Lecture 8 VAR Models Flashcards
Basic Facts about VAR
Vector autoregressions: Between variables a bi directional relationship is often possible eg Income up, consumption up vice versa. Generalisation of the univariate autoregressive model for forecasting a collection of variables (vector of time series). Right hand side includes a constant and lags of all variables in the system. VAR resembles a SEM modelling, we consider several endogenous variables together. Each endog. variable is explained by its lagged values and the lagged values of all other endog. variables in the model.
VAR uses?
Forcasting: Var forecasts extrapolate expected values of current and future values of each of the variables using observed lagged values of all variables assuming no further shock.
Impulse Response Fct. IRFs trace out the expected responses of the current and future values of each of the variables to a shock in one of the VAR equations.
FEDV: Provide the percentage of the variance of the error made in forecasting a variable at a given horizon due to a specific shock. Like a partial R2 for error forecast.
Granger causality test: GC requires that lagged values of variable A are related to subsequent values of variable B, keeping constant the lagged values of B and any other explanatory variable.
Definition VAR
Yt = At Yt-1 + … + A’Yt-k + et
If the data is stationary, we forecast them directly fitting VAR to the data, otherwise differences. For each equation parameters are estimated by minimizing the sum of squared eit values. Forcasts are generated in VAR by a recursive manner, VAR generates forecast for each variable included in the system, eg one step ahead forecast.
Two decisions necessary in VAR
How many variables (K)(based on the equation of interest) and how many lags(P) should be included in the system? The more coeffincients to be estimated the larger the estimation error entering forecast. P typically defined by information criteria (Prof likes Schwarz). at least 2 1/2 variables for VAR and not more than 4 lags-Otherwise problem of overfitting
R2 can be negative, if?
If you dont have a constant in your regression
Give example for GC test, Variance decomp and IRF!
GC test: eg the validity of the monetarist proposition that autonomous variations in the money supply have been a cause of output inflations.
Variance decomp.:eg fraction of the variance of the output that is due to mandatory versus due to real factors.
IRF: eg how output respongs to shock to money( ie return fast or slow?)
Granger causality
The existence of a relationship between variables doesnt prove causality or direction of influence. EG GDP and M or vice versa. Ftest for joint distri. t test for significance for a single coefficient. . assump.: stationary variables
Calculate IRF by derivatives of all error terms to each variable
Good to know!
Advantages of VAR
Method is simple, all variables in VAR are endogenous
Estimation is simple, OLS can be applied to each equation separately
Forecasts are often better than from more complex simultaneous models
Problems with VAR modelling?
It uses less prior information
VAR are less suited for policy analysis
If sample size is large, lot of degree of freedom
Pro: IRF, Contra: In m variable VAR, all m should be stationary otherwise we have to transform the data. If its a mix between I(0) and I(1) it is not be easy
KPSW test for cointegration, supply shock have permanent effects on GDP, demand shocks only transitory
Good to know!