Page 53 - FINAL CFA II SLIDES JUNE 2019 DAY 3

LOS 9.j: Describe implications of unit roots for time-series
analysis, explain when unit roots are likely to occur and how to READING 9: TIME SERIES ANALYSIS
test for them, and demonstrate how a time series with a unit root
can be transformed so it can be analyzed with an AR model.
MODULE 9.3: RANDOM WALKS AND UNIT ROOTS
LOS 9.k: Describe the steps of the unit root test for non-
stationarity and explain the relation of the test to autoregressive
time-series models. Unit Root Testing for Non-stationarity (or covariance stationarity)

2. Perform the Dickey Fuller (DF) test:

st
Transform the AR(1) model to run a simple regression using 1 DIFFERENCING:
Subtracting the value of the time series (i.e., the dependent variable) in the immediately preceding period from the current value
of the time series to define a new dependent variable, y. Subtracting Xt-1 on both sides of the time series equation!

If:

b − 1 ≠ 0, then
1
b 1 = 1.0 Meaning time series must have a unit root.

Rather than directly testing whether the original coefficient ≠1 (as you can’t
statistically-speaking, directly test whether the coefficient of on the
independent variable in an AR time series = 1),

• test whether the new, transformed coefficient (b − 1) ≠ 0 using a
1
modified t-test.

Model the change in the dependent variable such
that the change in x, x – x t–1 = ε ,
t
t