Lecture 6: Single equation regression model

Question 1

Order empirical to theoretical models:

Answer 1

Time Series models, VAR, SVAR, single equation error correction model, general equil models

Question 2

Maximum Likelihood

Answer 2

Idea to assume a particular model with unknown parameters, we can then define the prob. of observing a given event conditional on a particular set of parameters. It is possible to choose a set of parameters which are most likely to have produced our observed data.

Question 3

Advantage of MLE

Answer 3

An extremely general concept, but if the model is missspecified it may be particularly sensitive to this misspecification. It can reduce to single equation OLS (covariance structure=

Question 4

Cramer Rao Lower Bound

Answer 4

Smallest theoretical variance which can be achieved. . ML gives it. Var(betahatML) = I(I(betahat))^-1 (hessian inverse)

Question 5

Autoregressive models

Answer 5

Forecast the variable of interest using linear combination of past values of the variable. Autoregression indicates that it is a regression of the variable against itself: yt =…yt-1….

Question 6

AR and MA model

Answer 6

AR: yt = c + phi1yt-1 + et
for phi1 = 0 WN, =1 RW and c != 0 with drift
phi1 < 0 tends to oscillate between pos and neg values
MA: yt = c + et + theta1et-1 +….
uses past forecsat errors, we dont observe the values of et
Possible to write any stationary AR(p) as MA(infinite) and if MA is invertible MA(q) into AR(infinite)

Arima puts this together with order of integration:
yt = c + ....
WN ARIMA (0,0,0) , RW with drift ARIMA(0,1,0)

Question 7

Information Criteria

Answer 7

AIC which is useful in selecting predictors for regression, also useful for determining the order of an ARIMA, also BIC, AICc, our preference is AIC

Question 8

Modelling procedure:

Answer 8

1. Plot the data: Identify any unusual observations
2. If the necessary transform the data to stabilize the variance.
3. If the data are nonstationary, take first differences of the data until the data is stat.
4. Examine the ACF: AR or MA appropriate?
5. Try your chosen models and use the AIC to search for a better model.
6. Check the residuals from your chosen model by plotting the ACF of the residuals and doing a portmanteu test of the residuals. If they dont look like WN, try a modified model.
7. If they look like WN calculate forcasts.

Question 9

Model diagnostics. What can go wrong?

Answer 9

1. Errors may not be normally distributed.
2. Data may contain outliers
3. Errors may be autocorrelated
4. Time series may be non stationary
5. Errors may shown changing variances over time
6. mean of the errors may be non zero (only applies when the model doesnt contain a constant term)