Exponential GARCH Research Articles

BALANCE OF TRADE, EXCHANGE RATE AND ECONOMIC GROWTH IN NIGERIA

This study delved into the relationship between the balance of trade, exchange rates, and economic growth in Nigeria. Utilizing annual time series data spanning from 1981 to 2021 sourced from the Central Bank of Nigeria (CBN) statistical bulletin and the National Bureau of Statistics (NBS), the investigation employed a Heteroskedasticity Model. Within this framework, GARCH, an expanded version of ARCH, and the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGACH) were applied. The findings revealed that both trade balance and exchange rates exhibited heightened sensitivity to adverse news, indicating that uncertainties surrounding exchange rates significantly contributed to fluctuations. Moreover, the ARCH effects initially observed in the balance of trade and exchange rates were completely mitigated by the considered heteroskedastic models. Furthermore, the study identified a negative and statistically significant impact of the balance of trade on economic growth. Similarly, exchange rates were found to exert an undesirable significant influence on economic growth in Nigeria. This suggests that unfavorable changes in the Nigerian naira tend to exacerbate its volatility. Notably, while the relationship between trade balance and economic growth was positive, it did not reach statistical significance. In conclusion, the study underscores the critical role of external demand in driving economic growth in Nigeria, particularly highlighting the stimulative effect of a strong depreciation of the domestic currency. As a recommendation, the government is urged to adopt export-driven policies aimed at bolstering trade balance, fostering export, particularly of primary products, to attract foreign exchange inflows and foreign investment, thereby spurring economic growth in Nigeria.

Measuring Asymmetric Volatility of Bank Nifty Index using Egarch Model

The paper examines the significance of volatility models in forecasting future volatility for effective portfolio allocation and risk reduction. It compares the performance of symmetric and asymmetric models in estimating conditional variance, and linear versus non-linear GARCH models. Using secondary data from the National Stock Exchange's Nifty Bank index, the study applies Exponential GARCH (1,1) to measure asymmetric volatility and conducts various tests to confirm the suitability of the data for analysis. The results indicate clustering of volatility in Nifty Bank returns over a four-year period, with the presence of asymmetrical effects and leverage constants. The study concludes that negative information has a greater impact on volatility than positive surprises, and that market fluctuations are inversely related to stock market performance. This research provides valuable insights for portfolio selection, risk management, and asset pricing in the context of increasing volatility across various markets and industries.

Comparison of non-linear time series models (Beta-t-EGARCH and NARMAX models) with Radial Basis Function Neural Network usingReal Data

This paper presents a comparison of three different non-linear time series modelling approaches: NARMAX (Non-linear Autoregressive Moving Average with Exogenous Inputs), Beta-t-EGARCH (Beta t Exponential Generalized Autoregressive Conditional Heteroscedasticity), and Radial Basis Function Neural Networks (RBFNN) applied to weekly stock market index data. We will explain three types of models and compare their compositions and structures. Then, we will show which model gives better predictions. To study series data, the comparison involved analysing the structure of the model and its errors in various time series models and summarising their findings. We divide the data into two parts: training data to structure the time series and testing. The training data tests the model's predictions. Then, we can analyse the model with the errors and the best deterrence predictions. After selecting the NARMAX and Beta-t-EGARCH models, we test them with specific criteria. The best choice is finding the model with the lowest average errors. For this study, we analysed the weekly average closing of the Aramco 2222 index from 15 December 2019 to 16 July 2023 and made 187 observations.

