Least squares linear lags and limited memory filters

Pure autoregressive (AR) models which are linear in the short term, that is when a variable can be predicted by linear regression on a limited number of past observations, are discussed. When evenly spaced observations are available, a fixed set of AR coefficients can be calculated independent of the data. For filtering purposes, such a lag structure can be implemented recursively with an efficient algorithm. The method of computing variance recursively is also derived. A complete algorithm is presented in the appendix.