Monte Carlo simulation for comparison of different estimators of long memory parameter: An application of ARFIMA model for forecasting commodity price

Subtitle:

Article type: Research Article

Authors: Paul, Ranjit Kumar^* | Samanta, Sandipan | Gurung, Bishal

Affiliations: Indian Agricultural Statistics Research Institute, New Delhi, India

Correspondence: [*] Corresponding author: Ranjit Kumar Paul, Indian Agricultural Statistics Research Institute, New Delhi-110012, India. E-mail: [email protected]

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.

Keywords: Long memory, ARFIMA, spot price of mustard, Monte Carlo simulation

DOI: 10.3233/MAS-140317

Journal: Model Assisted Statistics and Applications, vol. 10, no. 2, pp. 117-128, 2015