L12 - Testing for functional form

Question 1

What is homoscedasticity?

Answer 1

Homoscedasticity describes a situation in which the error term (that is, the “noise” or random disturbance in the relationship between the independent variables and the dependent variable) is the same across all values of the independent variables.

• constant variance
• variance that changes over time is hetroscedesticity –> problem in our regress model

Question 2

What is the issue with regression analyse in the real world?

Answer 2

We want a model that is both unbiased and efficient(low variance) but these two things work in opposite directions

Sometime you may have to give up one to get the other in a model

Question 3

How do you test for function form?

Answer 3

• This is the Ramsey Reset test for functional form misspecification –> right or left hand side are no linear
• this test can be generalised by adding cubic and higher order powers of the fitted value series

Question 4

What is Serial Correlation?

Answer 4

• Serial correlation is a problem associated with time-series data –> always present
• It occurs when the errors of the regression model are correlated with their own past values (lagged values)
• Serial correlation by itself does not mean that OLS will be biased. ( if we can prove it is unbiased we do not need to check is the second GM assumption holds)
• The most common effect of serial correlation is to bias downwards the standard errors of the OLS estimator (though this is not always the case).

Question 5

What is the mathematical definition of Serial Correlation?

Answer 5

• the regression model is in the mean-deviation form for simplicity

Question 6

What is Auto correlation?

Answer 6

• the second equation descibes the autocorrelation that is a first order moving average error

Question 7

What does Positive Autocorrelation look like on a graph?

Answer 7

Question 8

What would a graph of negative autocorrelation look like?

Answer 8

Question 9

What would a graph of lagged residuals look like with no autocorrelation?

Answer 9

Question 10

What is Orders of Serial Correlation?

Answer 10

• with annual data you will usually have first or second order autocorrelation, quarterly will lead to 4th/5th orders autocorrelation, and monthly even 12th order

Question 11

How do you detect serial correlation?

Answer 11

Question 12

What does a correlogram look like?

Answer 12