Abstract
Among other stochastic models, fractional auto regressive integrating moving average (FARIMA) is distinct because of its appropriateness for modeling stationary time series with long range dependence (long memory or persistence). Results obtained in this manuscript shows appropriateness of FARIMA model for the analysis of sunspot number. Analyzing for stationary, each cycle out of the 24 sunspot cycles were modeled. FARIMA can be used for modeling using different techniques. In view of the parameters obtained by maximum likelihood test two most appropriate techniques are adopted. These two are Direct Method and Whittle approximation Method. Results are obtained by applying these two types of FARIMA, the significance of these two methods were observed and compared using significance tests. For FARIMA models the fractional differencing parameter d is most decisive for the determination of persistency. In this regard four types of model (0, d,0), (1, d,0), (0, d,1) and (1, d,1) are used. The adequacy of each of the models is determined with the help of Akaike, Bayesian-Schwarz and Hannan-Quinn Information criterion. The investigations made using these models are reliable for both short and long sunspot cycles. Finally, tail analysis is performed in view of the parameter (α) it is observed that heavy tails exist for each sunspots cycle confirming long range dependence. The study is useful to examine the sunspot historical data using the FARIMA model to understand their long term behavior.
