Model estimation and prediction of sunspots cycles through AR-GARCH models

Study of sunspots cycles is a significant tool to understand space weather and its influence on the earth’s climate. This communication aims to study the sunspots individual cycles ranging from cycle 1st–23rd (1755–2008). Cycle 24th is still in continuation, so it is not included. The oscillatory behavior of sunspots in consecutive cycles in all these 23rd cycles is separately investigated. The study of sunspots cycles is focused on the relevance of numerous generalized autoregressive conditional heteroskedasticity (GARCH) models fitted to analyze and study their performance for delivering volatility forecasts for sunspot cycles. The GARCH (1, 1) model is used for detecting the aptness of autoregressive conditional heteroscedastic (ARCH) effect on sunspot cycles data, and Lagrange multiplier test is also applied. Most of the sunspot cycles follow auto-regressive (AR (2))-GARCH except cycles 7th, 15th, and 17th which follow AR (3)-GARCH model. AR (2)-GARCH model is the finest model which forecasts better as compared to other models. However, AR (2)-GARCH model is the adequate model for estimation and forecasting most of the sunspot cycles.