Quantitative Burning the Brain II

The next burning of brain was done by Autogressive models (AR). AR may be invalid if it is not stationary covariance. Stationary covariance means

(1) Time series have constant and finite mean

(2) Time series have constant and finite variance

(3) Time series have constant and finite covariance itself with previous and future time series.

Mean reversion means = b0/ (1 - b1)

But a random walk means a time series equal to the previous + a random variable.

To test for nonstationarity:

1. Plot graphs - check for variation in mean/variance

2. Use AR and check the correlations

3. Use Dickey and Fuller (DF). Take the First Difference and test for correlation g=0. If g=0 Null Hypothesis no reject => unit root / non-stationary.

ARCH(1) - means Autoregressive conditional heteroskedasticity. Horrible name. Burnt another brain cell remembering this ARCH!!! ARCH means error residual's variance serially correlated with the previous error error residual's variance.