sample auto-covariance
auto-correlation
lag-t auto covariance
common mean
conditional mean
(weakly) Stationary
stochastic process
realization of stochastic process
time series
predictive distribution
auto covariance function
(weakly) stationary
strictly stationary (implied by weakly stationary plus Gaussian)
white noise
MA(1) process
AR(1) process
martingale difference series
random walk
Sample autocorrelation function
partial autocorrelation function (by regression)
Transform
Box-Cox (log) transform
Backward, differencing
Difference and Integration
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- white noise but not Martingal Difference Series( MDS) X_t = \epsilon_t + \epsilon_{t-1} \epsilon_{t-2}
- what is a random walk? ( sum of homoskestic MDSs)
- what is a Gaussian Process? why do we need it? What is a stationary process?
- AR(1) and MA(1) which is stationary? Why? (AR 1 has unit root condition, MA are always stationary)
- derive mean, variance, ACF for MA(1), AR(1), ARMA(1,1)
- ADF Test ？
- differencing operation , trend (polynomial trend)
- ARCH, leverge effect- APARCH, EGARCH , vol clustering - GARCH
- what is innovation? combine ARIMA and GARCH
- why do we need multi-variate T-S models? (correlated innovations)