Eur. Phys. J. Plus (2012) 127: 43
https://doi.org/10.1140/epjp/i2012-12043-9

Regular Article

Monthly sunspot number time series analysis and its modeling through autoregressive artificial neural network

¹ Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah, 711103, India
² Pailan College of Management and Technology, Kolkata, 700 104, India

^* e-mail: surajit_2008@yahoo.co.in
^** e-mail: surajcha@iucaa.ernet.in

Received: 13 January 2012
Revised: 9 March 2012
Accepted: 27 March 2012
Published online: 20 April 2012

Abstract

This study reports a statistical analysis of monthly sunspot number time series and observes nonhomogeneity and asymmetry within it. Using the Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p, q) . Based on the minimization of AIC we find 3 and 1 as the best values for p and q , respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott’s index of second order and the coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).