Forecasting of sunspots cycles thorough ANFIS model and ARMA (R, S)-GARCH (1,1) model

Only over extended periods of time can the impact of solar activity fluctuations on Earth's climate be measured. Because solar activity affects earth's climate, modelling sunspots is a necessary first step in humanity's utilization of advantages. When it comes to assessing and forecasting solar activities, time series analysis and modelling have shown to stand out from other statistical approaches. In order to provide forecasts volatility for Sunspot cycles, this study highlights the suitability of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) technique with autoregressive ARMA (R, S) process specification and adaptive neural-based fuzzy inference system (ANFIS). Individual sunspot cycles from cycle 1 to cycle 24 (1755-2019) are taken into consideration in this analysis. The Lagrange Multiplier test is used to determine whether the Autoregressive Conditional Heteroscedastic (ARCH) effect is appropriate for sunspot cycle dataset. Leptokurtic, or the fat and heavy tail, is expressed by the ARMA (R, S)-GARCH (1, 1) model (values are closely connected to each other). Sunspot cycles The positive skewness is expressed by the ARMA (R, S)-GRACH (1, 1) process, with the exception of cycles 4th and 19th. ARMA (2, 2))-GARCH (1, 1) is used for the majority of Sunspot cycles, which are the 1st, 4th, 12th, 13th, 14th, 15th, 16th, 19th, 20th, 23rd, and 24th. Sunspot cycles (3, 3)-GARCH (1, 1) model is followed by the 5th, 6th, 7th, and 15th cycles. On the other hand, cycles 2nd and 11th demonstrate that the ARMA (5, 1) -GARCH (1, 1) process is the suitable model. ARMA (5, 3)-GRACH (1, 1) technique shows that (18th and 19th). ARMA (2, 2)-GRACH (1, 1) static volatility model shows the best predicting technique compared to other process. However, ARMA (2, 2)-GRACH (1, 1) is a suitable model to estimate and forecast most sunspot periods. On the other hand, the ANFIS model (3-product and 2-term functions) provides a better prediction of the evolution of sunspot cycles in terms of Root Mean Square Error (RMSE). In terms of RMSE, ANFIS is more predictive than ARMA (p, q)-GARCH. The results of this study are very useful when looking at the effects of solar activity on Earth and climate.