Volatility Estimation of Multivariate ARMA-GARCH Model

Theoretical models of contagion and spillovers allow for asset-specific shocks that can be directly transmitted from one asset to another, as well as indirectly transmitted across uncorrelated assets through some intermediary mechanism. Standard multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, however, provide estimates of volatilities and correlations based only on the direct transmission of shocks across assets. As such, spillover effects via an intermediary asset or market are not considered. In this article, a multivariate GARCH model is constructed that provides estimates of volatilities and correlations based on both directly and indirectly transmitted shocks. The model is applied to exchange rate and equity returns data. The results suggest that if a spillover component is observed in the data, the spillover augmented models provide significantly different volatility estimates compared to standard multivariate GARCH models.

This paper collects a total of 541 groups of the RMB exchange rate to build the model of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) for forecasting of RMB exchange rate against US dollar. The empirical results show that the GARCH models can fit the series well and the prediction effects of both the GARCH (1, 1) model and the GARCH-M model are good.

This paper uses the prediction method of time series analysis to fit and predict the stock daily logarithmic return series of the four major banks. The ARMA model and the GARCH model are constructed and compared empirically. The results show that the GARCH model is better than that of the ARMA model in the fitting effect. In the prediction effect, The ARMA model is the best, followed by the GARCH model.

Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir

Volatility plays an important role in financial markets and has held the attention of academics and practitioners. Using Generalized autoregressive conditional heteroscedasticity (GARCH) is one of the effective perspective for forecasting volatility. This study focused on comparing GARCH (P, Q) model with GJR-GARCH (P, Q) model and EGARCH (P, Q) model to make prediction more reliable and accurate. The results suggested that both GARCH (P, Q) model and GJR-GARCH (P, Q) model are good choices for forecasting volatility in financial market, especially for describing heteroscedastic time series. GARCH models are consistent with various forms of efficient market theory. These theories state that asset returns observed in the past cannot improve the forecasts of asset returns in the future.

This paper explores the multifaceted phenomenon of stock market volatility, a critical aspect of financial markets with profound implications for investors, businesses, and policymakers. The study begins by introducing the concept of stock market volatility, defining it as the degree of price fluctuations and highlighting its significance in risk assessment, investment decision-making, and market stability. The paper then delves into the historical evolution of volatility studies, tracing its roots from early observations to the development of sophisticated models like GARCH and stochastic volatility models. It examines key theoretical frameworks, including the Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), Behavioral Finance, and GARCH models, that provide insights into the drivers of volatility. Furthermore, the paper explores the various determinants of volatility, encompassing macroeconomic factors (economic growth, interest rates, inflation, exchange rates), market-specific factors (company-specific news, industry trends, market sentiment, liquidity), and global factors (geopolitical events, global economic conditions).The study investigates the implications of volatility for different stakeholders, including investors (risk assessment, portfolio diversification, emotional decision-making), businesses (financial planning, cost of capital, investment decisions), policymakers (monetary policy, regulatory frameworks), and market participants (trading activity, market liquidity, market sentiment).A case study on stock market volatility during the COVID-19 pandemic is presented, highlighting the impact of economic uncertainty, market sentiment, and the oil price shock on market fluctuations. The paper concludes by emphasizing the importance of understanding and managing volatility, and proposes future research directions, including the application of machine learning, the integration of behavioral finance insights, and the analysis of regional and sectoral volatility. This research contributes to a deeper understanding of stock market volatility, enabling investors, policymakers, and researchers to make more informed decisions and navigate the complexities of financial markets.

