Week 10

Front 1

Define an autoregression

Back 1

An autoregression is where both the dependent and the independent variables are from the same stochastic process

Front 2

By repeating a substitution of lagged variables in an AR(1) what is the outcome?

Back 2

Front 3

What are the unconditional means and variance of an AR process

Back 3

Front 4

Describe Autocovariance and derive it

Back 4

Front 5

Derive Autocorrelation and explain it's meaning

Back 5

Therefore Autocorrelation is a decaying process. The smaller the persistence parameter the faster it decays

Front 6

Derive R^2 and adj R^2

Back 6

Front 7

What are the two substitutes instead of R^2 to measure goodness of fit?

Back 7

1. Akaike Information Criterion
2. Schwartz Information Criterion
   

Front 8

Derive both AIC and SIC

Back 8

Front 9

What are the key points about information criterion

Back 9

1. The model that minimizes ic is prefered
2. SIC is more parsimonious than AIC
3. Relative - not absolute - value matter.
4. They compare fit across models.
   

Front 10

What is the optimal lag length

Back 10

STEPS

1. Decide on the maximum possible lags.
2. Fit AR(p) and keep the number of observations in each model the same and collect SIC
3. Select the model with the lowest SIC
4. Test for Seriel correlation
5. If you fail to reject no seriel correlation, proceed otherwise, increase by one lag length
6. Repeat 4 & 5 until you succeed fail to reject.
   

Front 11

Explain Integration in a TSD sense

Back 11

A weakly dependent process is said to be integrated of order 0. Any or I(p) can be made to be weakly dependent and covariant stationary as an extension, by differencing p times. Otherwise put as having p unit roots.

In economics integrated process of order 0,1 and 2 are most common.

Front 12

Explain the unit root testing process. Both in terms of the persistence parameter and the differenced persisten parameter.

Back 12

Unit root testing tests for random walk. As previously discussed, unit root makes inferencing impossible. The testing is based on the null that unit root exists i.e b = 1. and the alternative is unit root doesn't exist i.e b < 1. This is a one sided test because should b>1 it is determined an explosive process and we find the same issues as before.

Another form of this test requires first order differencing. The null is then changed from unit root to 0. This is mostly done for convenience, i.e gamma = 0 and the alternative is the one sided gamma < 0.

However under the null the model becomes integrated of order 1 meaning the usually t statistics are no longer applicable.

Front 13

Explain Dickey Fuller distribution

Back 13

The asymptotic distribution of the t statistic under unit root test's null is called the Dickey Fuller distribution.

Front 14

Describe simply what a Dickey Fuller test is

Back 14

Firstly, conducting a regular testing process to procure a tstatistic. Then using a Dickey Fuller distribution to tabulate the correct critical values. conduct the rejction as you would any other one sided t-distribution.

Front 15

Name one major risk of a model being perceived to have unit root - a stochastic trend.

Back 15

Although a trend may appear stochastic, deterministic trend may still exist. As such it can be dealt with as any other deterministic trend, by incorporating a trend variable.

However this leads to its own distribution as well Dickey Fuller - case 2

Front 16

What is the Augmented Dickey Fuller test?

Back 16

The Dickey Fuller test is based on the assumption that error is white noise - mean 0 and constant variance, furthermore that it is uncorrelated with all past error terms.

In order to account for this run the DF test on an augmented AR(p) model.

Distributions are not affected and thus regular properties may be used.