GARCH Research Articles

Forecasting stock index closing points using ARIMA-GARCH with a rolling data window

This research develops and examines the efficacy of a hybrid ARIMA-GARCH model, augmented by a rolling data window approach, to enhance the accuracy of stock index prediction, specifically focusing on the NEPSE index. Accurate predictions of stock indices are of paramount importance to investors, analysts and policy makers to navigate and circumvent the market uncertainties. The AutoRegressive Integrated Moving Average (ARIMA) model captures linear trends and temporal dependencies in time series data, while the General AutoRegressive Conditional Heteroskedasticity (GARCH) model addresses volatility clustering—ubiquitous character of financial time series—thereby providing a comprehensive framework for prediction. Utilizing a dataset comprised of daily closing points of NEPSE index approximately three years and nine months, the study identifies the ARIMA (5,1,0)-GARCH (1,1) model as optimal fit, upon integrating 180-day rolling data window. This model achieved a Mean Percentage Error of -0.0058% and a correlation of 0.995, which is indicative of superior fit to the underlying time series data. These findings underscore the hybrid model’s capacity to adaptively respond to dynamic market conditions and acclimatize prediction parallel to most recent market trends and volatility. This research is useful for optimizing investment strategies for those invested in Nepalese stocks. Also, this research lays a foundational framework for future investigations into application of this advanced forecasting method in other emerging markets, financial instruments and indices.

IMPACT OF STOCK PRICE FLAKINESS ON DEVELOPMENT OF NIGERIAN EXCHANGE GROUP

This study is aimed to investigate what is happening in the Nigeria Stock Market under its new name, “Nigeria Exchange Group”, with respect to the uncertainty nature of share price behaviour in the capital market. Hence, the month end stock prices of four listed consumer companies from the period January 2017 to December 2022 were used as proxies. The study made use of the Autoregressive Conditional Heteroskedasticity (ARCH) to estimate and find out the presence of the volatility. The study identified the presence of volatility in all the four consumer stock prices used, while the volatility of stock price was then regressed against stock prices to determine their certainty. The results however revealed that out of the four consumer goods companies, only two consumer goods companies’ stock prices were predicted by volatility, while past stock prices predicted current stock prices implying that the market does not follow a random walk. The study therefore recommended that activities of corporate insiders should be critically scrutinized to reduce the predictability of stock prices. Also, that Information should be made available and in clear terms to stakeholders and all investors in particular. Also, that policy makers should carefully review their economic policies in their use of the Nigerian bourse as a barometer to measure performance in the general economy to avoid misleading the investing public.

Detecting anomalies in currency market of BRICS countries: insights into emerging economies

PurposeThe primary motive of the research paper is to investigate the efficiency of currency market of emerging economies (BRICS countries), by analyzing the presence and consistency of calendar anomalies – specifically the day-of-the-week (DOW) effect, the January effect and the Turn-of-the-month (TOM) effect. Daily data of around 23 years and 4 months were examined for the purpose of study. Segmented data of 8-year intervals were also analyzed to observe the changes in the pattern over a period. The findings are intended to offer insights into market behaviors and potential trading strategies for astute traders.Design/methodology/approachThe study employed a quantitative research design utilizing ordinary least squares regression with dummy variables and Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) (1,1) model. To study the calendar anomalies, the daily closing price of five currency pairs has been taken from Bloomberg’s software. The Kruskal–Wallis test was conducted to validate and check the robustness of analysis.FindingsThere are mixed results regarding calendar anomalies in the BRICS currency markets. Analysis of aggregate data revealed that DOW effect is present in all the currencies except USDZAR, with Monday showing positive return. The segmented analysis showed the presence of DOW effect in USDCNY and USDINR, while other currencies lacked consistent patterns. The January effect was evident for Indian Rupees and Chinese Yuan but not for other currencies. TOM effect was present only in Chinese Yuan. Overall, the Indian Rupee and Chinese Yuan displayed inefficiencies, indicating potential for trading strategies, while other currencies appeared efficient and lacked consistent patterns.Originality/valueThe literature on currency pricing anomalies is sparse, particularly in the context of developing and underdeveloped economies. While some research exists on anomalies within the currencies of developed nations, there is a significant gap in studies focusing on emerging economies. This paper seeks to address this deficiency by investigating the presence of calendar anomalies in the currencies of BRICS countries, providing new insights into the behaviors of these emerging economies.

