Multilevel modelling and time series analysis in ... - ERSO - Swov

3.6 State space modelsKoopman S.J., Harvey, A.C., Doornik, J.A. and Shephard, N. (2000).Stamp: Structural Time Series Analyser, Modeller and Predictor,London: Timberlake Consultants Press.Method of estimation is Maximum likelihoodThe present sample is: 1970 to 2003Equation 1.Log_NO_fat = Level + IrregularEstimation reportModel with 1 parameters ( 1 restrictions).Parameter estimation sample is 1970. 1 - 2003. 1. (T = 34).Log-likelihood kernel is 0.No estimation done.Eq 1 : Diagnostic summary report.Estimation sample is 1970. 1 - 2003. 1. (T = 34, n = 33).Log-Likelihood is 48.1408 (-2 LogL = -96.2816).Prediction error variance is 0.047433Summary statisticsLog_NO_fatStd.Error 0.21779Normality 1.3457H( 11) 3.6612r( 1) 0.58763r( 6) -0.073609DW 0.22639Q( 6, 6) 28.814R^2 0.00000Eq 1 : Estimated variances of disturbances.Component Log_NO_fat (q-ratio)Irr 0.048583 ( 1.0000) In the first part of the output (estimation report and above), check the outputon the estimation method (maximum likelihood), sample period (1970-2003),model components (level and irregular), the number of parametersestimated (1), and the number of observations (T=34).The diagnostic summary report gives some additional information: number of degrees offreedom (T-1), log-likelihood, and prediction error variance. The log-likelihood value given is thelog-likelihood function at its maximum value after estimation. This value is different from thevalue in Section 3.6.1.4 of the Methodology report, which is obtained from the above value byextracting a constant and dividing by another constant. Both constants depend on the number ofobservations T. The prediction error variance (PEV) is a basic measure of goodness-of-fit (thesmaller the PEV, the better the fit).Next, the summary of statistics can be used to evaluate model performancewith respect to the diagnostic tests (see Section 3.6.1.4 of the Methodologyreport). For this evaluation, we make a table like Table 3.6.1. A “+” in the lastcolumn of Table 3.6.1 means that the assumption is satisfied, a “-” indicatesviolation of the assumption.Statistic Value Critical 5%value aAssumptionsatisfiedP r o j e c t c o - f i n a n c e d b y t h e E u r o p e a n C o m m i s s i o n , D i r e c t o r a t e - G e n e r a l T r a n s p o r t a n d E n e r g yP a g e 1 9 1