Estimating and forecasting bitcoin daily prices using ARIMA-GARCH models

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).

Stock price prediction and volatility modeling are important for making financial decisions, especially in emerging markets like the Nairobi Securities Exchange (NSE). This study examines how well the Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models perform in forecasting stock prices and modeling volatility. The ARIMA (2,1,0) model was selected as the best fit using the Akaike Information Criterion (AIC), showing strong performance in capturing long-term price trends. However, an analysis of the residuals showed signs of volatility clustering, meaning ARIMA alone could not capture short-term fluctuations. To solve this, the study added a GARCH (1,1) model, which effectively captured changing volatility and improved prediction accuracy. The combined ARIMA-GARCH model reduced the Root Mean Squared Error (RMSE) from 3.1211 to 2.5786, demonstrating the value of including volatility modeling in financial time series. The results highlight the need for strong statistical models in emerging markets, where stock prices are often affected by external shocks and market inefficiencies. This research offers useful insights for investors, policymakers, and financial analysts by supporting better risk management and more accurate forecasting. Future studies could expand the model to include more stocks, macroeconomic data, and machine learning techniques to further improve results.

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.

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.

A company acquiring an ownership through transfer of resources and technical know-how is essential for a sustainable growth and to face competition in the existing industry. The aim is to study the effect of CAGR on Foreign Direct Investment (FDI) inflows into Indian Pharmaceutical sector, secondly to regress the stock prices of top listed Indian Pharmaceutical sector and finally to analyse the Generalised Auto Regressive Conditional Heteroskedasticity (GARCH) effect on the Stock prices of selected Pharmaceutical sector. The research methodology applied is descriptive, analytical and univariate analysis. Time series tool of Auto Regressive Integrated Moving Averages (ARIMA) and GARCH is applied for generating the output and the major findings from the study is Apollo Hospitals Enterprise Limited, Cipla Ltd and Dr. Reddy’s Laboratories Limited Lab are stationary and optimum model as per information criteria is at ARIMA, (1, 1, 0) for Apollo Hospitals Enterprise Limited and ARIMA (0, 1, 1) for Cipla Limited and Dr. Reddy’s Laboratories Limited Lab.

Executive Summary Before financial liberalization, interest rates were administered and exhibited near-zero volatility. The easing of financial repression in the 1990s generated experiences with interest rate volatility in India. Administrative restrictions on interest rates in India have been steadily eased since 1993. This has led to increased interest rate risk for financial firms. Most research studies have almost exclusively focused on the developed countries especially the banking sector of the United States. The present study attempts to examine the interest rate risk of non-banking financial institutions in India by using the methodology of panel regression and generalized autoregressive conditional heteroscedasticity (GARCH) (1, 1) model for the period from 1 April 1996 to 30 August 2014. The sample used in the study consists of all non-banking financial companies (NBFCs) listed in the S&P CNX 500 index which has continuous availability of share prices over the study period. The study also examines the impact of unanticipated changes in interest rate on stock returns of NBFCs. The Box–Jenkins methodology is applied to calculate unanticipated changes in interest rate variable, autoregressive integrated moving average (ARIMA) (24, 1, 0) model. The time series used in the present study is found to be stationary at the first logarithmic difference. Stock returns exhibit significant exposure with both market returns and interest rate changes. The interest rate sensitivity of large, medium, and small financial institutions is also found to be different. Estimation results for the variance equation in GARCH (1, 1) model suggest that the volatility for individual firm stock returns is time-variant. The ARCH and GARCH coefficients are found to be significant, providing evidence against using traditional model (ordinary least square (OLS)) that assumes time-invariant volatility. This implies that the market has a memory longer than one period and volatility is more sensitive to its own lagged values than it is to new surprises in the market. This study also investigates the possible determinants that account for cross-sectional variation in the interest rate sensitivity of NBFCs. It is found that the size of the firm is the preferred determinant that accounts for cross-sectional variation in the interest rate sensitivity of finance companies. When unanticipated changes in interest rate are used in lieu of actual interest rate changes, not much difference is observed in the significance coefficients. The only significant difference observed is in the magnitude. The impact of actual interest rate changes is more than the impact of unanticipated interest rate changes in absolute terms. This difference in the magnitude of impact arises because actual data incorporate movement in both anticipated and unanticipated components of interest rate. Hence, NBFCs managers and regulators should adopt policies and strategies to avoid the transmission of interest rate risk in their stock returns.

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.

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.

The major topic investigates how classical methods (ARCH and GARCH) and well-known machine learning algorithms, support vector regression, and hybrid methods. This paper aims to predict and forecast volatility to develop a two-stage forecasting approach the volatility of the Amman Stock Exchange Index (ASE) effectively. Additionally, the effectiveness of the machine learning techniques’ selection and utilization of information in stock data is evaluated. Methods the semiparametric estimating technique known as support vector regression (SVR) has been widely used for the prediction of volatility in financial time series. By integrating SVR with the GARCH model (GARCH-SVR) application with various kernels (Radial Basis Kernel Function (RBF), Polynomial Kernel Function (PF), and linear Kernel Function (lF)). The suggested learning approaches are compared to two well-known statistical time series models, Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH), in order to assess the assertion that they can properly anticipate ASE volatility. To compare their results, RMSE is employed as an error metric. There is evidence that the GARCH-SVR model performs best for predicting volatility time series, and classical volatility model techniques have an enormous predictive performance better than machine learning models.

Nowadays , nonlinear time series and artificial neural networks (ANN) models are used for forecasting in the field of business, agriculture and soon. Recent studies have shown, ANN have been successfully used for forecasting of financial and agriculture data series The classical methods used for time series prediction like Box-Jenkins or ARIMA assumes that there is a linear relationship between inputs and outputs. ANN have more advantages that can approximate to model both linear and nonlinear structures in time series, they are not able to handling both structures equally well. The autoregressive integrated moving average (ARIMA) model and two ANN models namely, Radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) methods were applied to Hyderabad airport traffic data. The data obtained for 15 years from 2002–2003 to 2016–2017 about domestic and international passenger of International Airport of Hyderabad, India. In this research paper, we compared the performances of ARIMA, RBFNN and ERNN were based on three measures: mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results showed that RBFNN obtained the smallest MAE, MAPE and RMSE in both the modeling and forecasting processes. The performances of the three models ranked in ascending order were: ARIMA, ERNN and the RBFNN model. Keywords: T ime series, forecasting, artificial neural networks, ARIMA models, radial basis function neural networks, and Elman recurrent neural networks Cite this Article R. Ramakrishna, Berhe Aregay, Tewodros Gebregergs. The Comparison in Time Series Forecasting of Air Traffic Data by Autoregressive Integrated Moving Average Model, Radial Basis Function and Elman Recurrent Neural Networks. Research & Reviews: Journal of Statistics . 2018; 7(3): 75–90p.

Accounting for Volatility Decay in Time Series Models for Leveraged Exchange Traded Funds

The purpose of the current study is to forecast the prices of Kijang Emas, the official Malaysian gold bullion. Two methods are considered, which are Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using Akaike's information criterion (AIC) as the goodness of fit measure and mean absolute percentage error (MAPE) as the forecasting performance measure, the study concludes that GARCH is a more appropriate model. Analysis are carried out by using the E-views software.

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.

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

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.