Multivariate Time Series Flashcards
What are the assumptions made for bivariate white noise?
We assume stationarity with mean vector 0 and coveraince function sigma not dependent on t. The cross covariance that is covariance of white noises from different times is 0, The covariance of different white noises ex: W1,T and W2,T at the same time is found using matrix sigma
How do we know multivariate white noise?
Each individual series is a white noise and the cross covariance for each pair of series is zero
Define the cross covariance
COV(Wi,t Wjt+k)
What does VAR stand for
Vector auto regressive model
How do we know if VAR is stationary?
If all eigenvalues of phi are less than 1 in magnitude
Define cointegration
Two non stationary time series Xt and Yt are cointegrated if some linear combination aXt+bYt with a and b real constants is a stationary time series. If this is the case they ahve a cointegration factor of a,b
What does Xt is integrated order d mean?
Xt needs d differences to become stationary
What is d
The minimum number of differences to achieve stationarity
What integrated order is a staionary time series
I(0) - zero
What is the hypothesis tested by the phillips ouliaris test
H0: Xt and Yt are not cointegrated
H1: Xt and Yt are cointegrated
Name the test that looks for cointegration
Phillips-ouliaris test
Name the r function used to test for cointegration
po.test
When do we reject the phillips ouliaris test?
Pvalue <alpha
