Tropical cyclones is one of the most devastating meteorological events. In the recent years we faced some very severe cyclones to super cyclone successively that caused heavy damages to life and property during the helpless situations of the global pandemic. In this paper, westudied the frequency of cyclones from the year 1891 to 2019 i.e. for 129 years on the Arabian Sea Basin, Bay of Bengal Basin and land. We have categorised the cyclones according to their wind speeds: i) Cyclonic storms and Severe cyclonic storms(CS + SCS) and ii) Depressions, Cyclonic storms and Severe Cyclonic storms(D + CS + SCS) where Depressions, Cyclonic storms and Severe Cyclonic storms have wind speeds of more than equal to 17 knots, 34 knots and 48 knots respectively. We examined the Markovian dependence of the discretized time series of the two categories mentioned earlier for the first, second, third and fourth order of a two-state Markov chain model. It is found that CS + SCS represents the First Order Two State (FOTS) model of Markov chain and D + CS + SCS represents the Second Order Two State (SOTS) model of Markov chain. Thereafter we have developed autoregressive models for the two categories and checked its goodness of fit using Willmott’s indices of order 1 and 2. Its is found that CS + SCS best represents the autoregressive model of order 5 whereas D + CS + SCS could not be efficiently represented by the developed autoregressive models. So we further developed autoregressive neural networks for D + CS + SCS and obtained some significant hike in the prediction yield. Nevertheless, it is found that both the categories are clearly not serially independent.