Exchange rate can be defined as a ratio the value of currency. The exchange rate shows a currency price, if it exchanged with another currency. Exchange rates of a currency fluctuate all the time. Rise and fall exchange rates of a currency in the money market shows the magnitude of volatility occurred in a country currency to other's. To estimate the volatility behavior of the data gave rise to volatility clustering or heteroscedasticity problems, can’t be modeled using ARMA model and asymmetric effects that can‘t be modeled by ARCH or GARCH, can be modeled by Asymmetric Power ARCH (APARCH). In determining the estimated parameter values of APARCH model, used the maximum likelihood method, followed by using the iteration method is Berndt, Hall, Hall and Hausman (BHHH). The APARCH model used to the data return of exchange rate against dollar is APARCH(2,1) or in the form as follows : = 0,00000268 + 0,830902 + 0,130516 + 0,074784 + 0,151157

This paper develops a bivariate asymmetric non-linear smooth-transition Generalized Autoregressive Conditional Heteroskedasticity (GARCH) (BANST-GARCH) model to hedge the risk in the shipping freight rate market. Our dataset consists of 1,768 daily spot and forward freight agreement (FFA) prices of two tanker routesTD3 and TD5with the latter showing an asymmetric pattern. The empirical results of hedging effectiveness strongly support the concept that the BANST-GARCH model outperforms other models in both in- sample and out-of-sample periods with the largest variance reduction. Thus, our model is able to capture the asymmetric pattern in the tanker freight market. This study contributes to the literature by providing a new overview of the interaction between tanker spot and FFA markets, discovering the asymmetric effect of shocks in the shipping market, developing an advanced econometric model to capture the asymmetrical effect, and constructing a better hedge strategy on the basis of our BANST-GARCH model.

A general autoregressive conditional heteroskedasticity (GARCH)-typed variance-gamma (VG) model, the VG-GARCH model, developed by Kao, Wu, and Lee (2011) is adopted for the analysis of high-frequency intraday price data in a price-duration setting. The advantages of the proposed VG-GARCH model are in three respects: (1) The price process is based on an Ito's semi-martingale, namely, a VG process, which is a desirable feature in finance theory; (2) The VG process has its physical-economical implication in that it can be expressed as the market liquidity measure VNET defined by Engle and Lange (2001); (3) By allowing time-varying scale parameter that obeys a nonlinear GARCH (NGARCH) process, the feedback and leverage effects of price changes on elapsed time, and the resulting temporal dependency and clustering in elapsed times and price changes are accounted for. An empirical study is implemented by comparing the proposed model to the EACD-VAR model by Dufour and Engle (2000) of using one-minute S&P 500 index from January 2, 2001 to May 31, 2001. The performance is demonstrated, specifically through a comparison of the proposed model and the competing model.

In the field of business research method, a literature review is more relevant than ever. Even though there has been lack of integrity and inflexibility in traditional literature reviews with questions being raised about the quality and trustworthiness of these types of reviews. This research provides a literature review using a systematic database to examine and cross-reference snowballing. In this paper, previous studies featuring a generalized autoregressive conditional heteroskedastic (GARCH) family-based model stock market return and volatility have also been reviewed. The stock market plays a pivotal role in today’s world economic activities, named a “barometer” and “alarm” for economic and financial activities in a country or region. In order to prevent uncertainty and risk in the stock market, it is particularly important to measure effectively the volatility of stock index returns. However, the main purpose of this review is to examine effective GARCH models recommended for performing market returns and volatilities analysis. The secondary purpose of this review study is to conduct a content analysis of return and volatility literature reviews over a period of 12 years (2008–2019) and in 50 different papers. The study found that there has been a significant change in research work within the past 10 years and most of researchers have worked for developing stock markets.

For the limitations of vibration signals caused by non-stationary autoregressive (AR) model which can not effectively describe the signal characteristics, it is presented a fault diagnosis based on autoregressive conditional heteroskedasticity (ARCH) model. This method firstly uses ARCH model to fit various fault signals and regard the proceeds of the model parameters as the characteristics of fault diagnosis, using RBF neural network classification as fault diagnosis method. The experimental results verify the feasibility and effectiveness of the ARCH model, and at the same time it makes the comparison with the method based on same AR model and another modified method based on AR model. The results show that the method has significantly improvements in the diagnosis rate.

