Augmented GARCH Research Articles

Stock Volatility Modelling With Augmented Garch Model For Voltas Ltd

This research paper seeks to examine the efficiency of the augmented GARCH models in estimating the stock volatility. GARCH models that were introduced by Bollerslev (1986) became popular for the modelling of time varying volatility in the financial markets. However, due to the specificity of financial markets and variation of factors that define it, extra parameters may be required to improve the model. To investigate further, the study uses an extended GARCH model that integrates other features including leverage effects, exogenous variables and non-linearities. These components seek to establish features giving clearer volatility patterns of stock markets. In this paper, empirical comparison of the extended GARCH model with the basic forms of the models is done. The outcomes are expected to be of interest to financial investors, advisors and risk managers

Examining the Volatility of Conventional Cryptocurrencies and Sustainable Cryptocurrency during Covid-19: Based on Energy Consumption

The present study proposes to investigate the influence of the covid-19, on the adjusted closing price of the digital currency based on energy consumption during the process of mining. The study employed the secondary data analysis of top ten market capitalization of cryptocurrencies with the combination of high energy consume mechanism (proof of work) and low energy consume mechanism (proof of stake). Statistical tools like Descriptive analysis,Augmented Dickey-Fuller (ADF) test, ARCH, and GARCH models were used in the study. The present study finds that the prices of cryptocurrencies were highly volatile. This study could assist investors towards better understanding of the dynamics of the cryptocurrency market based on energy consumption which helps them to make more effective decisions, on investing cryptocurrencies with a scientific approach.

How do empirical estimators of popular risk measures impact pro-cyclicality?

AbstractRisk measurements are clearly central to risk management, in particular for banks, (re)insurance companies, and investment funds. The question of the appropriateness of risk measures for evaluating the risk of financial institutions has been heavily debated, especially after the financial crisis of 2008/2009. Another concern for financial institutions is the pro-cyclicality of risk measurements. In this paper, we extend existing work on the pro-cyclicality of the Value-at-Risk to its main competitors, Expected Shortfall, and Expectile: We compare the pro-cyclicality of historical quantile-based risk estimation, taking into account the market state. To characterise the latter, we propose various estimators of the realised volatility. Considering the family of augmented GARCH(p, q) processes (containing well-known GARCH models and iid models, as special cases), we prove that the strength of pro-cyclicality depends on the three factors: the choice of risk measure and its estimators, the realised volatility estimator and the model considered, but, no matter the choices, the pro-cyclicality is always present. We complement this theoretical analysis by performing simulation studies in the iid case and developing a case study on real data.

Inconsistency for the Gaussian QMLE in GARCH-type models with infinite variance

We are occupied with the issue of consistency of the Gaussian QMLE in GARCH-type models with very heavy tailed squared innovations. We show that the appropriately scaled likelihood function weakly epi-converges to a stochastic process that is a.s. lower semi-continuous and proper. When moreover the volatility filter is increasing w.r.t. the parameter, inconsistency follows due to that the true parameter value misses the set of minimizers of the limit. This holds for models like the AGARCH, the Augmented GARCH, and the GQARCH.

Forecasting risk measures using intraday and overnight information

Volatility forecasts are important for a number of practical financial decisions, such as those related to risk management. When working with high-frequency data from markets that operate during a reduced time, an approach to deal with the overnight return volatility is needed. In this context, we use heterogeneous autoregressions (HAR) to model the variation associated with the intraday activity, with distinct realized measures as regressors, and, to model the overnight returns, we use augmented GARCH type models. Then, we combine the HAR and GARCH models to generate forecasts for the total daily return volatility. In an empirical study, for returns on six international stock indices, we analyze the separate modeling approach in terms of its out-of-sample forecasting performance of daily volatility, Value-at-Risk and Expected Shortfall relative to standard models from the literature. In particular, the overall results are favorable for the separate modeling approach in comparison with some HAR models based on realized variance measures for the whole day and the standard GARCH model.

Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations

This paper considers stationary autoregressive (AR) models with heavy-tailed, general GARCH (G-GARCH) or augmented GARCH noises. Limit theory for the least squares estimator (LSE) of autoregression coefficient ρ=ρn is derived uniformly over stationary values in [0,1), focusing on ρn→1 as sample size n tends to infinity. For tail index α∈(0,4) of G-GARCH innovations, asymptotic distributions of the LSEs are established, which are involved with the stable distribution. The convergence rate of the LSE depends on 1−ρn2, but no condition on the rate of ρn is required. It is shown that, for the tail index α∈(0,2), the LSE is inconsistent, for α=2, logn/(1−ρn2)-consistent, and for α∈(2,4), n1−2/α/(1−ρn2)-consistent. Proofs are based on the point process and the asymptotic properties in AR models with G-GARCH errors. However, this present work provides a bridge between pure stationary and unit-root processes. This paper extends the existing uniform limit theory with three issues: the errors have conditional heteroscedastic variance; the errors are heavy-tailed with tail index α∈(0,4); and no restriction on the rate of ρn is necessary.

