Econometrics-I-10

# Econometrics-I-10 - Applied Econometrics William Greene...

This preview shows pages 1–6. Sign up to view the full content.

Applied Econometrics William Greene Department of Economics Stern School of Business

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Applied Econometrics 10. Prediction in the Classical Regression Model
Forecasting Objective:  Forecast Distinction:  Ex post vs. Ex ante forecasting Ex post: RHS data are observed Ex ante: RHS data must be forecasted Prediction vs. model validation.   Within sample prediction “Hold out sample”

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Prediction Intervals Given x 0  predict y 0 . Two cases:         Estimate E[y| x 0 ] =  β ′ x 0       Predict y 0  =  β ′ x 0  +  ε 0    Obvious predictor,  b’x 0 + estimate of  ε 0 .   Forecast  ε 0  as 0, but allow for  variance.  Alternative:  When we predict y 0  with  b x 0 , what is the 'forecast error?'        Est.y 0   -  y 0  =  b x 0   -   β ′ x 0   -   ε 0 , so the variance of the forecast error is               x 0 Var[ b -  β ] x 0   +  σ 2 How do we estimate this?  Form a confidence interval.  Two cases:       If  x 0  is a vector of constants, the variance is just  x 0  Var[ b x 0 .  Form  confidence interval as usual.       If  x 0  had to be estimated, then we use a random variable.  What is the  variance of the product?  (Ouch!)  One possibility:  Use bootstrapping.
Forecast Variance       Variance of the forecast error is              σ 2  +  x 0 ’ Var[ b ] x 0   =  σ 2  +  σ 2 [x 0 ’ ( X’X ) -1 x 0 ]       If the model contains a constant term, this is        In terms squares and cross products of deviations from  means.  Interpretation:  Forecast variance is smallest

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 13

Econometrics-I-10 - Applied Econometrics William Greene...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online