Summary: Given data, \(u_ j\), \(y_ j\), \(j=1,...,n\), with \(u_ j\) an input sequence to a system while output is \(y_ j\), an approximation to the structure of the system generating \(y_ j\) is to be obtained by regressing \(y_ j\) on \(u_{j-i}\), \(y_{j-i}\), \(i=1,...,p_ n\), where \(p_ n\) increases with n. In this paper the rate of convergence of the coefficient matrices to their asymptotic values is discussed. The context is kept general so that, in particular, \(u_ j\) is allowed to depend on \(y_ i\), \(i\leq j\), and no assumption of stationarity for the \(y_ j\) or \(u_ j\) sequences is made.