Handout on Unit Roots , Spurious Regressions and Cointegration

A time series is a random walk if 1 t t t y y u    where t u is iid. A time series is a martingale if 1 1 ( ) t t t E y y    . A time series is a martingale difference sequence if 1( ) 0 t t E y   . A time series is (weakly) stationary if it’s first two moments exist and do not change over time. A time series is invertible if it can be written as an autoregression. A time series is I(0) if it is both stationary and invertible. A time series is I(d) if its’ dth differences are I(0). If a time series is I(1), it is said to have a unit root. An ARIMA(p,d,q) model is a time series the dth differences of which form a stationary and invertible ARMA(p,q) model.