GARCH Research Articles

Bayesian influence diagnostics for a multivariate GARCH model

Bayesian influence diagnostics for a multivariate GARCH model

VOLATILITY ANALYSIS AND INFLATION PREDICTION IN PANGKALPINANG USING ARCH GARCH MODEL

One of the concerns of both developed and developing countries, as well as in a region, is the amount of inflation that occurs. Inflation is a serious problem. Inflation is a macroeconomic variable that affects people's welfare and is defined as a complex phenomenon resulting from general and continuous price increases. This research aims to analyze the volatility and projected value of the inflation rate, especially in Pangkalpinang City, using the Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. This research uses time series data on inflation rate of Pangkalpinang, Bangka Belitung Island Province from January 2014 to May 2024. This data was obtained through publications from the Central Statistics Agency of Bangka Beliltung Islands Province. The ARCH model is used to handle heteroscedasticity in data, while the GARCH model is a development of the ARCH model and serves as a generalization of the volatility model. This research shows that the predicted inflation rate in Pangkalpinang City from June 2024 to November 2024 tends to decrease with a MAPE prediction accuracy level of 200.04%. The high MAPE value is caused by actual data moving toward 0.

Russia, China and the USA: perception of effects in the corporate bond market

Purpose: is to identify the dynamics of mutual influences and risks in the corporate bond markets of Russia, China, and the United States under conditions of external environmental instability.Methods: the methods of comparative and econometric analysis of daily data from 2016 to 2024 were used, including the average yields of short- and medium-term corporate and the government bonds of the Russian Federation, China and the United States, selling prices of gold, oil, exchange rates, refinancing rates. GARCH models for forecasting the volatility of the index of corporate bonds of the Russian Federation and China under the influence of internal and external factors, multidimensional quantile regression for industries of the Russian Federation are calculated.Results: six stages of changes in the dynamics of the corporate bond debt market under the influence of the market itself and external factors were highlighted. Periodization made it possible to study the impact of short-term and long-term effects of shocks on the debt market. For the Russian Federation, the volatility weight of the previous period is more than twice the weight of the long-term average volatility. For China, this ratio is even higher. The debt market of the Russian Federation is influenced by the debt markets of China and the United States, but the opposite has not been proven. Three groups of branches of the Russian economy have been formed according to the generality of reaction to external influences.Conclusions and Relevance: during crisis periods, the weight of long-term average market volatility and local factors increases, while that of external factors decreases. Understanding the interactions of internal and external factors allows investors to anticipate market fluctuations, adapt and protect capital. For the Government, this provides an opportunity to develop scientifically sound risk forecasts and use new financial instruments such as yuan bonds.

Multivariate GARCH models with spherical parameterizations: an oil price application

In popular Baba-Engle-Kraft-Kroner (BEKK) and dynamic conditional correlation (DCC) multivariate generalized autoregressive conditional heteroskedasticity models, the large number of parameters and the requirement of positive definiteness of the covariance and correlation matrices pose some difficulties during the estimation process. To avoid these issues, we propose two modifications to the BEKK and DCC models that employ two spherical parameterizations applied to the Cholesky decompositions of the covariance and correlation matrices. In their full specifications, the introduced Cholesky-BEKK and Cholesky-DCC models allow for a reduction in the number of parameters compared with their traditional counterparts. Moreover, the application of spherical transformation does not require the imposition of inequality constraints on the parameters during the estimation. An application to two crude oils, WTI and Brent, and the main exchange rate prices demonstrates that the Cholesky-BEKK and Cholesky-DCC models can capture the dynamics of covariances and correlations. In addition, the Kupiec test on different portfolio compositions confirms the satisfactory performance of the proposed models.

Cryptocurrencies fall from grace: Snatched safe flight to which haven during Russia-Ukraine conflict?

The unprecedented upheaval in an economic and financial system facilitates herding behaviour and flight-to-safety (FTS) episodes from a riskier asset into a safer one. The Russia-Ukraine conflict shows that the financial market assets are still prone to external shock. In line with this, the study explores the inconclusive insights on an FTS from cryptocurrencies to US treasury securities. The paper employs dynamic conditional correlation – generalized autoregressive conditional heteroskedasticity (DCC-GARCH) to test the FTS episode for a period from February 24, 2022 to February 23, 2023. The findings hold a sizeable negative and significant volatility coefficient, particularly DCCα, which directs to support the notion of short-lived FTS from cryptocurrencies to treasury securities during the invasion period. Nevertheless, some evidence of the positive volatility effect points out the risk diversification benefits. The results also show flight-to-quality from BTC, ETH, USDT, BNB, ADA and MATIC to the US dollar index (USDX), however, for other cryptocurrencies, it acts as a diversifier. We unfolded several implications that could be interesting for a market participant looking for evidence on the behaviour of cryptocurrencies and govt. backed securities during times of market uncertainty in the future.

