stationary time series; multistep prediction; Levinson’s algorithm; innovations algorithm
Important characteristics of any algorithm are its complexity and speed in real calculations. From this point of view, we analyze some algorithms for prediction in finite stationary time series. First, we review results developed by P. Bondon  and then, we derive the complexities of Levinson and a new algorithm. It is shown that the time needed for real calculations of predictions is proportional to the theoretical complexity of the algorithm. Some practical recommendations for the selection of the best algorithm are given.