Asymptotics for semi-strong augmented GARCH(1,1) model

In this article, we study a family of so-called semi-strong augmented GARCH(1,1) model where the innovation process is strictly stationary and mixing instead of independent and identically distributed. We give a necessary and sufficient condition for stationarity of the process and study the functional central limit theorems for and ut when the process is stationary. We also investigate the dynamic behavior of semi-strong GARCH(1,1) model when it is non stationary.

Augmented Real-Time GARCH: A Joint Model for Returns, Volatility and Volatility of Volatility

We propose a model that extends the RT-GARCH model by allowing conditional heteroskedasticity in the volatility process. We show we are able to filter and forecast both volatility and volatility of volatility simultaneously in this simple setting. The volatility forecast function follows a second-order difference equation as opposed to first-order under GARCH(1,1) and RT-GARCH(1,1). Empirical studies confirm the presence of conditional heteroskedasticity in the volatility process and the standardised residuals of return are close to Gaussian under this model. We show we are able to obtain better in-sample nowcast and out-of-sample forecast of volatility.

Improved Volatility Prediction and Trading Using StockTwits Sentiment Data

Volatility prediction plays an important role in the financial domain. The GARCH family of prediction models is very popular and efficient in using past returns to forecast volatility. It has also been observed that news, scheduled and unscheduled, have an impact on return volatility of assets. An enhanced GARCH model, called News Augmented GARCH (NAGARCH) includes an additional component for news sentiment. With the rise in popularity of the world wide web and social media, it has become a rich source for opinions and sentiments. Twitter is one such platform. It is a micro-blogging site and a popular source for public view on different topics. StockTwits is a social media platform that started as an application built using Twitter’s API. It has since grown into an independent financial social media platform for news and sentiment. StockTwits is a rich source of opinions from subject experts and analysts. This data provides first systematic exploration of social media. It reflects raw sentiments of traders, investors, media, public companies, and investment professionals as opposed to sentiments from curated news wires. This research attempts to determine if the sentiment on stocks from StockTwits micro-blogs can improve volatility prediction. The experiment is performed on 9 NASDAQ100 stocks. The GARCH model with stock returns, and the NA-GARCH model with stock returns and micro-blog sentiment are tuned and their prediction results are evaluated. NA-GARCH, with the sentiment data from StockTwits performed better than the GARCH model in 7 out of the 9 cases.

Volatility of Islamic Stock Markets and Developed Stock Markets of G6 Countries

The objective of this to measure and compare Volatility of Islamic stock markets with equity markets of developed(G6) countries by taking daily values for period 2000-2016. The technique of Augmented fuller test (ADF), Heteroscedasticity test, ARCH (1,0), GARCH (1,1), TARCH and E-GARCH are applied. The results show Islamic stock markets shows positive returns as compare to previous day return but the Developed equity markets (G6) shows negative returns as compare to previous day return expect span and Poland equity market. The study explored that in all the stock markets the previous day volatility transfers in the next day volatility and there are many other factors affect the stock market volatility. The study is helpful in building stock portfolio for individual or institutional investor and for policy maker in decision making.

Bivariate FCLT for the Sample Quantile and Measures of Dispersion for Augmented GARCH( <i>p</i>, <i>q</i>) processes

In this note, we build upon the asymptotic theory for GARCH processes, considering the general class of augmented GARCH(p, q) processes. Our contribution is to complement the well-known univariate asymptotics by providing a bivariate functional central limit theorem between the sample quantile and the r-th absolute centred sample moment. This extends existing results in the case of identically and independently distributed random variables. We show that the conditions for the convergence of the estimators in the univariate case suffice even for the joint bivariate asymptotics. We illustrate the general results with various specific examples from the class of augmented GARCH(p, q) processes and show explicitly under which conditions on the moments and parameters of the process the joint asymptotics hold.

