## Algorithms and technical material for Chapter 2

There are now (17.10.2017) three descriptions provided of methods used in the MATLAB functions. The first of these gives the calculations for producing the covariance function of a VAR(p) model using either of the MATLAB functions VARcovfun.m and VARcovfunX.m. This description is provided here in the file VARcovfunCalculation.

The second description, in the file SSFilterSmooth.pdf, gives the methods used for state space filtering and smoothing in the MATLAB function SSfilsmoMV.m.

The third description, in the file WhittleMultistep.pdf, gives an account of Whittle’s recursions for solving the mutivariate Yule-Walker equations, as implemented in the MATLAB function PredCoef.m. It also explains how this is used to construct the predictor of an exponentially weighted sum of future values of a time series, as presented in section 2.6 of the book and illustrated in Figure 2.6. A brief outline is given of Whittle’s proof that the VAR model obtained by solution of the Yule-Walker equations is stationary. Simple examples are given to show that models determined by sub-set autoregression, i.e. using past values at selected lags, are not necessarily stationary.