A COMPARISON OF ARCH MODELS: THE DETERMINANTS OF BITCOIN’S PRICE

The aim of this study is to determine the number of transactions among the currencies, which will eventually become a part of our lives, cannot be physically held, can move quickly, and emerge as a new shopping and investment tool in the changing world order, as of the year (2023) when this study was conducted. The study focuses on the analysis of the variables that affect the most popular currency, Bitcoin. Although the analysis of variables that influence Bitcoin was determined as the primary aim of the study, the study also attempted to reach a general conclusion about the variables affected by the cryptocurrencies. Since there is no other cryptocurrency that is traded as much as Bitcoin, Bitcoin is thought to be a good model for the analysis of cryptocurrencies. The method used in the study was autoregressive conditional heteroskedastic (ARCH) models. It is believed that the most suitable models for the Bitcoin variable, whose value changes every second, are ARCH and its derivatives. Other models selected from the ARCH models were also added to the analysis as a method. The models used in the study can be listed as follows: linear ARC, generalized ARC (GARCH), exponential GARCH and threshold GARCH. A statistical model called autoregressive conditional heteroscedasticity (ARCH) is used to study the volatility of time series. Through the provision of a volatility model that more closely mimics actual markets, ARCH modeling is utilized in the financial sector to quantify risk. According to ARCH modeling, periods of high volatility are followed by even higher volatility, and periods of low volatility are followed by even lower volatility. In this study, 5 different variables were selected using literature to analyze the variables affecting Bitcoin returns using ARCH models. The dependent variable in the study is the price of Bitcoin. The remaining variables were included in the models as independent variables. These variables are actually variables that are accepted and selected as the best among a set of variables. In other words, 15 variables were first added to the study using the literature. After this, a correlation analysis was carried out. As a result of the correlation analysis, the variables with the highest correlation with the price of Bitcoin, which is the dependent variable, and the lowest correlation with each other were retained in the model. These variables are Bitcoin Price, Crude Oil Spot Price, Euro-Dollar Parity, Gold Spot Price and NASDAQ Composite Index. The study period is between 2020 and 2023 and it was studied using daily data. Days with no data were removed from the daily period from 2020 to 2023 and loss of information was prevented. After removing missing observations, this study examined the remaining 837 observations. During the research, while running the models created using different methods, it was found that the model that gives the best result is the GARCH model. In other words, when modeling the variables affecting bitcoin (cryptocurrency from the perspective of the population), it was seen that the GARCH model gave the best results when comparing linear ARCH, generalized ARCH (GARCH), exponential GARCH, and threshold GARCH of the ARCH model. Comparing the output of the GARCH model with other ARCH models not included in this study can be a recommendation for the future study

Modeling the Effects of Volatility and Uncertainty in Psychological Errors on Collective Decision-Making of Investors in the Iranian Capital Market

Objective: The aim of the present study is to model the effects of volatility and uncertainty in psychological errors on the collective decision-making of investors in the Iranian capital market. Methodology: To test the hypotheses, a sample consisting of 204 companies from those listed on the Tehran Stock Exchange was selected using the systematic elimination method over a 5-year period from 2018 to 2022. The research data were collected on a monthly basis with a panel data approach and were analyzed using three multiple linear regression models. These models were calculated using the Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) and Threshold Generalized Autoregressive Conditional Heteroskedasticity (TGARCH) methods, with the help of Excel 2016 and Eviews13 software for statistical analysis. Findings: According to the results of the statistical tests of the research hypotheses, the volatility of the psychological error index and investors' trading behavior has a significant and negative impact on abnormal stock returns. Additionally, the volatility of the psychological error index has a significant and positive impact on the volume and frequency of abnormal stock trades. However, the volatility of investors' trading behavior has a significant and negative impact on the volume and frequency of abnormal stock trades. Conclusion: The results of the analysis of the EGARCH and TGARCH conditional heteroskedasticity models indicate asymmetry in the influence of collective investment decisions from past data and past volatility, which is consistent with the Prospect Theory that claims positive and negative returns have different effects on investor utility.

Managing extreme cryptocurrency volatility in algorithmic trading: EGARCH via genetic algorithms and neural networks