Forecasting VaR and Returns Distribution Using the Real-Time GARCH Models with Standardized Two-Sided Lindley Distribution

Forecasting VaR and Returns Distribution Using the Real-Time GARCH Models with Standardized Two-Sided Lindley Distribution

Macroeconomic volatility and terrorism incidents in Africa

AbstractThis article investigates the impact of macroeconomic volatility on terrorism in 38 African economies spanning the period from 1980 to 2012, using available data. It examines four categories of terrorism markers: domestic, transnational, uncertain, and total, and their correlation with the volatility of four macroeconomic indicators—inflation, output growth, domestic credit to the private sector, and government expenditures. The study employs the negative binomial regression estimator on both the conditional variance structures of the generalized autoregressive conditional heteroskedasticity (GARCH) and exponential GARCH (EGARCH) and the unconditional measure of a 3‐year interval time varying of measuring macroeconomic variables' volatilities on other regressors. I find, first, that inflation volatility is a significant predictor of all terrorism markers, except for transnational terrorism. This implies that high inflation volatility is linked to increased domestic terrorism. Second, the role of domestic credit to the private sector in mitigating transnational terrorist activities highlights the importance of stable private sector access to credit in reducing such incidents. Third, government consumption expenditure volatility has a dual effect on terrorism: it amplifies domestic terrorism but serves as a mitigating factor for total terrorism. This indicates that stable government expenditure can reduce overall terrorism, but might increase domestic terrorism. Last, other variables—such as population, ethnicity, conflicts, surface areas, and lagged terrorism values—are also found to influence the examined terrorism measures. For robustness, I employ alternative statistical techniques, including Poisson Pseudo‐maximum likelihood (PPML) estimation with multiple high‐dimensional fixed effects (HDFE). In summary, this study emphasizes the critical role of addressing inflation volatility in macroeconomic policies as a primary measure to counter terrorism. Stable economic conditions, particularly in relation to inflation, can significantly contribute to reducing terrorism in African economies.

Credit spread drivers and cross-country connectedness: a study of emerging economies in Asia

PurposeWhile the existing literature lacks a holistic approach to determining credit spreads and is limited to mostly developed countries, this study investigates credit spread determinants and their cross-country connectedness in the context of four emerging economies in Asia by incorporating bonds, market risk, macroeconomic and global factors.Design/methodology/approachThis study utilizes principal component analysis for dimensionality reduction and variable representation. Furthermore, we employ the dynamic conditional correlation–generalized autoregressive conditional heteroskedasticity model to capture the cross-country credit spread connectedness between the variables.FindingsThe findings indicate that market volatilities are the most significant drivers of credit spreads, while global factors play a moderating role. Furthermore, the results provide compelling evidence of cross-country credit spread connectedness, with China as the primary transmitter and Malaysia as the primary receiver among the selected emerging economies.Originality/valueThis study addresses the limitations of previous research by extending the analysis beyond the commonly studied developed economies and focusing on emerging economies in Asia. It also employs a comprehensive approach to determine credit spread and explores cross-country credit spread connectedness in developing economies, thereby shedding light on financial risks and vulnerabilities within interconnected global financial systems.

Testing in GARCH‐X models: boundary, correlations and bootstrap theory

In this article, we consider the so‐called Fixed Shrinkage (FS) bootstrap for the class of GARCH models with explanatory variables (GARCH‐X). Under the assumption of stationary covariates, the proposed FS bootstrap does not require modeling the covariates, as these are kept fixed in the bootstrap generating process. Our main focus is on testing whether one or more of the covariates can be excluded in the GARCH‐X model. As is well‐known the limiting distribution of the likelihood‐ratio (LR) statistic in this setting is non‐standard and depends in particular on whether nuisance parameters are on the boundary or in the interior of the parameter space. In particular, and as detailed here, the non‐standard limiting distribution depends on correlations, or dependence, between the explanatory variables. The FS bootstrap takes the presence of nuisance parameters into account by implementing shrinking as proposed in Cavaliere et al. (2022) for pure ARCH models. We establish asymptotic validity of the FS bootstrap for GARCH‐X models, and demonstrate by simulations that the bootstrap‐based test performs extremely well even when nuisance parameters lie on the boundary of the parameter space. The empirical illustration amplifies that the presence of nuisance parameters (especially whether or not on the boundary) are vital for interpreting the dynamics of conditional volatility in financial stock market indices.

