A general framework for spatial 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.

Volatility is a matter of concern for time series modeling. It provides valuable insights into the fluctuation and stability of concerning variables over time. Volatility patterns in historical data can provide valuable information for predicting future behaviour. Nonlinear time series models such as the autoregressive conditional heteroscedastic (ARCH) and the generalized version of the ARCH model, i.e. generalized ARCH (GARCH) models are popularly used for capturing the volatility of a time series. The realization of any time series may have significant statistical dependencies on its distant counterpart. This phenomenon is known as the long memory process. Long memory structure can also be present in volatility. Fractionally integrated volatility models such as the fractionally integrated GARCH (FIGARCH) model can be used to capture the long memory in volatility. In this paper, we derived the out-of-sample forecast formulae along with the forecast error variances for the AR (1) -FIGARCH (1, d, 1) model by recursive use of conditional expectations and conditional variances. For empirical illustration, the modal spot prices of onion for Delhi, Lasalgaon and Bengaluru markets, India and S&P 500 index (close) data are used.

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.

GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models are new statistical methods that are used especially in economic time series. There is a consensus that speech signals exhibit variance that changes through time. GARCH models are a popular choice to model these changing variances. In this chapter, we propose three methods for VAD, which are based on GARCH models. In the first method, heteroscedasticity will be modeled by GARCH process and hard detection is the result of comparing a Multiple Observation Likelihood Ratio Test (MOLRT) with a threshold function. In the second method, no distinct probability functions are assumed for speech and noise distributions and no LRT is employed. We will show that VAD is related to the parameter constancy test in GARCH process. For testing parameter constancy in GARCH models, the algorithm of the Cramer-von Mises (CVM) test is described. In the last method, the process of outlier detection in GARCH model is presented and the motivation for using it and its relation with VAD are discussed.

Homoscedasticity is an important assumption for statistical models, one of which is linear regression models from economic aspects which generally have time series type data. The Almon method is one approach used to handle lag effects in time series data. However, the residuals produced by the Almon method do not meet the assumption of homoscedasticity. To overcome this, it is necessary to handle the residuals from the Almon method using the GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model. This research uses 4 different types of GARCH models. The GARCH (1,1) model is the most appropriate model as evidenced by the smallest BIC value, namely 18.19199. The result was that the GARCH (1,1) model could handle the heteroskedasticity problem in the Almon method residuals.

Crude oil is an important energy commodity to mankind. The fluctuation of crude oil prices has affected many related sectors and stock market indices. Hence, forecasting the crude oil prices is essential to avoid the future prices of the non-renewable natural resources to raise sky-rocket. In this study, daily West Texas Intermediate (WTI) crude oil prices data is obtained from Energy Information Administration (EIA) from 2nd January 1986 to 30th September 2009. This study uses the Box-Jenkins methodology and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) approach in analyzing the crude oil prices. ARIMA(1,2,1) and GARCH(1,1) are found to be the appropriate models under model identification, parameter estimation, diagnostic checking and forecasting future prices. In this study, the analyses are done with the aid of EViews software where the potential of this software in forecasting daily crude oil prices time series data is explored. Finally, using several measures, comparison performances between ARIMA(1, 2, 1) and GARCH(1,1) models are made. GARCH(1,1) is found to be a better model than ARIMA(1, 2, 1) model. Based on the study, it is concluded that ARIMA(1,2,1) model is able to produce good forecast based on a description of history patterns in crude oil prices. However, the GARCH(1,1) is the better model for daily crude oil prices due to its ability to capture the volatility by the non-constant of conditional variance.

This study aims to predict the ESG (environmental, social, and governance) return volatility based on ESG index data from 26 October 2017 and 31 March 2023 in the case of India. In this study, we utilized GARCH (Generalized Autoregressive Conditional Heteroskedasticity) and LSTM (Long Short-Term Memory) models for forecasting the return of ESG volatility and to evaluate the model’s suitability for prediction. The study’s findings demonstrate the GARCH effect inside the ESG return volatility data, indicating the occurrence of volatility in response to market fluctuations. This study provides insight concerning the suitability of models for volatility predictions. Moreover, based on the analysis of the return volatility of the ESG index, the GARCH model is more appropriate than the LSTM model.