<abstract> <p>The blockchain ecosystem has seen a huge growth since 2009, with the introduction of Bitcoin, driven by conceptual and algorithmic innovations, along with the emergence of numerous new cryptocurrencies. While significant attention has been devoted to established cryptocurrencies like Bitcoin and Ethereum, the continuous introduction of new tokens requires a nuanced examination. In this article, we contribute a comparative analysis encompassing deep learning and quantum methods within neural networks and genetic algorithms, incorporating the innovative integration of EGARCH (Exponential Generalized Autoregressive Conditional Heteroscedasticity) into these methodologies. In this study, we evaluated how well Neural Networks and Genetic Algorithms predict "buy" or "sell" decisions for different cryptocurrencies, using F1 score, Precision, and Recall as key metrics. Our findings underscored the Adaptive Genetic Algorithm with Fuzzy Logic as the most accurate and precise within genetic algorithms. Furthermore, neural network methods, particularly the Quantum Neural Network, demonstrated noteworthy accuracy. Importantly, the X2Y2 cryptocurrency consistently attained the highest accuracy levels in both methodologies, emphasizing its predictive strength. Beyond aiding in the selection of optimal trading methodologies, we introduced the potential of EGARCH integration to enhance predictive capabilities, offering valuable insights for reducing risks associated with investing in nascent cryptocurrencies amidst limited historical market data. This research provides insights for investors, regulators, and developers in the cryptocurrency market. Investors can utilize accurate predictions to optimize investment decisions, regulators may consider implementing guidelines to ensure fairness, and developers play a pivotal role in refining neural network models for enhanced analysis.</p> </abstract>

Transition E-Garch Model for Modeling and Forecasting Volatility of Equity Stock Returns in Nigeria Stock Exchange

The mean-equations that exhibit unconditional variance do not reflect real-world data characteristics and do not always fully embrace the thick tail properties of high-frequency financial time series. However, there are cases when mean-equations exhibit conditional and unconditional variances, which conventional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models do not accommodate with assumptions of normal error innovation. The behaviour of equity in stock returns volatility was investigated using mean-equations that reflect both conditional and unconditional variances under the variants innovation distribution. The Nigeria Stock Exchange’s, (NSE’s), daily All Stock Index, (ASI) data from 3rd May 1999 to 18th March 2019 was utilized to characterize the volatility structure of equity in Nigeria Stock returns. The Transition Exponential GARCH Model (TEGM) with non-normal innovations was used to demonstrate the dynamic model performance and predictive power in modeling variances that transit between unconditional and conditional structures. Under various error innovations, the structural characteristics of the TEGM were examined, and the parameters were estimated. The TEGM result under Student’s t innovation distribution was significant for forecasting and predicting random series data. The error distribution has both the minimal and sufficient requirements for the best predictive capacity and forecasting capabilities. Over a longer period, the NSE’s daily ASI showed more unconditional variance than conditional variation. The Transition Exponential GARCH Model was found to be the best model for describing the volatility structure of financial assets in Nigerian stock returns, and is thus recommended for making informed investment decisions with better forecast performance.

Price Discovery and Volatility Spillover: An Empirical Analysis of Indian Futures-Spot Cardamom Markets

Price discovery and its related volatility spillover effect are significant indicators in commodity derivatives market to hedge the risk against sharp price fluctuations. This study empirically analyses the price discovery and volatility spillover using vector error correction model, Granger causality and bivariate exponential GARCH model (EGARCH) in Indian cardamom spot-futures markets. Daily time series data of spot market and near month futures contracts spanning the period from January 2009 to December 2020 have been used for the study. These price series data are based on the authenticated sources of Multi Commodity Exchange. The results of vector error correction model supported by Granger causality test indicates that spot market plays the role of leader as it is more efficient in reflecting the new information to prices. The results of bivariate EGARCH (1,1) model show that volatility spillover from cardamom spot market to futures market is dominant.

Exchange Rate Responses and Volatility Spillover Effects during the COVID-19 Pandemic in Indonesia

This paper aims to assess the impact of the confirmed COVID-19 cases, the timing of the outbreak, and physical measures on the returns and spillover effects of exchange rate in Indonesia. The model will be tested by the exponential generalized autoregressive conditional heteroskedastic (EGARCH) process and the spillover volatility index. The study discovers that the confirmed cases, outbreak news, and the implementation of large-scale social restrictions simultaneously contribute to a leverage effect on the volatility of a direct quote of Indonesian Rupiah to Australian Dollar, Euro, US Dollar, Singapore Dollar, and Great British Pound. To a certain extent, the heatwave as well as the meteor-shower effects as a result of clustering events and intense spillover effects in the currency market of Indonesia are observed.

Analysing volatility patterns in emerging markets: symmetric or asymmetric models?

