Page 54 - 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 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. READING 9: TIME SERIES ANALYSIS
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.
EXAMPLE: Unit root: Suppose we decide to model the capacity utilization data. Using an AR(1) model, the results indicate that the
capacity utilization time series probably contains a unit root and is, therefore, not covariance stationary. Discuss how this time series can
be transformed to be covariance stationary.

Answer: By transforming the data using 1sy differencing and modeling the first-differenced time series as an AR time series.

EXAMPLE: First differencing: The table below contains the 1st-differences of our manufacturing capacity utilization time series for the
period 2013.1 through 2016.3. The first two columns contain the original time series. The 1st differences of the original series are contained
in the third column, and the one-period lagged values on the 1st-differences are presented in the 4th column. Note that the 1st differences in
this example represent the change in manufacturing capacity from the preceding period (designated as y and y ).
t–1
t
After this transformation, we regress the AR(1) model, y = b + b y .
0
t
1 t–1
Next table shows the results: notice that the estimated coefficient on the
lag variable is statistically significant at 5% SL.

> p-value.

Recall: The critical 2TT (5% SL and 100 df) = 1.98
If: b 1 − 1 ≠ 0, then
b 1 = 1.0 SO?