[Gretl-users] ARMAX prediction/fitted values function ESTIMATES

Humour me please. Let us suppose we have an ARMAX(1,0,0) model with 2 independent variables and a constant. ie (1-ΦB)Yt = α +µ1*X1t +µ2*X2t where B is the lag or backshift operator Assuming Φ is positive this is equivalent to *Yt =α + Φ*Yt-1 +µ1*X1t +µ2*X2t* which is relatively straightforward to check against Gretl output using the estimated coefficients and relevant rhs variables .However, the results of doing so do not correspond to the predicted or fitted values from Gretl. Estimating the equation via OLS, produces marginally different coefficient estimates (all the same sign) with the exception of the intercept, and manually checking the equation does correspond to the gretl output fitted values for OLS similarly specified model. So my question is what is the ARMAX prediction function in this case Is it the expansion of the solution for Yt by dividing by (1-ΦB) ? Here is the ARMAX estimated equation; coef st.err z pval const 3.81738 0.250722 15.23 2.39e-052 *** coef st.err z pval const 3.81738 0.250722 15.23 2.39e-052 *** phi_1 0.492142 0.282172 1.744 0.0811 * X1 −0.06129 0.0232348 −2.638 0.0083 *** X2 0.183408 0.0832595 2.203 0.0276 ** Adjusted R-squared 0.645 S.D. of innovations 0.230 Log-likelihood 0.5967 Schwarz criterion 12.346 Here are the OLS equivalents coef st.err z pval const 1.99713 0.686194 2.910 0.0142 ** Yt-1 0.517002 0.181787 2.844 0.0160 ** X1 −0.04545 0.0152909 −2.973 0.0127 ** X2 0.183119 0.0835570 2.192 0.0508 * S.E. of regression 0.2245 Adjusted R-squared 0.719 Log-likelihood 3.447668 Schwarz criterion 3.9368 An explanation would be helpful Thanks *Brian Revell*