Regression, Autoregression Models

The accuracy of least squares fitted regression autoregression models as approximations to more general stochastic structures is considered, attention being paid to the accuracy of the estimates of coefficients, of the innovations sequence and to the behaviour of the order (i.e., maximum lag) as determined by methods such as IAC, BIC. A key part is played by an accurate evaluation of the quantity where ετ(t) is the estimated innovation sequehce from an h T th‐ order regression, autoregression. Attempts are made to attain results near to the best possible and to establish almost sure convergence rates.