Forecasting Malaysian gold using GARCH model

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).

Time series analysis of aerosol optical depth over New Delhi using Box–Jenkins ARIMA modeling approach

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.

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.

Food and non-alcoholic beverages are highly important for individuals to continue staying alive and living healthy lives. The increase in the prices of food and non-alcoholic beverages experienced across the world over years has continued to make food and non-alcoholic beverages not to be accessible and affordable to individuals and families having a low income. The aim of this particular research study was to identify how Kenya’s CPI of food and non-alcoholic beverages could be modelled using Autoregressive Integrated Moving Average (ARIMA) models for forecasting future values for the next two years. The data used for the study was that of Kenya’s CPI of food and non-alcoholic beverages for the period starting from February 2009 to April 2024 obtained from the International Monetary Fund (IMF) database. The best specification for the ARIMA model was identified using Akaike Information Criterion (AIC), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean absolute scaled error (MASE) and assessing whether residuals of the model were independent and normally distributed with a variance that is constant an whether the model has most of its coefficients being significant statistically. ARIMA (3, 1, 0) (1, 0, 0) model was identified as the best ARIMA model for modeling Kenya’s CPI of food and non-beverages for forecasting future values among the ARIMA models considered. Using this particular model, Kenya’s CPI of food and non-alcoholic beverages was forecasted to increase only slightly with time to reach a value of about 165.70 by March 2026.

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.

Forecasting the dynamics of cumulative COVID-19 cases (confirmed, recovered and deaths) for top-16 countries using statistical machine learning models: Auto-Regressive Integrated Moving Average (ARIMA) and Seasonal Auto-Regressive Integrated Moving Average (SARIMA)

Gold investment is one of the favorite investments during the Covid-19 pandemic because the price of gold is relatively volatile but shows an increasing trend. Savvy investors investing in gold need to be able to predict future opportunities. Therefore, price estimation is needed to develop a buying and selling strategy to maximize profits. The Autoregressive Integrated Moving Average (ARIMA) model is a suitable method for predicting time series data, so the best ARIMA model will be applied for forecasting world gold prices. The best ARIMA model is selected based on the Akaike Information Criterion (AIC) and Mean Absolute Percentage Error (MAPE) criteria. Monthly world gold price data for 146 periods are applied in this study and will be used to predict gold prices for the following six periods. ARIMA(0,1,1) is the best model obtained from the analysis results, with AIC and MAPE values ​​of 1264.731 and 11.972%, respectively. Forecasting results show that world gold prices will increase for the next periods.

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.

An important development in the modelling of exchange rate volatility is the use of artificial neural networks (ANN) to create enhanced generalised autoregressive conditional heteroskedasticity (GARCH) models. Conventional GARCH models are good at capturing the clustering of volatility in financial time series, but they have trouble understanding complex linkages and non-linear patterns in the data. This paper aims to investigate the hybrid approach in modelling exchange rate volatility of two currency pairs: South African Rand against Brazilian Real (ZAR/REAL) and South African Rand against Chinese Yuan (ZAR/YUAN) using monthly observations over the period of January 1996-March 2024. The paper introduced ANN as an additional factor to both symmetric and asymmetric GARCH models that capture most common stylised facts about exchange rate volatility and leverage effects. The GARCH (1,1)-ANN, EGARCH (1,1)-ANN, and GJR-GARCH (1,1)-ANN models were used, and their performance was assessed using mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results revealed that the EGARCH (1,1)-ANN model had the best overall performance when compared to the other hybrid models based on all three evaluation measures for both the currency pairs’ data. The paper recommends further similar studies to predict future exchange rate trends and also incorporating other nonlinear methods.

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.

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.

Rate changes can occur hourly, daily, or in large incremental shifts. These changes may impact firms by changing the cost of commodities imported from other countries and the demand for their goods among foreign consumers. Therefore, it is essential to forecast exchange rates to manage this business effect. This study aims to determine the best model for predicting volatility in the exchange rate between USD and GBP. In particular, we analyze exchange rates using the Autoregressive Integrated Moving Average (ARIMA) model and the volatility or variance model by Generalized Autoregressive Conditional Heteroscedasticity (GARCH). To determine the best model, the performance of each model is evaluated with several criteria, namely Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The results show that EGARCH(1,1) has the best forecasting performance in the out-sample section because it can better capture out-sample data patterns with minimum RMSE, MAE, and MAPE.

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

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.