Modeling and Forecasting of Sunspots Cycles: An Application of ARMA (p, q)-GARCH (1, 1) Model

Abstract The influence of the earth climatic condition of oscillations of solar activity is measurable only in the long run duration. Modeling of the sunspots is an initial role for the mankind utilization of the benefits because solar activity has influenced on the earth’s climates. Time series analysis and modeling have proved to stick out amidst with other statistical tools when estimating and predicting solar activities. This study emphasis on the appropriateness of the generalized autoregressive conditional heteroskedasticity (GARCH) models with specification autoregressive ARMA (p, q) process in terms of their performance for delivering volatility forecasts for Sunspot cycles. In this study, individual sunspots cycle’s ranging from cycle 1st to 24th (1755–2019) are considered. To notice the appropriateness of Autoregressive Conditional Heteroscedastic (ARCH) effect on sunspot cycles data, Lagrange Multiplier test is used. ARMA (p, q)-GARCH (1, 1) process expresses leptokurtic that is fat and heavy tail (values are strongly correlated to each other). The sunspot cycles ARMA (p, q)-GRACH (1, 1) process expresses the positive skewness except cycles 4th and 19th. Most of the Sunspot cycles (1st, 4th, 12th, 13th, 14th, 15th, 16th, 19th, 20th, 23rd and 24th ) follow Auto-Regressive and moving Average (ARMA (2, 2))-GARCH (1, 1). Sunspot cycles (5th, 6th, 7th and 15th ) follow ARMA (3, 3)-GARCH model. Whereas the cycles (2nd and 11th ) show appropriate model is ARMA (5, 1) -GARCH (1, 1) process. ARMA (5, 3) -GARCH (1, 1) process expresses cycles (18th and 19th ). The ARMA (2, 2)-GARCH (1, 1) stationary volatility model expresses the finest forecasting model as compared with other models. Though, ARMA (2, 2)-GARCH (1, 1) is the adequate model for estimation and forecasting most of the sunspot cycles. The results that are obtained by this study are very beneficial for observing the influence of solar activity on the earth's climate.