Global commodity markets, particularly crude oil markets, are inherently characterized by pronounced price volatility driven by geopolitical tensions, macroeconomic shocks, financial speculation, and structural changes in energy demand and supply.Accurately modeling and forecasting such volatility is essential for policymakers, investors, and risk managers seeking to design effective stabilization, hedging, and investment strategies.This study provides a comprehensive empirical investigation of oil price volatility by applying three prominent members of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family-namely the standard GARCH, Threshold GARCH (TGARCH), and Exponential GARCH (EGARCH) models-to monthly West Texas Intermediate (WTI) crude oil prices over the period from January 2008 to June 2024.The selected timeframe captures multiple episodes of extreme market turbulence, including the global financial crisis, oil price collapses, the COVID-19 pandemic, and recent geopolitical disruptions.The analysis proceeds through a structured econometric methodology, beginning with the transformation of price levels into return series, followed by stationarity testing, descriptive statistical analysis, and volatility modeling.Empirical results reveal strong volatility clustering and persistence in WTI oil returns, confirming the suitability of GARCH-type models for capturing oil price dynamics.While asymmetric specifications (TGARCH and EGARCH) provide valuable insights into the differential effects of positive and negative shocks, the findings indicate that the GARCH(1,1) model offers the most 207 -www.imcra.az.org,

Stock price data at State Gas Company is defined as the time-series data comprising varying volatility and heteroscedasticity. One of the best models used to solve the problem of heteroscedasticity is the GARCH (generalized autoregressive conditional heteroscedasticity) model. Therefore, this study aims to build the most suitable model for predicting the 186 days before and 176 days after the Covid-19 pandemic, as well as to provide recommendations to reduce the impact of daily stock price movements. Data were obtained by examining the daily stock price data in Indonesian National Gas Companies from 2019 to 2020. The study also discusses the Event Window, with the best model identified as AR (1) -GARCH (1,1). The result showed that an error of less than 0.0015 is AR (1) - GARCH (1,1), provided the best model for price forecasting of Indonesian National Gas Companies.Keywords: Stock Price, Heteroscedasticity, GARCH Model, Event WindowJEL Classifications: C5, O42, Q4, Q47DOI: https://doi.org/10.32479/ijeep.10999

Finding low-dimensional chaos is a relevant issue as it could allow short-term reliable forecasting. However, the existence of chaos in shipping freight rates remains an open and outstanding matter as previous research used methodology that can produce misleading results. Using daily data, this paper aims to unveil the nonlinear dynamics of the Baltic Dry Index that has been proposed as a measure of the shipping rates for certain raw materials. We tested for the existence of nonlinearity and low-dimensional chaos. We have also examined the chaotic dynamics throughout three sub-sampling periods, which have been determined by the volatility pattern of the series. For this purpose, from a comprehensive view we apply several metric and topological techniques, including the most suitable methods for noisy time series analysis. The proposed methodology considers the characteristics of chaotic time series, such as nonlinearity, determinism, sensitivity to initial conditions, fractal dimension and recurrence. Although there is strong evidence of a nonlinear structure, a chaotic and, therefore, deterministic behavior cannot be assumed during the whole or the three periods considered. Our findings indicate that the generalized autoregressive conditional heteroscedastic (GARCH) model and exponential GARCH (EGARCH) model explain a significant part of the nonlinear structure that is found in the dry bulk shipping freight market.

Nearly 1% of the world population in all ages suffer from epilepsy. An automatic seizure detection system is an important tool, which helps diagnose epilepsy. In this study, a new approach for epileptic detection based on generalised autoregressive conditional heteroscedasticity (GARCH) model is proposed. First, the electroencephalogram (EEG) signals are decomposed into the frequency sub-bands using wavelet transform. To choose an efficient statistical model for EEG signal wavelet coefficients, the statistical characteristics of these coefficients are studied. The authors show that these coefficients are heteroscedastic. To capture this important property, GARCH model, that is, heteroscedastic, is employed for these coefficients. Moreover, the authors show that GARCH model is compatible with other properties of wavelet coefficients such as heavy tail marginal distribution. GARCH parameters are calculated for each sub-band to represent the wavelet coefficients' distribution of EEG signals. These parameters are then utilised for EEG classification. Next, Markov random field is used to feature selection. The features found are then fed to multilayer perceptron classifier with three discrete outputs: healthy volunteers, epilepsy patients during seizure-free interval and epilepsy patients during seizure. The results clearly indicate that the performance of the new method in classification of EEG signals outperforms previous methods.