Forecasting Bitcoin volatility using machine learning techniques

This paper studies the Bitcoin volatility forecasting performance between popular traditional econometric models and machine learning techniques. We compare the 1-day to 2-month ahead forecasting performance of the Long Short-Term Memory (LSTM) and a hybrid Convolutional Neural Network-LSTM (CNN-LSTM) model to the traditional models. We find that neural networks outperform Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models for all forecasting horizons. Furthermore, the LSTM model outperforms the Heterogeneous Autoregressive (HAR) model and by integrating the Markov Transition Field (MTF) into the CNN-LSTM model, we achieve superior forecasting results in the short-term, particularly for the 7-day forecasts.

Predicting the volatility of Chinese stock indices based on realized recurrent conditional heteroskedasticity.

The realized recurrent conditional heteroscedasticity (RealRECH) model improves volatility prediction by integrating long short-term memory (LSTM), a recurrent neural network unit, into the realized generalized autoregressive conditional heteroskedasticity (RealGARCH) model. However, at present, there is no literature on the ability of the RealRECH model to fit and predict volatility in the Chinese market. In this paper, a study is conducted to test the in-sample explainability and out-of-sample prediction ability of the RealRECH model for the SSE50, CSI300, CSI500 and CSI1000 indices in the Chinese market and to determine whether it performs better than the RealGARCH model. The results of the in-sample analysis show that the RealRECH model not only provides better in-sample interpretability for all four indices but also captures the complex dynamics of time series volatility that the RealGARCH model cannot capture, such as long-term dependence and nonlinearity. The results of out-of-sample volatility prediction show that the RealRECH model better predicts the volatility of the CSI500 and CSI1000 indices but yields worse predictions for the SSE50 and CSI300 indices. Thus, the RealRECH model can be used for CSI500 and CSI1000 prediction.

Matrix GARCH model: Inference and application*

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use of a univariate GARCH specification for the trace of conditional row or column covariance matrix, which allows for the model identification. Moreover, we introduce a quasi-maximum likelihood estimator (QMLE) for model estimation and develop a portmanteau test for model diagnostic checking. Simulation studies are conducted to assess the finite-sample performance of the QMLE and portmanteau test. To handle large dimensional matrix time series, we also propose a matrix factor GARCH model, and establish its theoretical properties. Finally, we demonstrate the superiority of the matrix GARCH and matrix factor GARCH models over existing multivariate GARCH-type models in volatility forecasting and portfolio allocations using three applications on credit default swap prices, global stock sector indices, and future prices.

Modelling and Estimation of Volatility Using ARCH Models in India’s Stock Market of Amazon

Modelling and Estimation of Volatility Using ARCH Models in India’s Stock Market of Amazon

Does index options trading destabilize Indian stock market volatility: an application of ARCH and GARCH models

Does index options trading destabilize Indian stock market volatility: an application of ARCH and GARCH models

PERBANDINGAN METODE EXPONENTIAL GARCH (EGARCH) DAN GLOSTEN-JAGANNATHAN-RUNKLE GARCH (GJR-GARCH) PADA MODEL VOLATILITAS SAHAM TUNGGAL

Financial data, such as stock prices, usually have a tendency to fluctuate rapidly and create a heteroscedastic effect on the variance of residuals. The Covid-19 pandemic that occurred from 2020 to 2022 is one factor that can affect economic movements, especially in Indonesia, and has an impact on the volatility of financial data. The problem of heteroscedasticity can be addressed using the ARCH/GARCH model. However, this model has a weakness in capturing the asymmetry of volatility resulting from good news and bad news. Several models that can overcome the problem of volatility asymmetry are EGARCH and GJR-GARCH. The purpose of this thesis research is to determine the best volatility model using the daily stock price data of PT Bank Rakyat Indonesia (Persero) Tbk. covering the period from February 2020 to February 2023. The result of the asymmetric GARCH model suggests that the ARIMA(2,0,2) EGARCH(1,1) model has an AIC value of -4.8850, and the ARIMA(2,0,2) GJR-GARCH(1,1) model has an AIC value of -4.8907. Therefore, the model with the minimum AIC value, which is the ARIMA(2,0,2) GJR-GARCH(1,1) model, is considered the best model. Furthermore, this model exhibits very good forecast accuracy, as evaluated by the sMAPE value of 5,17%.