Forecasting the Volatility of OPEC Oil Prices using Fractionally Integrated GARCH models

Some time series are characterized by their great volatility over time, especially time series related to the movement of the economy, and those related to the change in stock prices or the movement of financial transactions and stock markets, which are characterized by being non- stationary over time due to the change in the behavior of observations, making them suffer from the problem of Heteroscedasticity . The paper aims the use of predictive models that a time series can adapt to with large fluctuations and with long memory over time, a number of important models used to deal with FIGARCH time series when the error distribution follows the t-distribution were studied and reviewed, which were used For the first time by Researcher Engel in 1982 and developed by other researchers, the characteristics of these models were reviewed and applied for the purpose of forecasting daily oil prices according to the prices approved by OPEC for the period from 2004 to 2022, where the practical analysis of oil price data showed that the best prediction model is the ARMA(2,2)-FIGARCH(1,d,2) model in which the error follows the t-distribution, and the best predictor performance is out of sample .

A Functional Garch Model with Multiple Constant Parameters

A Functional Garch Model with Multiple Constant Parameters

Influence of oil price fluctuations on inflation uncertainty

PurposeThe purpose of this study is to achieve a comprehensive understanding of how the intricate interconnections between oil price fluctuations, supply chain disruptions and shifting demand patterns collectively shape inflation dynamics within the Chinese economy, especially during critical periods such as the Covid-19 pandemic and geopolitical events like the Russia–Ukraine conflict. The importance of assessing the impact of oil price volatility on China’s inflation becomes particularly pronounced amidst these challenging circumstances.Design/methodology/approachThis study uses the Markov Regime-Switching generalized autoregressive conditional heteroskedasticity (MRS-GARCH) family of models under student’s t-distributions to measure the uncertainty of oil prices and the inflation rate during the period spanning from 1994 to 2023 in China.FindingsThe results indicate that the MRS-GJR-GARCH-in-mean (MRS-GARCH-M) models, when used under student’s t-distributions, exhibit superior performance in modeling the volatility of both oil prices and the inflation rate. This finding underscores the effectiveness of these models in capturing the intricacies of volatility dynamics in the context of oil prices and inflation. The study has identified compelling evidence of regime-switching behavior within the oil price market. Subsequently, the author conducted an analysis by extracting the forecastable component, which represents the expected variation, from the best-fitted models. This allowed us to isolate the time series of oil price uncertainty, representing the unforecastable component. With this unforecastable component in hand, the author proceeded to estimate the impact of oil price fluctuations on the inflation rate. To accomplish this, the author used an autoregressive distributed lag model, which enables us to explore the dynamic relationships and lags between these crucial economic variables. The study further reveals that fluctuations in oil prices exert a noteworthy and discernible influence on the inflation rate, with distinct patterns observed across different economic regimes. The findings indicate a consistent positive impact of oil prices on inflation rate uncertainty, particularly within export-oriented and import-oriented industries, under both of these economic regimes.Originality/valueThis study offers original value by analyzing the impact of crude oil price volatility on inflation in China. It provides unique insights into the relationship between energy market fluctuations and macroeconomic stability in one of the world’s largest economies. By focusing on crude oil – a critical but often overlooked component – this research enhances understanding of how energy price dynamics influence inflationary trends. The findings can inform policymakers and stakeholders about the significance of energy market stability for maintaining economic stability and guiding inflation control measures in China.

A simulation analysis of returns-risk portfolio optimization models

Portfolio optimization is the process of choosing the best investment decision across a set of financial instruments or assets. Investors seek to maximize their (expected) returns, but higher expected return usually means taking on more risk. So, investors are faced with a tradeoff between risk and expected return. This problem can be approached in several ways, including: maximize a portfolio’s expected return for a given risk, minimize a portfolio’s risk for a given expected return, or apply a fractional model with a returns over risk ratio that keeps both expected returns and risk flexible simultaneously. The objective of this paper is to compare these modeling strategies through real world financial data as well as simulation of returns using the Moving Average-Integrated Generalized Autoregressive Conditional Heteroskedastic (MA-IGARCH) model. Our results find that the ratio model provides a more balanced portfolio and provides more stable results than the other two approaches.

