1. Unit Root Tests

2. Integrated Process Integrated Process I(1): Yt = Y(t-1) + ARMA(p, q)t
A Key Model (Hypothesis) for Macroeconomic Variables

3. Behavior of Two Trend Models - Long Run Forecast Implications
For t = h (for h=0, Y0=b0)
Fixed Trend Yh = b0 + b1 h + eh eh is WN(0, s)
Variable Trend Yh = Y0 + d h + e1 + e2…. eh …
SD of (e1 + e2…. eh) =

4. Unit Root Test Using t H1: Stationary AR(1) with mean 0
H0 : Random Walk
H1: Stationary AR(1) with mean 0

5. Unit Root Test Using tm H0 : Random Walk
H1: Stationary AR(1) with mean m

6. Unit Root Test Using tt H0 : Random Walk with Drift
H1: Linear Trend with Stationary
Deviation (cycle)

7. Unit Root Test - Why So Called?
Note that:
Yt - Y(t-1) = (1 - L) Yt = ARMA(p, q) process, i.e.,