This study examines the relationship between investor sentiment and stock market volatility in the West African Economic and Monetary Union (WAEMU) using data from the West African Regional Stock Exchange (BRVM). Based on daily data spanning the period 2010–2022, five volatility models are estimated and compared: Generalized Autoregressive Conditional Heteroskedasticity [GARCH(1,1)], Exponential Generalized Autoregressive Conditional Heteroskedasticity [EGARCH(1,1)], Asymmetric Power ARCH [APARCH(1,1)], Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity [FIGARCH(1,d,1)] and the RiskMetrics model. The empirical results indicate a high degree of volatility persistence, pronounced asymmetric effects, and the presence of long-memory dynamics in BRVM stock returns. Among the competing specifications, the EGARCH model with an asymmetric Student’s t distribution provides the best overall performance in terms of model fit and forecasting accuracy. Furthermore, the inclusion of an investor sentiment index leads to an improvement in volatility forecasts, highlighting the relevance of behavioral factors in explaining market risk dynamics. These findings suggest that investor sentiment plays an important role in volatility dynamics in emerging African stock markets, while also underscoring the need for caution in interpreting sentiment-based measures due to potential methodological limitations.

This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration, the proposed model is also applied to the daily returns of the Hong Kong Hang Seng index (1983–1984).

Three important parametric models for describing the correlation functions and spectra of stationary stochastic processes are the autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Quite recently, the MATLAB toolbox “ARMASA” has been made publicly available. This toolbox provides state-of-the-art algorithms to perform automatic identification and selection between the models based on the estimated prediction error. ARMASA works on a single segment of data, whereas in some applications, the data are available as multiple segments. We could process each segment independently and average the estimated autocorrelation functions or spectra afterward. Better performance, however, can be expected when all segments are processed simultaneously, for two reasons. Initially, the bias in the estimated model parameters depends on the number of observations in a segment. Averaging models from segments does not reduce this bias, in contrast to identification from all the data at once. In either case, the variance of the estimated model parameters will decrease. By considering all the data at once this variance reduction can be considered in the order selection stage, decreasing the selection bias. In this paper, we extend the parameter estimation algorithms of the ARMASA toolbox to the case of multiple segments. AR parameter estimation from segments has been considered before, but not for the MA and ARMA models. In addition, in the AR case, model order selection can be done easily when the segments are independent. But, in the application we are primarily interested in, the segments are formed by lines of scanning transmission electron microscopy (STEM) images, which can be correlated with each other. Because the correlation among data segments influences the effective number of independent observations available it becomes necessary to estimate that number. This is not an easy problem in general. For observations from a stochastic process with an isotropic 2-D autocorrelation function we can, however, formulate an accurate estimator in terms of the line autocorrelation function. This situation arises, for example, in STEM images of amorphous specimens. From the AR model identification for segments, the extension to the MA and ARMA models is rather straightforward because MA and ARMA algorithms are based on Durbin's methods, whose first step is the estimation of a long AR model. We compare the segment-based algorithms to conventional ARMASA with simulations of stationary stochastic processes. An illustrative example involving simulated STEM images shows large potential benefits.

As the world trade is growing, exchange rate acts as a bridge between different economies and its volatility can affect price level, output, exports and imports. The purpose of this study is to investigate the effects of real exchange rate volatility on the export demand for the two products of apple and potato in the nine developing counteries of producing and exporting the two products during the period of 1992-2009 years.To achieve the goal, using Autoregressive Conditional Heteroskedasticity (ARCH) model, the real exchange rate volatility was estimated. Then the effects of exchange rate volatility on the export demand for apple and potato were analysed based on the panel data approach. The results indicate positive effects of real exchange rate and negative effects of real exchange rate volatility on the export demand. The weighted average income of importing countries has a positive effect and the relative export price of apple and potato has a negative effect on the export demand.