Economic Conditions and Predictability of US Stock Returns Volatility: Local Factor Versus National Factor in a GARCH‐MIDAS Model

ABSTRACTThe aim of this paper is to utilize the generalized autoregressive conditional heteroscedasticity–mixed data sampling (GARCH‐MIDAS) framework to predict the daily volatility of state‐level stock returns in the United States (US), based on the weekly metrics from the corresponding broad economic conditions indexes (ECIs). In light of the importance of a common factor in explaining a large proportion of the total variability in the state‐level economic conditions, we first apply a dynamic factor model with stochastic volatility (DFM‐SV) to filter out the national factor from the local components of weekly state‐level ECIs. We find that both the local and national factors of the ECI generally tend to affect state‐level volatility negatively. Furthermore, the GARCH‐MIDAS model, supplemented by these predictors, surpasses the benchmark GARCH‐MIDAS model with realized volatility (GARCH‐MIDAS‐RV) in a majority of states. Interestingly, the local factor often assumes a more influential role overall, compared with the national factor. Moreover, when the stochastic volatilities associated with the local and national factors are integrated into the GARCH‐MIDAS model, they outperform the GARCH‐MIDAS‐RV in over 80% of the states. Our findings have important implications for investors and policymakers.

Volatility Dynamics Analysis of Bitcoin (BTC-USD) and MicroStrategy (MSTR)

This study examines the volatility dynamics of Bitcoin (BTC-USD) and MicroStrategy (MSTR) from September 2019 to September 2024 using the GARCH (1,1) model. Volatility is a key measure of risk in the financial market, understanding its patterns is crucial for effective portfolio management, risk management, and corporate financial strategies. Bitcoin, while known to be volatile, is very unpredictable, and given the high holding of that on MicroStrategy's balance sheet, it is closely tagged to the volatility of Bitcoin. Critical periods, such as the COVID-19 and the subsequent crypto market downturn between 2022 and 2023, demonstrate the linkages between traditional equities and digital assets. The findings of such analysis will prove that MicroStrategy's volatility has indeed closely followed the footsteps of Bitcoin, especially during the 2024 rally in that market, including all its shocks and recoveries. These find great importance in understanding volatility due to the growing integration of digital assets into corporate portfolios. This research will offer investors and corporate managers alike extensive insight into risk management and portfolio diversification by accounting for volatility dynamics between cryptocurrencies and stocks.

Realized GARCH Model in Volatility Forecasting and Option Pricing

Realized GARCH Model in Volatility Forecasting and Option Pricing

Impact of Narrow Framing on Portfolio Allocation: A Numerical Simulation-Based Approach

Many phenomena observed in financial markets remain unexplained by the Expected Utility Theorem (EUT), a framework which is commonly used to analyze decision-making behavior. In recent years, several theories related to behavioral economics have been proposed to address the limitations of this model and provide solutions to the problems that the EUT cannot explain. While this has significant theoretical importance, there have been few studies that have used real-world dynamics to validate the new findings. This study explores the behavioral patterns explained by a model that includes the narrow framing effect using three products in financial markets. Specifically, the study uses a multivariate GARCH model and asset simulations to validate theoretical predictions and investigates the theoretical impact of the narrow framing on portfolio allocation decisions. The results show that the theory is consistent with the real-world financial markets. This study provides new insights into understanding the changes in financial markets.

Weak dependence and optimal quantitative self-normalized central limit theorems

Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry–Esseen bound of optimal order n^{-1/2} for studentized (self-normalized) partial sums, both for the Kolmogorov and Wasserstein (and L^{p} ) distances. The results show that in general, (minimax) optimal estimators of the long-run variance lead to suboptimal bounds in the central limit theorem, that is, the rate n^{-1/2} cannot be reached, refuting a popular belief in the literature. This can be salvaged by simple methods. We reveal that in order to maintain the optimal speed of convergence n^{-1/2} , simple over-smoothing within a certain range is necessary and sufficient. The setup contains many prominent dynamical systems and time series models, including random walks on the general linear group, products of positive random matrices, functionals of GARCH models of any order, functionals of dynamical systems arising from stochastic differential equations, iterated random functions and many more.

Price Volatility in the European Wheat and Corn Market in the Black Sea Agreement Context

The outbreak of war in Ukraine has severely disrupted global food and agricultural markets and affected commodity prices. The grain agreement, also known as the Black Sea Initiative, was concluded on 22 July 2022 by Ukraine, Russia, Turkey, and the United Nations, to alleviate the global food crisis caused by the conflict. This study aims to ascertain whether the agreement has resulted in the stabilization of cereal markets, examining the evolution of prices of wheat and corn, which are of significant importance in Ukrainian exports, throughout the duration of the agreement, including its signing, implementation, and expiration. The analysis, based on the GARCH model and using daily quotations of corn and wheat futures contracts of the European futures exchange Euronext from December 2021 to May 2024, indicates that prices were characterized by exceptionally high volatility in the period preceding the signing of the agreement, and at the time of its expiration. The uncertainty regarding cereal trade conditions has triggered shocks, with a long-lasting impact on price volatility.

