276) means an observed tendency of the crude oil price shock to be higher by approximately 1.83 per cent in declining oil prices in the crude oil market than in rising prices in the oil markets. Based on the above, the study recommended appropriate export diversification policies to reduce the dependency on crude oil exports as the major export (revenue) in the economy. This will offset crude oil price shocks such as the COVID-19 pandemic shock on Oil price, especially from an unanticipated decrease in crude oil prices in the international market. Key Words: Oil price, Oil Price Shocks, Asymmetry, EGARCH, Nigeria