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					Financial Econometrics I

            Part II
        Hans Dewachter
Vector Autoregression (VAR)
   Why use only one variable?
   Financial variables depend on past
    values of other variables
   VAR
       Linear model
       Used for forecasting and impulse
        responses and variance decomposition
VAR: A simple example
2-variable VAR(1): output gap (y), interest rate (r)
VAR: A simple example
VAR: A simple example
Results
Impulse Response Function (IRF)
   Innovations are correlated


   Choleski decomposition



   Uncorrelated innovations
Impulse Response Function (IRF)
Impulse Response Function (IRF)
   So, to estimate a VAR you need to
    decide on:
       Variables to be included
       Ordering of the variables
       Number of lags
Variance decomposition
Forecasting
Forecasting
Model selection
   Variables:
       Important economic effects on each other
       Adjusted R squared
   Lags
      Monetary policy rules
   3-variable VAR(p): output (y), inflation (pi),
    interest rate (r)
Additional variable: inflation
VAR(1)
Impulse response funcion
Variance decomposition
Forecasting
Forecasting
Forecasting
VAR: the general case
   N-variable VAR(p)



       Y is a n x 1 vector of variables
       B1…Bp are n x n matrices of coefficients
VAR: the general case
   Write your VAR(p) as:




   And you have again a VAR(1):
Impulse response function
   Applying Choleski decomposition




   Response function will follow easily as:
Forecasting
   Forecast conditional on time t
    information k-periods ahead:



   Can also be computed recursively:
Conclusion
   VAR does not impose rigid a priori restrictions
    on the data generation process
   Estimation is easy (OLS equation by
    equation)
   IRFs allow us to analyze dynamic behavior
   Variance decompositions show us the relative
    importance of each shock
   Forecasting can be done in a simple way

				
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