Impact of Green Bonds on Traditional Equity Markets

Impact of Green Bonds on Traditional Equity Markets

Stochastic behavior of green bond premiums

Stochastic behavior of green bond premiums

Sustainable finance, herding behavior and risk aversion during market volatility

PurposeWe investigate herding behavior and explore how risk aversion interacts with herding in a sample of selected sustainability indices. Furthermore, we evaluate volatility co-movements and dynamic and time-varying correlations of two notable indicators: the cross-sectional absolute deviation of returns (CSAD) and the risk aversion index (RAI). Moreover, we explore a spillover mechanism (in the short and long run) of risk aversion to sustainable investing.Design/methodology/approachOur study uses daily prices from 01/06/2012 to 15/07/2022 obtained from S&P Dow Jones Indices. We use autoregressive - Glosten, Jagannathan, and Runkle generalized autoregressive conditional heteroscedastic (AR(1)-GJR GARCH) methodologies to measure the impact of cross-sectional absolute deviation of returns (CSAD) and risk aversion (RAI) indicators on the conditional variance of selected sustainability indices. Furthermore, we employ dynamic conditional correlation with generalized autoregressive conditional heteroscedasticity, generalized autoregressive conditional heteroscedasticity generalized autoregressive conditional heteroscedasticity mixed data sampling and dynamic conditional correlation with mixed data sampling models to examine any dynamic correlation, spillover volatility effects and the predictability stance of the CSAD and the RAI factors on sustainable investing.FindingsOur empirical outcomes capture no-herding behavior but display herding on the risk aversion indicator. The cross-sectional dispersion of returns positively affects the conditional variance of all selected sustainable markets, besides emerging markets, while the risk aversion factor negatively influences the conditional variance for Europe and the USA. We have identified long-term contagion effects relating to the variability of returns in our sample, with the exception of emerging markets.Practical implicationsThe dispersion of returns can predict the swings of long-term volatilities of Nordic and Europe markets, while the risk aversion factor can predict the long-run volatilities of sustainable markets except Nordic.Originality/valueThe current study presents, for the first time in the sustainable finance literature, an empirical analysis of herding and risk aversion in sustainable investment returns over time. Our findings offer valuable insights to fund managers, finance professionals and investors, providing them with an opportunity to proactively manage their portfolios and reduce financial risk by understanding the volatility behavior of sustainable investing. Furthermore, it is crucial to explore and understand how the dispersion of returns and risk aversion interact with sustainable markets for the construction of optimal portfolios.

Application of a combined arching model in the load transfer platform of rigid inclusion system with raft through FEM evaluation

Application of a combined arching model in the load transfer platform of rigid inclusion system with raft through FEM evaluation

STOCK PRICE FORECASTING USING THE HYBRID ARIMA-GARCH MODEL

In the current era, many people have made investments, namely capital investment activities within a certain period to seek and get profits. One of the most popular investment instruments in the capital market is stocks, which consist of conventional stocks and Islamic stocks. Conventional stocks are shares traded on the stock market without adhering to Sharia principles. In contrast, Sharia-compliant stocks meet Islamic principles and are traded in the sharia capital market. One form of development of the Islamic capital market in Indonesia is the existence of the Indonesian Sharia Stock Index (ISSI), which projects the movement of all Islamic stocks on the Indonesia Stock Exchange (IDX). Stock prices change every day so modeling is needed that can be used by investors to determine decisions. The Autoregressive Integrated Moving Average (ARIMA) model is one of the forecasting models that is applicable. Stock prices have volatility that tends to be high, this results in variance that is not constant or there is a heteroscedasticity problem, at the same time the ARIMA model must fulfill the assumption of homoscedasticity. Therefore, it is necessary to combine the ARIMA model with a model that can overcome the problem of heteroscedasticity, namely the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. This research aims to get the best hybrid ARIMA-GARCH model that will be used to forecast the stock price of the ISSI. The daily closing data of the ISSI stock price from May 4, 2020, to January 13, 2023, is the data that was used. The study’s findings suggest that ARIMA (0,1,3)-GARCH (2,0) is the best model among all possible models for ISSI stock price forecasting. By evaluating the predictive accuracy of the model using Mean Absolute Percentage Error (MAPE), the forecasting result for ISSI stock prices using the best model, ARIMA(0,1,3)-GARCH(2,0) at 0,6092%, shows a forecasting that is close to the actual data, which means that the model used is highly effective at forecasting stock priced