Flashcards in Defintions Deck (19)

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1

## Define MLE?

### A method of estimating parameters, given observations; it finds parameter estimates by finding the parameter values that maximise the LLF

2

## Define strong stationarity?

### Describes a stochastic process whose unconditional probability distribution does not change when shifted in time

3

## Define weak stationarity?

### Describes a stochastic process where the mean and variance are fixed through time, but the covariance can change through time

4

## 3 conditions for weak stationarity?

###
E(yt)=mu for t=1->infinity

E(yt-mu)(yt-mu) = sigma^2 (where sigma squared is less than infinity)

E(yt1-mu)(yt2-mu) = gamma(t2-t1) for all t1, t2

5

## What is the invertibility condition?

### Invertibility allows MA models to be written as AR models, which implies, more generally, that a stochastic process is invertible if an ARMA model can be written as AR models

6

## When is an ARMA(p,q) model stationary?

### If the roots of fi(L) polynomial lie outside the unit circle

7

## When is an ARMA(p,q) model invertible?

### If the roots of theta(L) polynomial lie outside the unit circle

8

## Explain the key difference between a non-stationary and stationary series?

### Both have unconditional means of 0 if both start a 0, therefore the key difference lies in the conditional mean (ie. the mean of the process given the most recent observation) (see notes)

9

## Define non-stationarity?

### A non-stationary series has at least one unit root, and therefore its probability distribution will change through time. It will have non-constant mean/variance and therefore will look different in different time periods.

10

## Two types of non-stationarity, and how to deal with them?

###
1) RW with drift (ie. stochastic trend): yt=mu+y(t-1)+error(t)

requires differencing

2) Deterministic trend (ie. trend stationary): y(t)=mu(t)+error(t)

11

## See

### very important in notes: finding mean and variance of RW with drift

12

## Key difference between RW with drift and deterministic trend?

###
Deterministic is non-stationary in its mean, but constant in its variance

RW with drift is non-stationary in its mean and variance

13

## How is stationarity induced in a stochastic trend? (expand)

### Differencing it; a non-stationary series that must be differenced 'd' times to induce stationarity is integrated of order d, where d=number of unit roots

14

## Initial hypotheses for Dickey-Fuller unit root test?

###
H0: fi=1 (non-stationary)

H1: fi less than 1 (stationary)

THESE CHANGE THOUGH!!!

15

## Explain why we cannot use a t-test to establish DF test result?

### Because under the null, the process is non-stationary (ie. yt and y(t-1) etc.) and therefore CLT doesn't apply!

16

## Show in detail how to set up a DF test? Explain why this method works? Explain why we STILL can't use a t-test to test this?

### See notes

17

## What did Dickey-Fuller do? What is the test statistic equation? When do we reject the null of non-stationarity?

###
They tabulated the asymptotic distribution of the LSE for fork under the null hypothesis of it being a unit root, therefore we can just compare the ordinary t-statistic with values of the DF distribution!

Statistic (see notes)

Reject H0 if test statistic is more negative than the CV

18

## See

### CVs for DF test

19