Modelling and forecasting monthly Brent crude oil prices: a long memory and volatility approach
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The Standard Generalised Autoregressive Conditionally Heteroskedastic (sGARCH) model and the Functional Generalised Autoregressive Conditionally Heteroskedastic (fGARCH) model were applied to study the volatility of the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model, which is the primary objective of this study. The other goal of this paper is to expand on the researchers' previous work by examining long memory and volatilities simultaneously, by using the ARFIMA-sGARCH hybrid model and comparing it against the ARFIMA-fGARCH hybrid model. Consequently, the hybrid models were configured with the monthly Brent crude oil price series for the period from January 1979 to July 2019. These datasets were considered as the global economy is currently facing significant challenges resulting from noticeable volatilities, especially in terms of the Brent crude prices, due to the outbreak of COVID-19. To achieve these goals, an R/S analysis was performed and the aggregated variance and the Higuchi methods were applied to test for the presence of long memory in the dataset. Furthermore, four breaks have been detected: in 1986, 1999, 2005, and 2013 using the Bayes information criterion. In the further section of the paper, the Hurst Exponent and Geweke-Porter-Hudak (GPH) methods were used to estimate the values of fractional differences. Thus, some ARFIMA models were identified using AIC (Akaike Information Criterion), BIC (Schwartz Bayesian Information Criterion), AICc (corrected AIC), and the RMSE (Root Mean Squared Error). In result, the following conclusions were reached: the ARFIMA(2,0.3589648,2)-sGARCH(1,1) model and the ARFIMA(2,0.3589648,2)-fGARCH(1,1) model under normal distribution proved to be the best models, demonstrating the smallest values for these criteria. The calculations conducted herein show that the two models are of the same accuracy level in terms of the RMSE value, which equals 0.08808882, and it is this result that distinguishes our study. In conclusion, these models can be used to predict oil prices more accurately than others.
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- الكلمات المفتاحية
ARFIMA, volatility, fGARCH, sGARCH, modelling and forecasting, hybrid model
ON THE CHROMATIC POLYNOMIAL OF A CYCLE GRAPH
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The aim of this article is to study the chromatic polynomial of cycle graph, and to describe some algebraic properties about the chromatic polynomial’s coefficients and roots to the same graph.
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- الكلمات المفتاحية
cycle graph, chromatic polynomial
Comparing the performances of symmetric and asymmetric generalized autoregressive conditionally heteroscedasticity models based on long-memory models under different distributions
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This research compares the symmetric and asymmetric effects of generalized autoregressive conditional heteroscedasticity (GARCH)-type models to investigate the volatility of the autoregressive fractionally integrated moving average (ARFIMA) model using the monthly Brent crude oil price series for the period of January 1979–July 2019. The best model of volatility is determined by comparing 13 hybrid models of GARCH (sGARCH, fGARCH, EGARCH, TGARCH, IGARCH, AVGARCH, NGARCH, NAGARCH, APARCH, apARCH, GJRGARCH, gjrGARCH, and csGARCH) in terms of symmetric and asymmetric effects at the level of (1,1). R/S analysis is used to achieve this target. The aggregated variance method, the Higuchi method, and the structural break test are performed to determine the presence of long memory in the dataset. Furthermore, the Hurst exponent method and the Geweke and Porter–Hudak method are used to estimate the fractional difference values. The ARFIMA(2,0.3589648,2)–IGARCH(1,1) model under normal distribution is selected as the best model based on the Akaike information criterion, Schwartz Bayesian information criterion, and by the smallest value for root-mean-squared error, in which this model can be used to predict more accurately than other models
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- الكلمات المفتاحية
Asymmetric effect; Autoregressive fractionally integrated moving average; Generalized autoregressive conditionally heteroscedasticity; Hybrid model; Modeling and forecasting; Symmetric effect
Comparing the Performances of Artificial Neural
Networks Models Based on Autoregressive
Fractionally Integrated Moving Average Models
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The autoregressive fractional integrated moving
average (ARFIMA) has become one of the popular linear
models in time series modeling and forecasting in the past
decades. Recent research in modeling and forecasting with
artificial neural networks (ANN) suggests that these networks
are a promising alternative to the traditional linear and
nonlinear methods. ARFIMA models and ANNs are often
compared with mixed conclusions in terms of superiority in
forecasting performance. In this research, a hybrid methodology
that combines both ARFIMA and multilayer perceptron (MLP)
models is proposed to take advantage of the unique strength
of the ARFIMA and MLP models in linear and nonlinear
modeling, which is the primary objective of this study. This
research uses the monthly Brent crude oil price series for the
period of January 1979-July 2019. As for our other goal, the
researchers’ previous works are also extended by examining the
linear and nonlinear methods for the dataset simultaneously and
comparing individual models with the hybrid models. The best
model is determined by comparing 19 individual and hybrid
models in terms of forecasting accuracy based on the root mean
squared error and Ljung–Box test. Empirical results with real
datasets indicate that the ARFIMA (1,0.3589648,0)–MLP (1,2,1)
hybrid model outperforms the separately used models and the
other hybrid models, and the Akaike information criterion value
is not the smallest for this model.