PurposeInvestors aim for returns when investing in stocks, making return volatility a crucial concern. This study compares symmetric and asymmetric GARCH models to forecast volatility in emerging nations like the G4 countries. Accurate volatility forecasting is vital for investors to make well-informed investment decisions, forming the core purpose of this study.Design/methodology/approachFrom January 1993 to May 2021, the study spans four periods, focusing on the global economic crisis of 2008, the Russian crisis of 2015 and the COVID-19 pandemic. Standard generalized autoregressive conditional heteroscedasticity (GARCH), exponential GARCH (E-GARCH) and Glosten-Jagannathan-Runkle GARCH models were employed to analyse the data. Robustness was assessed using the Akaike information criterion, Schwarz information criterion and maximum log-likelihood criteria.FindingsThe study's findings show that the E-GARCH model is the best model for forecasting volatility in emerging nations. This is because the E-GARCH model is able to capture the asymmetric effects of positive and negative shocks on volatility.Originality/valueThis unique study compares symmetric and asymmetric GARCH models for forecasting volatility in emerging nations, a novel approach not explored in prior research. The insights gained can aid investors in constructing more effective risk-adjusted international portfolios, offering a better understanding of stock market volatility to inform strategic investment decisions.

Oil Price Fluctuation And Exchange Rate In Nigeria: Is There A Volatility Transmission Effect

Over the period 1980-2022, we examined the transmission effect of oil prices on Nigeria's exchange rate. E-GARCH (Exponential GARCH) model is employed in this study. We used Augmented Dickey Fuller to determine a unit root, integrating exchange rates, crude oil prices, external reserves, GDP, inflation, and interest rates to one I(1) and zero I(0). We used Johansen Co-integration to determine long-term relationships. Interest rates, inflation, and crude oil prices all correlated positively with each other. A statistically insignificant result is shown by the variance equation, indicating there is no correlation between crude oil prices and exchange rates. The Nigerian exchange rate is not affected by volatility transmission or leverage due to fluctuations in crude oil prices. According to the study, governments should take monetary policy measures to stabilize exchange rates during unpredictable oil price fluctuations. It is necessary to adjust the naira exchange rate when oil prices fluctuate.

GARCH Models and Distributions Comparison for Nonlinear Time Series with Volatilities

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is extensively used for handling volatilities. However, with numerous extensions to the standard GARCH model, selecting the most suitable model for forecasting price volatilities becomes challenging. This study aims to examine the performance of different GARCH models in forecasting crude oil price volatilities using West Texas Intermediate (WTI) data. The models considered are the standard GARCH, Integrated GARCH (IGARCH), Exponential GARCH (EGARCH), and Golsten, Jagannathan, and Runkle GARCH (GJR-GARCH), each with normal distribution, Student’s t-distribution, and Generalized Error Distribution (GED). To evaluate the performance of each model, the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) are used as the model selection criteria, along with forecast accuracy measures such as absolute error, root mean squared error (RMSE), and mean absolute error (MAE). Post-estimation tests, including the Autoregressive Conditional Heteroskedasticity Lagrange Multiplier (ARCH-LM) test and the Ljung-Box test, are conducted to ensure the adequacy of all models. The results reveal that all GARCH models are suitable for modeling the data, as indicated by statistically significant estimated parameters and satisfactory post-estimation outcomes. However, the EGARCH (1, 1) model, particularly with Student’s t-distribution, outperforms other models in both data fitting and accurate forecasting of nonlinear time series.

Volatility Forecasting Using Quasi-Score-Driven Models with an Application to the Coronavirus Pandemic Period

