Trend estimation and univariate forecast of the sunspot numbers: Development and comparison of ARMA, ARIMA and Autoregressive Neural Network models

In the present study, a prominent 11-year cycle, supported by the pattern of the autocorrelation function and measures of Euclidean distances, in the mean annual sunspot number time series has been observed by considering the sunspot series for the duration of 1749 to 2007. The trend in the yearly sunspot series, which is found to be non-normally distributed, is examined through the Mann-Kendall non-parametric test. A statistically significant increasing trend is observed in the sunspot series in annual duration. The results indicate that the performance of the autoregressive neural network-based model is much better than the autoregressive moving average and autoregressive integrated moving average-based models for the univariate forecast of the yearly mean sunspot numbers.