On the residuals of autoregressive processes and polynomial regression

Abstract

AbstractThe residual processes of a stationary AR(p) process and of polynomial regression are considered. The residuals are obtained from ordinary least squares fitting. In the AR case, the partial sums converge to Brownian motion. In the polynomial case, they converge to generalized Brownian bridges. Other uses of the residuals are considered. Parameter estimation based on approximate log likelihood function of the residuals is considered