Abstract: Time series with long memory or long-range dependence occurs frequently in agricultural commodity prices. For describing long memory, fractional integration is considered. The autoregressive fractionally integrated moving-average (ARFIMA) model along with its different estimation procedures is investigated. For the present investigation, the daily spot prices of mustard in Mumbai market are used. Autocorrelation (ACF) and partial autocorrelation (PACF) functions showed a slow hyperbolic decay indicating the presence of long memory. On the basis of minimum AIC values, the best model is identified for each series. Evaluation of forecasting is carried out with root mean squares prediction error (RMSPE), mean absolute…prediction error (MAPE) and relative mean absolute prediction error (RMAPE). The residuals of the fitted models were used for diagnostic checking. Long memory parameter of ARFIMA model is computed by Geweke and Porter-Hudak (GPH), Gaussian semiparametric and wavelet method by using Maximal overlap discrete wavelet transform (MODWT). To this end, a comparison in the performance of different estimation procedures is carried out by Monte Carlo simulation technique. The R software package has been used for data analysis.
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Keywords: Long memory, ARFIMA, spot price of mustard, Monte Carlo simulation
Abstract: Exponential autoregressive (EXPAR) and generalized autoregressive conditional heteroscedastic (GARCH) models are usually employed for fitting of cyclical and volatile data respectively. However, in practical situations, there may be data which embodies both this phenomena at the same time. To tackle such situations, a new form of parametric nonlinear time-series model, EXPAR-GARCH is proposed. Methodology for estimation of parameters of this model is developed by using a powerful optimization technique called Genetic Algorithm (GA). Entire data analysis is carried out using SAS and MATLAB software packages. For illustration, monthly price series of edible oils in domestic and international markets is considered.…The individual models as well as the proposed model were assessed on their ability to predict the correct change of direction in future values as well as by computing various measures of goodness-of-fit and forecast performance.
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