Abstract We study the statistical and volatility forecasting performances of the recent quasi-score-driven EGARCH (exponential generalized autoregressive conditional heteroscedasticity) models. We compare the quasi-score-driven EGARCH models with GARCH, asymmetric power ARCH (A-PARCH), and all relevant score-driven EGARCH models of the literature. For score-driven and quasi-score-driven EGARCH, we use the following seven score-driven probability distributions: Student’s t-distribution; general error distribution (GED); generalized t-distribution (Gen-t); skewed generalized t-distribution (Skew-Gen-t); exponential generalized beta distribution of the second kind (EGB2); normal-inverse Gaussian distribution (NIG); Meixner distribution (MXN). We use all combinations of those distributions for (i) the probability distribution of the dependent variable, and (ii) the probability distribution which defines the quasi-score function updating term of the quasi-score-driven filters. We use daily data for the Standard & Poor’s 500 (S&P 500) index. We find that both in-sample and out-of-sample, quasi-score-driven EGARCH is superior to GARCH, A-PARCH, and score-driven EGARCH. We report in-sample results for the period of January 2000 to December 2020, providing evidence in favor of the quasi-score-driven EGARCH model for the last two decades. We report out-of-sample volatility forecasting results for a period within the coronavirus disease 2019 (COVID-19) pandemic, providing evidence in favor of the quasi-score-driven EGARCH model for a crisis period.

Research on Risk Measurement of China’s Carbon Trading Market

In today’s environmentally conscious world, carbon trading has emerged as a widely accepted economic instrument to mitigate the externalities resulting from deteriorating environmental problems. Consequently, the use of market-based mechanisms to address environmental issues has reached a global consensus. Many countries are implementing progressive steps by establishing carbon markets to promote low-carbon development and meet their carbon reduction targets. However, the inherent risks in carbon trading markets may hamper the formation of a reasonable carbon price signal, leading to inadequate stimulation of low-carbon technology investments and potential failure to achieve national emission reduction goals. Therefore, managing the risks associated with carbon trading markets is crucial. This study focuses on measuring the risk of China’s carbon market, with the primary aim of exploring carbon price fluctuation patterns and precisely measuring market risks. The risks associated with China’s carbon market are quantified and analyzed using the exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model, extreme value theory (EVT), and the value at risk (VaR) method. Results show that (1) the effect of external shocks on each carbon market is asymmetrical, and positive shocks exert considerable leverage effects on carbon price fluctuations. (2) EVT can be used to effectively fit the risks in the carbon markets. The risks of each carbon market show different characteristics. The risk of Hubei and Guangdong carbon markets is relatively small, and the dynamic VaR is nearly ±0.2. (3) Compared with the performance of the Chinese carbon market, the performance of the European Union Emission Trading Scheme is more stable, and its dynamic VaR for most of the period is within ±0.1, which is considerably lower than the VaR of other Chinese carbon markets. This study also proposes suitable policy implications to ensure the healthy and sustainable development of China’s carbon market.

Long-range, time-varying statistical prediction of annual precipitation in a Mediterranean remote site

In the Mediterranean basin, climate change signals are often representative of atmospheric transients in precipitation patterns. Remote mountaintop rainfall stations are far from human influence and can more easily unveil climate signals to improve the accuracy of long-term forecasts. In this study, the world’s longest annual precipitation time-series (1884–2021) from a remote station, the Montevergine site (1284 m a.s.l.) in southern Italy, was investigated to explain its forecast performance in the coming decades, offering a representative case study for the central Mediterranean. For this purpose, a Seasonal AutoRegressive-exogenous Time Varying process with Exponential Generalised Autoregressive Conditional Heteroscedasticity (SARX(TVAR)-EGARCH) model was developed for the training period 1884–1991, validated for the interval 1992–2021, and used to make forecasts for the time-horizon 2022–2051, with the support of an exogenous variable (dipole mode index). Throughout this forecast period, the dominant feature is the emergence of an incipient and strong upward drought trend in precipitation until 2035. After this change-point, rainfall increases again, more slightly, but with considerable values towards the end of the forecast period. Although uncertainties remain, the results are promising and encourage the use of SARX(TVAR)-EGARCH in climate studies and forecasts in mountain sites.

The information content of sentiment indices in forecasting Value at Risk and Expected Shortfall: a Complete Realized Exponential GARCH-X approach

The aim of this paper is to investigate the impact of public sentiment on tail risk forecasting. In this framework, we extend the Realized Exponential GARCH model to directly incorporate information from realized volatility measures and exogenous variables, thus resulting in a novel dynamically complete specification denoted as the Complete REGARCH-X model. Several sentiment indices related to social media and journal articles regarding the economy and stock market volatility are considered as potential drivers of volatility dynamics. An application to the prediction of daily Value-at-Risk and Expected Shortfall for the Standard & Poor’s 500 index provides evidence that combining the information content of realized volatility and sentiment measures can lead to significant accuracy gains in forecasting tail risk.

