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 [1] 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...

One of the basic estimation problems for continuous time stationary processes $X_t$, is that of estimating $E\left\{X_{t+\beta }\right|X_s:s\in [0,t]\}$ based on the observation of the single block $\{X_s:s\in [0,t]\}$ when the actual distribution of the process is not known. We will give fairly optimal universal estimates of this type that correspond to the optimal results in the case of discrete time processes.