Predicting the Number of Sunspots Per Month and Per Quarter Using ARIMA Models

Abstract

The number of sunspots in a given year changes as the sun goes through solar cycles, with peaks happening at regular intervals. When these peaks are plotted, a curve appears, similar to the oscillating sinusoidal wave. Because of its oscillatory nature, predictions of future sunspot values could be found since it is safe to assume that the number of sunspots would always follow a pattern. However, a simple, ordinary sine function, or any algebraic function for that matter, would not allow us to plot and predict future data points due to the complexity of the curve at hand. This led us to the hypothesis that in order to predict the future number of sunspots, models that involve autoregressive and moving average components (namely the ARIMA model) would be the most effective. In order to measure effectiveness, the mean-squared error (MSE) would be used, with a lower value (closer to 0) meaning better fit. The reason why we chose these sophisticated models was because these models took into account prior data points and their trends and seasonality to predict future data points. This essentially meant that this model would predict based on prior points, not on a fixed point or equation, like the sine curve. After plotting all of these models and finding the MSE for each, we drew the conclusion that the ARIMA model proved to produce the most accurate curve, with a MSE of only 460, as compared to the MSE that the best sine curve could produce: 21 million.