Download TSM4 Documentation - Time Series Modelling (TSM)

8.3 Hamilton’s Markov switching model ............................................ 32 8.4 The Smooth Transition (ST) Model .............................................. 33 8.4.1 Single Transition Model ............................................................................33 8.4.2 Double Transition Model ...........................................................................34 8.4.3 Structural Change (Date-Transition) Model ..............................................34 8.5 Testing for Breaks and Regimes ................................................... 34 9 Post-Estimation Options....................................................... 35 9.1 Residuals and Associated Series ................................................... 35 9.2 Model Performance and Selection Criteria ................................... 36 9.3 Q Tests ........................................................................................... 37 9.4 Ex-post forecasts ........................................................................... 37 9.5 Ex-ante Multi-step Forecasts ......................................................... 38 9.5.1 Analytic Forecasts ......................................................................................38 9.5.2 Moving Average Coefficients (Impulse and Step Responses) ..................39 9.5.3 Forecast Error Variance Decomposition....................................................39 9.5.4 Forecasting Regime-Switching Models .....................................................39 9.5.5 Monte Carlo Forecasts ...............................................................................40 10 Estimation Criteria ............................................................... 41 10.1 Single Equation Methods ............................................................ 41 10.1.1 Least Squares ...........................................................................................41 10.1.2 Instrumental Variables .............................................................................41 10.1.3 Gaussian maximum likelihood ................................................................41 10.1.4 Student-t maximum likelihood ................................................................41 10.1.5 Skew-student maximum likelihood .........................................................41 10.1.6 GED maximum likelihood .......................................................................42 10.1.7 Whittle maximum likelihood ...................................................................42 10.1.8 Probit and Logit .......................................................................................42 10.1.9 Ordered Probit and Logit .........................................................................43 10.1.10 Poisson ...................................................................................................43 10.1.11 Zero-inflated Discrete ............................................................................43 10.2 System Methods .......................................................................... 43 10.2.1 Least Generalized Variance .....................................................................43 10.2.2 Generalized Method of Moments ............................................................44 10.2.3 Gaussian ML with Conditional Heteroscedasticity .................................44 10.2.4 Student-t ML with Conditional Heteroscedasticity .................................44 10.2.5 GED ML with Conditional Heteroscedasticity ........................................45 10.3 Markov Switching Models.......................................................... 45 11 Standard Errors and Covariance Matrix Formulae............... 46 11.1 Information Matrix Formulae ..................................................... 46 11.2 Robust Formulae ......................................................................... 46 11.3 HAC Variance Estimators .......................................................... 46 11.3.1 Bandwidth Selection ................................................................................46 11.3.2 Pre-whitening ...........................................................................................47 11.4 KVB Inconsistent Variance Estimates........................................ 48 12 Test Statistics ....................................................................... 49 12.1 Wald Tests................................................................................... 49 12.2 Lagrange Multiplier Tests ........................................................... 49 3
James Davidson 2015