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

TL;DR

This paper analyzes monthly sunspot numbers, identifies trends and stationarity, and models the data using autoregressive neural networks, demonstrating improved performance over traditional AR and ARMA models.

Contribution

It introduces an autoregressive neural network model for sunspot data and compares its performance with classical models, showing superior results.

Findings

AR-NN(3) outperforms AR(3) and ARMA(3,1) models

Identifies non-homogeneity and asymmetry in sunspot data

Detects linear trends and stationarity in the series

Abstract

This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using 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 minimization of AIC we find 3 and 1 as the best values of 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 coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).