Stock Returns and Volatility: Comparative Investigation from SAARC Countries

This research article analyses the stock return and volatility of three selected SAARC countries (Pakistan, India, and Bangladesh), focusing on the role of natural resources in influencing market performance. This study aims to determine the robustness of the performance, considering the economic significance of these countries' natural resources. The daily data from the PSX 100 index (Pakistan Stock Exchange), BSE index (Bombay Stock Exchange), and DSE index (Dhaka Stock Exchange) for the years 2019 to 2021 has been obtained from their websites. The data is treated in MS Excel to compute the daily Geometric Returns for BSE, PSX, and DSE indices. Furthermore, the data were analyzed using the specialized package EViews for Time Series Graph, Descriptive Statistics, Unit Root Test, and GARCH Model. The findings of this research show that the BSE index has the highest return value of 6.78 percent compared with 4.56 percent and 3.75 percent for DSE and PSX, respectively. The Half-life model has been applied to calculate the volatility observed by the indices. The result shows that BSE is the most volatile and takes the highest time of 45 days to revert to its mean position, followed by PSX and DSE, which take 19 and 10 days, respectively. Therefore, investing in the BSE index is better for risk-lover investors. At the same time, DSE has the fastest mean reversion compared to the other two indices. Therefore, it is feasible for risk-averse investors.

Exploring the principal factors driving the volatility structure of stock trade levels in New Zealand: a Covid-19 perspective

This paper explores factors that drive the volatility structure of New Zealand stock trade levels, with the aim of understanding unusual volatility of stock trade levels that may pose a risk to the critical operations of a trading venue. Weekly number of trades from 2014–2024 for the sampled stocks were examined within principal axis factoring (PAF) and GARCH models. The results showed that three factors accounted for around 60% of volatility in the number of stock trades over the sampled period; they were driven primarily by electricity generation stocks, consumer discretionary stocks, and commercial property stocks respectively. During the sampled period, two subperiods of market shock showed unusual levels of volatility in all principal factors, with the second subperiod, which coincided with the Covid-19 outbreak, being particularly notable. An implication of the study is that given the volatilities of stock trade levels are little studied in the literature, the findings of this study could be a useful complement to existing studies examining stock price volatility for the purposes of mitigating unusual stock trading volatility.

Comparative Performance of ARIMA and ARCH Models On Time Series of Monthly Libyan Brent Oil Price

Many economic and financial time series exhibit a phenomenon known as heteroscedastic, where the variance of the series changes over time. This research study focuses on financial time series modelling, with special application to modelling the price of Libyan Brent Oil. In particular, the theory of univariate nonlinear time series analysis is explored and applied to the price Libyan of Brent Oil, spanning from January 2000 to December 2010. The data was obtained from Bullent of the Platts Market Wire of Statistics. This study aims to evaluate the performance of ARIMA as a linear model and ARCH as a nonlinear modelling data. Multiple time series models were considered for fitting the data, and the best ARIMA models were selected based on the Akaike Information Criteria (AIC). ARIMA (0, 1, 1), and ARIMA (1, 1, 0) were identified as the best models. After estimating the parameters of the selected models, model checking revealed that these models were not suitable for modeling the data, as they lacked validity according to the test of squared residuals. The goodness of fit was assessed using the AIC, and based on minimum AIC values, the best fit ARCH models were found to be ARIMA (0, 1, 1) - ARCH (1). After estimating the parameters of the selected model, a series of diagnostic and forecast accuracy tests were performed. Based on this model, a twelve-month forecast of the price of Libyan Brent crude was made.