Is the Evergrande crisis spilling beyond China?

This study investigates whether Evergrande transmits shocks to regional and global equity markets using the vector autoregressive (VAR), asymmetric dynamic conditional correlation (ADCC), and exponential generalised autoregressive conditional heteroskedasticity (EGARCH) models. The results show that Evergrande has caused notable and enduring shocks to both domestic and foreign equities markets. The spillover test further supports the idea that the Evergrande crisis has spread to important markets. The findings have practical implications for regulators, sovereign wealth managers, institutional and retail investors, and policymakers trying to come up with ways to deal with external shocks.

Modelling and Forecasting Volatility on Electric Power Exchange SEEPEX

Research Question: The launch and the beginning of trade on the South East Electric Power Exchange (SEEPEX) in Belgrade, early in 2016, opened the issue of forecasting volatility and price movements in the market. Motivation: The issue is of vital importance for all market actors for the purpose of maximising profits, reducing risks, planning production and making investment decisions. Forecasting volatility and price movements in electric power markets is important for traders with profit maximisation and yield-to-risk ratio optimisation in mind and, equally, for producers, large industrial consumers, investors and portfolio managers. Idea: Exploring models and techniques to forecast volatility in electricity markets and subsequently testing statistical methods based on time series data, the ARMA-GARCH being the preferred model, with a view to identifying optimal methods for this market. The volatility of the power market and price movements have been tested during a given period. The results can be used to gauge market parameters and opportunities to extrapolate future volatility and movements in electricity prices. Data: For the purposes of this analysis, a time series involving price movements and trade volumes were used, covering a period between the SEEPEX trade launch and the end of 2019. Tools: In the empirical part of the paper, "Stata 13" statistical and econometric software was used to explore stylised facts and model the volatility of SEEPEX electricity price returns. Findings: The authors offer an overview of different methods used in the research, having selected different specifications of the ARMA-GARCH model as the most reliable in predicting volatility in the given market. The exponential GARCH model with student-t error distribution is believed to have provided the best overall performance in modelling the SEEPEX return volatility, as well as the best volatility forecast. Contribution: This is one of the first empirical studies of the Serbian power market that deals with risk modelling. Forecasting time-varying electricity exchange volatility is important for all market participants interested in variance forecasts to be used to calculate risk and hedging measures.

Study the Effect of Exchange Rate Volatility on House Price in Iran (Exponential GARCH and Quantile Regression Approach)

Study the Effect of Exchange Rate Volatility on House Price in Iran (Exponential GARCH and Quantile Regression Approach)

Assessing the impact of the COVID-19 pandemic on the performance of the Vietnam stock exchange: An empirical analysis

The emergence of COVID-19 in Wuhan, China, in December 2019 led to a global crisis with profound implications for public health and the global economy. This study investigates the ramifications of the pandemic on the Vietnam Stock Exchange, recognizing its interconnectedness with global financial markets. Despite the considerable speculation surrounding the pandemic's influence on economic and financial systems worldwide, limited empirical research has been conducted on its specific impact on the Vietnam Stock Exchange. Employing historical data spanning from January 30, 2020, to April 27, 2022, sourced from a secondary dataset, this research empirically explores the performance of the Vietnam Stock Exchange during the COVID-19 pandemic period compared to a normal period. The findings reveal a significant decline in stock returns and heightened volatility during the pandemic, signaling adverse effects on the exchange's performance. Furthermore, the study applies Quadratic GARCH (QGARCH) and Exponential GARCH (EGARCH) models, incorporating a dummy variable, to scrutinize stock returns. The results corroborate the pandemic's negative impact on stock returns in Vietnam. This research underscores the importance of implementing strategic political and economic policies, including maintaining a stable political environment, promoting indigenous enterprises, diversifying the economy, and adopting a flexible exchange rate regime. These measures are recommended to enhance the resilience of the financial market and attract new investors to the Ho Chi Minh Stock Exchange.