Financial Econometrics I

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Financial Econometrics I

• Part II
• Hans Dewachter

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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

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VAR A simple example
2-variable VAR(1) output gap (y), interest rate
(r)
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VAR A simple example
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VAR A simple example
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Results
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Impulse Response Function (IRF)

• Innovations are correlated
• Choleski decomposition
• Uncorrelated innovations

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Impulse Response Function (IRF)
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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

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Variance decomposition
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Forecasting
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Forecasting
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Model selection

• Variables
• Important economic effects on each other
• Adjusted R squared
• Lags

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Monetary policy rules

• 3-variable VAR(p) output (y), inflation (pi),
  interest rate (r)

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Additional variable inflation
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VAR(1)
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Impulse response funcion
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Variance decomposition
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Forecasting
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Forecasting
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Forecasting
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VAR the general case

• N-variable VAR(p)
• Y is a n x 1 vector of variables
• B1Bp are n x n matrices of coefficients

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VAR the general case

• Write your VAR(p) as
• And you have again a VAR(1)

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Impulse response function

• Applying Choleski decomposition
• Response function will follow easily as

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Forecasting

• Forecast conditional on time t information
  k-periods ahead
• Can also be computed recursively

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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