Analyzing the Impact of Demonetization on the Indian Stock Market: Sectoral Evidence using GARCH Model

On 8th November 2016, the Government of India demonetized its two highest currency notes in the denomination of Rs. 500 and Rs. 1000. The purpose of demonetization was to tackle the corruption and black money prevailing in the country. The stock market is one of the areas which pools a large amount of funds, the present study is an analytical attempt to examine the impact of demonetization on Indian stock market. For the purpose of the study, various statistical techniques have been used such as Graphical Analysis, Summary Statistics (i.e. Mean, Standard Deviation, Skewness, and Kurtosis), Augmented Dickey-Fuller Test and GARCH Model. The study utilizes the GARCH model to examine the impact of demonetization on Nifty 50 Index and across sectoral indices in India considering a period of 200 days prior and post event date by framing necessary dummy variables. The study found the data to be stationary using the Augmented Dickey-Fuller Test. A significant negative impact of demonetization on stock market returns was evidenced from Nifty 50 Index and sectoral indices such as Nifty Auto Index, Nifty Financial Services Index, Nifty FMCG Index, Nifty IT Index, Nifty Media Index, Nifty Private Bank Index, and Nifty Realty Index. The study found the Nifty Realty Index to be affected most because of demonetization. The results of the study will help the Governing bodies to examine the impact of demonetization and frame necessary policies. The results will also be useful for investors and other market participants for framing investment and trading strategies.

Spillover effects between US ETFs and emerging stock markets

The current paper focuses on return and volatility spillovers between the US ETF market and emerging stock markets using a sample of 40 US-listed iShares, which track several emerging stock markets indices from the Americas, Europe, Asia and South Africa. Advanced econometric and correlation analysis techniques are employed in our investigation. More specifically, a comprehensive correlation analysis, which includes the Pearson's simple correlation coefficient and the conditional constant correlation and dynamic conditional correlation coefficients, is performed to answer whether a significant comovement pattern exists between the two markets. Going further, three alternative models, namely an ARMA model, an ARMA-GARCH model and an ARMA-EGARCH model, are used to assess the existence of material spillover effects on returns. Finally, five models are used to accentuate any significant spillovers on volatilities between US emerging markets ETFs and their benchmarks. These models are the augmented GARCH model, the ARMA-GARCH model, the ARMA-EGARCH model, the scalar-BEKK model, and the ARMA-scalar-BEKK model. The empirical findings of correlation analysis reveal a high degree of comovement between the US ETF market and the underlying emerging stock markets. Furthermore, the results on return spillovers demonstrate that significant bilateral such effects exist between ETFs and benchmarks. This is also the case for volatilities.

Forecasting stock market volatility and information content of implied volatility index

ABSTRACTThis study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.

Volatility Spillover USD-IDR Exchange Rate With Indonesia Stock Price

Value of imports higher than exports, causing the trade deficit, the appreciation of the currency in the developed countries, and withdrawals by foreign investors on the Indonesian stock exchange market. These things cause the movement of the exchange rate USD-IDR and Indonesian Stock Price are volatile and tend to weaken in the period from January 3, 2011 - August 31, 2016. This study to determine spillover volatility of the exchange rate USD-IDR with Indonesian Stock Price. By using current time series data, analyzed by Augmented Dickey-Fuller (ADF), GARCH, and Granger Causality. The results of the data processing rate of USD-IDR and data Indonesian Stock Price stationary at first difference by changing the level of daily data into a return of the respective data. Data having problems heteroskedasticity so it can be analyzed using GARCH. Results of the analysis showed that there is a volatility spillover between the two data. Then granger causality test results show that the causality occurs in both directions, meaning that changes in the foreign exchange market to give effect to the capital markets, and vice versa.

Optimal Rate of Convergence for Empirical Quantiles and Distribution Functions for Time Series

Given a stationary sequence , we are interested in the rate of convergence in the central limit theorem of the empirical quantiles and the empirical distribution function. Under a general notion of weak dependence, we show a Berry–Esseen result with optimal rate n−1/2. The setup includes many prominent time series models, such as functions of ARMA or (augmented) GARCH processes. In this context, optimal Berry–Esseen rates for empirical quantiles appear to be novel.

Asymmetric impacts of fundamentals on the natural gas futures volatility: An augmented GARCH approach

We investigated the determinants of daily volatility for natural gas nearby-month futures traded on the NYMEX within a GARCH framework augmented with market fundamentals. Consistent with the previous literature, we found that volatility is much higher on the natural gas and crude oil storage report announcement days, on Mondays and during winters. We also confirmed that high volatility is associated with divergence of storage levels and temperatures from seasonal norms. The asymmetric impact of storage levels on volatility across different seasons is empirically investigated and documented. The mainstream finding in the literature that lower storage levels result in higher volatility is valid only during winter. At other times, it is actually higher storage levels causing higher volatility. Also, time to maturity effect is present only in winters. Additionally, weather shocks have asymmetric impact on volatility depending on the sign of the shock. Finally, we found that augmentation with market fundamentals improves the out-of-sample forecast accuracy of standard GARCH models.