Can Bitcoin trigger speculative pressures on the US Dollar? A novel ARIMA-EGARCH-Wavelet Neural Networks

In recent years, Bitcoin has garnered attention as a digital currency, prompting increasing debate regarding its effects on traditional financial markets, particularly the US dollar. This study investigates the relationship between Bitcoin and the US dollar, especially in the contexts of speculative attacks, where investors attempt to devalue a currency, and short squeezes, where rapid price rises force short sellers to quickly buy back assets to avoid further losses. The study employs a novel hybrid model combining an autoregressive moving average, Generalized Autoregressive Conditional Heteroskedasticity, and Wavelet Neural Networks techniques with neural networks approaches. The results suggest that significant trading activity in Bitcoin/US dollar, particularly during speculative attacks and short squeezes, can substantially impact the US dollar/EUR market, increasing price volatility as traders adjust their strategies. These adjustments, along with risk management strategies, drive higher trading volumes and further volatility. Our findings demonstrate that our novel hybrid model combined with Quantum Recurrent Neural Networks provides the most accurate predictions, offering valuable insights to inform trading strategies in both Bitcoin/US dollar and US dollar/EUR markets. This study has important implications for policymakers and market participants, emphasising the need to understand the relationship between Bitcoin and the US dollar for financial stability and effective policy formulation. It also highlights the necessity of advanced modeling techniques to accurately predict cryptocurrency market behavior.

PM10 AIR QUALITY INDEX MODELING USING ARFIMA-GARCH METHOD: BUNDARAN HI AREA OF DKI JAKARTA PROVINCE

Air quality is an essential factor in urban life, and its’ assessment often relies on the concentration of measurable air pollution parameters. One critical parameter is Particulate Matter (PM), particularly PM10, which comprises solid or liquid particles dispersed in the air from various sources. One of the methods employed for predicting stock index prices is ARFIMA. ARFIMA is used to model long memory data characterized by a slowly decreasing Autocorrelation Function (ACF) plot (hyperbolic) or a difference value in the fractional from. This method is widely used due to its ability to handle nonstationarity issues in time series. However, the time series data often contain heteroskedasticity problems. Data with heteroscedasticity are then further addressed using the GARCH model, because it can model volatility changes occurring over longer periods and capture the persistence of volatility. The ARFIMA-GARCH model can explain long-memory patterns in time series data and address heteroscedasticity issues. The data are sourced from the Jakarta open data web, which is integrated with DLH DKI Jakarta Province. The aim of this research was to forecast the PM10 air quality index at the Bundaran HI Area in the Province of DKI Jakarta for the next 14 days, from January 1st to January 14th, 2021, using an ARFIMA model enhanced with GARCH. The analysis reveals that the best model is ARFIMA ([17], d, [1])-GARCH (1,1). Forecasting using this model resulted in a MAPE of 3.47%, indicating that the model is highly capable of forecasting several periods.

Impact of central bank digital currency uncertainty on international financial markets

Is the impact of central bank digital currency (CBDC) uncertainty on investment and financial stability significant? To address this pivotal question in the era of CBDC development, we employ a combination of models: the time-varying parameter vector autoregression with stochastic volatility (TVP-SV-VAR); the Baba, Engle, Kraft, and Kroner multivariate generalized autoregressive conditional heteroskedasticity (BEKK-MGARCH) model, and wavelet quantile correlation (WQC) analysis. Based on the findings, macrofinancial variables significantly respond to CBDC uncertainty shocks, exhibiting time-varying, heterogeneous, and stage-specific characteristics. These effects are most pronounced in the short term, but diminish over the long term. Notably, the impact of CBDC uncertainty shocks on other financial variables exceeds the reverse impact. In addition, asymmetric volatility spillovers are found, suggesting complex interdependencies. The implication of the findings is that interactions between CBDC uncertainty and financial variables evolve across short-, medium-, and long-term horizons, emphasizing the need for central banks to adopt a flexible approach in CBDC design to alleviate market concerns and enhance overall financial stability.

Forecasting of sunspots cycles thorough ANFIS model and ARMA (R, S)-GARCH (1, 1) model

Forecasting of sunspots cycles thorough ANFIS model and ARMA (R, S)-GARCH (1, 1) model