Conditional Projection by Means of Kalman FilteringWe establish that the recursive, state-space methods of Kalman filtering and smoothing can be used to implement the Doan, Litterman, and Sims (1983) approach to econometric forecast and policy evaluation. Compared with the methods outlined in Doan, Litterman, and Sims, the Kalman algorithms are more easily programmed and modified to incorporate different linear constraints, avoid cumbersome matrix inversions, and provide estimates of the full variance covariance matrix of the constrained projection errors which can be used directly, under standard normality assumptions, to test statistically the likelihood and internal consistency of the forecast under study. |
Common terms and phrases
1050 Massachusetts Avenue approach to econometric avoid cumbersome matrix best linear projection Buiter Bureau of Economic chi-squared statistic companion matrix constrained conditional projections constrained projections construct covariance matrix cumbersome matrix inversions different linear constraints easily programed econometric forecast filtering and smoothing forecast and policy forecast under study implement the Doan incorporate different linear internal consistency Kalman algorithms KALMAN FILTERING Richard Kalman smoothing linear combination linear dynamic system linear restrictions Litterman Macroeconomics MEANS OF KALMAN methods of Kalman methods outlined Michael Rothschild Models with Rational modified to incorporate moving average coefficients NBER TECHNICAL normal distribution number of post-sample policy evaluation post-sample constraints post-sample path post-sample periods programed and modified PROJECTION BY MEANS provide estimates PT/T Rational Expectations Models recursive Richard H Sims approach standard normality assumptions state-space methods subject to linear subroutine system's variables T'th pass TECHNICAL WORKING PAPER test statistically Title Date vector autoregression Willem H XT/T Zvi Griliches