Variance decomposition of forecast errors 1

Variance decomposition of forecast errorsIn econometrics and other applications of multivariate time series analysis, a variance decomposition or forecasterror variance decomposition is used to aid in the interpretation of a vector autoregression (VAR) model once ithas been fitted.[1] The variance decomposition indicates the amount of information each variable contributes to theother variables in the autoregression. It determines how much of the forecast error variance of each of the variablescan be explained by exogenous shocks to the other variables.

Calculating the forecast error varianceFor the VAR (p) of form

.This can be changed to a VAR(1) structure by writing it in companion form (see general matrix notation of aVAR(p))

where

, , and

where , and are dimensional column vectors, is by dimensional matrix and , and are dimensional column vectors.The mean squared error of the h-step forecast of variable j is

and where

• is the jth column of and the subscript refers to that element of the matrix• where is a lower triangular matrix obtained by a Cholesky decomposition of such that

, where is the covariance matrix of the errors • where so that is a by dimensional matrix.

The amount of forecast error variance of variable accounted for by exogenous shocks to variable is given by

Notes[1] Lütkepohl, H. (2007) New Introduction to Multiple Time Series Analysis, Springer. p. 63.

Article Sources and Contributors 2

Article Sources and ContributorsVariance decomposition of forecast errors  Source: http://en.wikipedia.org/w/index.php?oldid=532184072  Contributors: 8ung3st, Dgianotti, Duoduoduo, FilipeS, Johnpseudo, Kappie24,Kateshortforbob, Melcombe, Sullivan.t.j, 39 anonymous edits

LicenseCreative Commons Attribution-Share Alike 3.0 Unported//creativecommons.org/licenses/by-sa/3.0/