Page 52 - FINAL CFA II SLIDES JUNE 2019 DAY 3
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LOS 9.i: Describe characteristics of random walk READING 9: TIME SERIES ANALYSIS
processes and contrast them to covariance
stationary processes.
MODULE 9.3: RANDOM WALKS AND UNIT ROOTS
Random walk:
The predicted value in one period is equal to the value
in the previous period plus a random error term.
Simple random walk equation: x = x t–1 + ε t (bo = 0)
t
Random Walk with a Drift: bo ≠ 0 and expected to change by a constant amount each period (constant drift).
Covariance Stationarity: Exhibits neither simple random walk nor a random walk with a drift.
Recall, a time series must have a finite MRL to be covariance stationary.
As this MRT is undefined (not finite), it is NOT covariance stationary, but
exhibits unit root (b = 1).
1
For such a time series, the AR(1) model will not work without first
transforming the data! How?
(1) run an AR model & examine autocorrelations (we did this already), or
(2) perform the Dickey Fuller test.