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- الكلمات المفتاحية
Autoregressive Fractionally Integrated Moving
Average, Multilayer perceptron, Modeling and Forecasting,
Hybrid Model.
Forecasting the Exchange Rate of the Jordanian Dinar versus the US Dollar Using a Box-Jenkins Seasonal ARIMA Model
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Seasonal Autoregressive Integrated Moving Average (SARIMA)
model was fitted for the time series data either to better understand
the data or to predict the future points in the series (forecasting). Using the forecasting for the exchange rate is very important at the national, regional and international levels. It can help investors minimize
financial risk as well maximize earnings in the volatility of the global
economy. The aim of this study was to use the time series model to
forecast the exchange rate of Jordan dinar based on the monthly data
collected for Jordanian dinar vs US dollar. Exchange rate prediction is
performed using two methods; Autoregressive Integrated Moving Average (ARIMA) and Seasonal Autoregressive Integrated Moving Average (SARIMA) time series. After comparing the forecasting method
using ARIMA (1, 0, 1) and SARIMA (1, 0, 1)(1, 0, 0)12 models, we find
that the second model shows a smaller mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE) and mean absolute square error (MASE) as compared to the
first; That is, SARIMA (1, 0, 1)(1, 0, 0)12 model is the most appropriate method to forecast the exchange rate of the Jordanian dinar vs
US dollar.
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- الكلمات المفتاحية
ARIMA, SARIMA, Jordanian Dinar, Modeling,
R software, Time series, Forecasting.
Overview of Long Memory for Economic and Financial Time Series Dataset and Related Time Series Models: A Review Study.
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Verifying the existence of long-memory feature is a crucial activity performed during the development process of the autoregressive integrated moving average (ARIMA) model. The verifying step will determine whether a researcher needs to use the ARIMA model or the autoregressive fractionally integrated moving average (ARFIMA) model, which depends on the estimated value of the fractional difference (d). This study focuses on analytical techniques for verifying the long-memory feature (graphs and statistical tests); determines estimation methods/functions for approximating long-memory parameters (ie, d), limitations, extensions, comparisons, applications, and performs an in-depth review of the recent literature on the ARFIMA model. The discussion will also include the hybrid method for forecasting in different fields. Although the validation of the existence of the long-memory feature and its estimation, limitations, extensions, comparisons, and applications has been extensively investigated, specific criteria should be considered to avoid obtaining invalid or wrong ARFIMA models remain unclear. We examine the literature to validate these issues and identify effective methods and tests to avoid these errors. Thus, the results of this study can provide an initial classification of the literature on long memory and the ARFIMA model that can be used as a basis for future work when the value of d is a non-integer number.
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- الكلمات المفتاحية
—Long memory, Autoregressive fractionally integrated moving average, Individual and Hybrid models, Modeling and forecasting, Time series.