Impact of futures trading on volatility of spot market-a case of guar seed

Purpose– Guar Seed crop is ruling the Indian International business mainly due to its application as a drilling fluid in shale energy industry concentrated in the USA. One of the allegations against futures market is its possible role in increasing the volatility of underlying physical market prices. Suspension of guar seed futures contract in 2012 at National Commodity Derivatives Exchange of India (NCDEX)-India, has reignited the controversy and raised an alarm bell to peek into obscure world of Indian commodity derivatives market. Against the backdrop of fiasco in guar futures trading, the purpose of this paper is to investigate whether sudden surge in futures trading volume leads to increase in the volatility of spot market prices.Design/methodology/approach– Guar seed spot returns volatility is modeled as a GARCH (1, 1) process. Futures trading volume and open interest are segregated into expected and unexpected components. The data are analyzed from 2004 to 2011 using Augmented GARCH model to study the contemporaneous relationship between spot volatility and unexpected futures trading activity and Granger Causality test for examining the dynamic relationship between them and ascertaining causality.Findings– Augmented GARCH model reports positive relationship between unexpected futures trading volume (UTV) and spot returns volatility, and, Granger Causality flows from UTV to spot volatility. Therefore, when the level of futures trading volume increases unexpectedly, the volatility of spot prices increases pointing toward the destabilizing impact of futures trading. However, hedger’s activity, represented by open interest is not seen to have any causal/destabilizing impact on spot price volatility of guar seed.Practical implications– The study provides empirical evidence to support the concern of regulators, genuine hedgers and other traders about the presence of excessive speculation and market manipulations perpetrated through futures market that is disturbing the underlying physical market instead of strengthening it by aiding in price discovery and risk mitigation.Originality/value– There are very few studies which have empirically investigated the temporal relation between volume and volatility in Indian agricultural commodity markets. With guar seed as a special case the present study investigates statistically the impact of futures trading on spot price volatility. In light of the findings of the study, the curb imposed on guar seed futures trading in 2012 was justified.

The Impact Of Financial Crisis On Islamic And Conventional Indices Of The GCC Countries

<p>We study performance of Islamic and conventional indices of the Gulf Cooperation Council (GCC) countries in the wake of financial crisis of 2008 and test whether Islamic indices were less risky than conventional indices. We make use of data of the six GCC markets as well as the Dow Jones Islamic Market Index GCC. The mean and variance of each of the indices are analyzed based on augmented GARCH models. The results show that the financial crisis impacted on the mean returns of Bahrain, the other indices remained unaffected. The financial crisis, however, impacted volatility in three GCC markets (Kuwait, Bahrain, and the UAE), while the impact on the remaining markets (Saudi Arabia, Oman, and Qatar) and the Islamic index was insignificant. More interestingly, we show that the Islamic index did not exhibit lower volatility than its conventional counterparts.</p>

AN EMPIRICAL ANALYSIS OF THE INTERRELATION BETWEEN SPOT MARKET & NONDELIVERABLE FORWARD MARKET OF USD/INR IN THE PRE AND POST CURRENCY FUTURES ERA

The main objective of this paper is to study whether the introduction of the currency futures had an impact of the interrelation and information flows between the INR-USD spot and offshore forward (i.e., non-deliverable forward) markets. The econometric models have been used in this study, and long-term equilibrium relationship is measured through Johansen Co-integration test and Granger causality test is employed measure the short-term relationship. The result of the co-integration test proves that there exists a significant long-term equilibrium relation between the USD-INR spot and NDF rates. Causality test confirms that there is bidirectional causality between the spot and the NDF market in Sub-period 1, whereas a unidirectional causality exists in the Sub-period 2. We adopt the augmented GARCH formulation to compare NDF and spot market. We find that before currency future was introduced there existed a mean and volatility spillover effect from the NDF to spot market and vice versa, i.e., both directions. But after the introduction of currency futures, however, the results reversed with unidirectional mean spillover effect only from the NDF to the spot market. Also, the volatility spillover effect exists only in the same direction. These findings suggest that there is information flows between NDF and spot markets, Hence it is concluded that introduction of currency future has changed the direction of the dynamic relation in these two markets.