This paper estimates and compares alternative distribution density forecast methodology of three generalised autoregressive conditional heteroscedasticity (GARCH) models for Botswana and Namibia stock market returns. The symmetric GARCH and asymmetric Glosten Jagannathan and Runkle (GJR) version of GARCH (GJR-GARCH) and exponential GARCH methodology are employed to investigate the effect of stock return volatility in both stock markets using Gaussian, Student-t and generalised error distribution densities. The evidence reveals that the current shocks to the conditional variance will have less impact on future volatility in both markets. News impact is asymmetric in both stock markets leading to the existence of leverage effect in stock returns. Besides, both markets exhibit reverse volatility asymmetry, contradicting the widely accepted theory of volatility asymmetry. Regarding forecasting evaluation, the results reveal that the symmetric GARCH model coupled with fatter-tail distributions present a better out-of-sample forecast for both stock markets.

In order to model and forecast exchange rates in both developed and emerging countries, majority of time series analysts have employed various technical and fundamental approaches, the forecast outcome differs depending on the approach chosen or implemented. In this view, this study is about hybridization of Autoregressive Integrated Moving Average (ARIMA) with Generalized Autoregressive Conditional Heteroscedastic (GARCH) model in forecasting exchange rate using monthly data of the Nigerian Naira against the U.S. Dollar for the period of January 2002 to February 2020. The stationarity of the exchange rate series is examined using unit root test of Augmented Dickey Fuller (ADF) test and Kwaitkowski-Philips-Schmidt-Shin (KPSS) which showed that the series is non stationary. To make the exchange rate series stationary, the data was transformed by first differencing and appropriate ARIMA models were obtained using Box-Jenkins method. ARIMA (0,1,1) and ARIMA(0,1,2) models were selected using AIC criteria and the residuals of these models were found to be serially correlated and heteroscedastic; hence the need for the hybridization of ARIMA with GARCH model. Therefore ARIMA models were hybridized with GARCH(1,1) to form ARIMA(0,1,1)-GARCH(1,1) and ARIMA(0,1,2)-GARCH(1,1). The results of forecast performance indicates that the best model is ARIMA(0,1,1)–GARCH(1,1) which has the lowest Root Means Square Error (RMSE) and Mean Absolute Error( MAE).

PurposeThe purpose of this paper is to deal with the different phases of volatility behavior and the dependence of the variability of the time series on its own past, models allowing for heteroscedasticity like autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), or regime‐switching models have been suggested by reserachers. Both types of models are widely used in practice.Design/methodology/approachBoth regime‐switching models and GARCH are used in this paper to model and explain the behavior of crude oil prices in order to forecast their volatility. In regime‐switching models, the oil return volatility has a dynamic process whose mean is subject to shifts, which is governed by a two‐state first‐order Markov process.FindingsThe GARCH models are found to be very useful in modeling a unique stochastic process with conditional variance; regime‐switching models have the advantage of dividing the observed stochastic behavior of a time series into several separate phases with different underlying stochastic processes.Originality/valueThe regime‐switching models show similar goodness‐of‐fit result to GARCH modeling, while has the advantage of capturing major events affecting the oil market. Daily data of crude oil prices are used from NYMEX Crude Oil market for the period 13 February 2006 up to 21 July 2009.

This paper proposes a method that uses mean square error (MSE) and model confidence set (MCS) as the loss function of back‐propagation neural network (BPNN), aiming to train and find a generalized autoregressive conditional heteroskedastic (GARCH) model that has the best forecasting performance of a time series. Combining MSE and the p‐value of MCS can not only estimate better parameters for the GARCH models but also find the best GARCH model to forecast the volatility of a time series. Meanwhile, we divide a time series into several parts and use each part as the input of the BPNN. Through the BPNN, each part of the time series will be turned into several forecasting values. These values will be used to calculate the MSE and the p‐value of MCS, which will then be used to update the parameters of the BPNN. In the end, we use MCS to choose the best GARCH model among the trained GARCH models and compare this method with maximum likelihood estimation (MLE) and the generalized least squares estimation (GLS). The result shows that the p‐value of MCS of the best model estimated by this method is higher than the p‐value of MCS of the best model estimated by MLE and GLS. According to the theory of MCS, a model that has a larger p‐value does have a better forecasting performance. The method proposed by this paper can provide a potential application of neural network in GARCH model forecasting and estimation.