Modelling and parameter estimation for discretely observed fractional iterated Ornstein–Uhlenbeck processes

In this work we present how to model an observed time series by a FOU(p) process. We will show that the processes can be used wide range of varying from short dependence long dependence, with performance similar ARMA or ARFIMA models and in several cases outperforming them. Also, extend theoretical results for any case which Hurst parameter is less than 1/2 theoretically simulations under some conditions on T sample size n it possible obtain consistent estimators parameters when process discretized equispaced interval [0,T]. Lastly, give way explicit formulas auto-covariance function application FOU(2) FOU(3).