Affiliations: [a] University of São Paulo, Av. Duque de Caxias Norte 225, 13635-900, Brazil. sergiodavid@usp.br | [b] Institute of Engineering, Polytechnic of Porto, Rua Dr. António B. de Almeida 431, 4249-015, Porto, Portugal. jtm@isep.ipp.pt | [c] University of Illinois at Urbana-Champaign, 1304 W. Pennsylvania Av. Urbana, IL 61801, USA. trevisa2@illinois.edu | [d] University of São Paulo, Av. Duque de Caxias Norte 225, 13635-900, Brazil. claudio.inacio@usp.br | [e] UISPA - LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal. aml@fe.up.pt
Correspondence:
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Address for correspondence: University of São Paulo, Av. Duque de Caxias Norte 225, 13635-900, Brazil
Abstract: This paper examines the time series of four important agricultural commodities, namely the soybean, corn, coffee and sugar prices. Time series can exhibit long-range dependence and persistence in their observation. The long memory feature of data is a documented fact and there has been an increasing interest in studying such concepts in the perspective of economics and finance. In this work, we start by analyzing the time series of the four commodities by means of the Fractional Fourier Transform (FrFT) to unveil time-frequency patterns in the data. In a second phase, we apply Auto Regressive Integrated Moving Average (ARIMA) and Auto Regressive Fractionally Integrated Moving Average (ARFIMA) models for obtaining the spot price composition and predict future price. The ARFIMA process is a known class of long memory model, representing a generalization of the ARIMA algorithm. We compare the performances of the ARIMA and the ARFIMA models and we show that the ARFIMA has a superior performance for future price forecasting.
Keywords: Fractional statistic systems, business and management, Fractional Fourier Transform, computer modeling and simulation
