Page 55 - FINAL CFA II SLIDES JUNE 2019 DAY 3

LOS 9.l: Explain how to test and correct for seasonality in READING 9: TIME SERIES ANALYSIS
a time-series model and calculate and interpret a
forecasted value using an AR model with a seasonal lag.
Module 9.4: Seasonality

A pattern (e.g. monthly sales data for a retailer) that tends to repeat from year to year. When present, modeling the associated
time series data would be mis-specified unless the AR model incorporates the effects of the seasonality.

EXAMPLE: Detecting seasonality: You are interested in predicting occupancy levels for a resort hotel chain and have obtained the
quarterly occupancy levels for the most recent 40 quarters (10 years), with the following data:

Does seasonality exists using the above results?

Answer: At a 5% SL, the critical t-value is 2.026.

Fail to Reject (Lag 1, 2, 3): NOT significantly different from
zero.

Reject Ho (for Lag 4): Significantly different from zero
Autocorrelation (hence seasonality) is present!

Thus, we conclude that this model is mis-specified and will be
unreliable for forecasting purposes.

We must include a seasonality term to make the model more
correctly specified.

Interpretation of seasonality in this is that the 4th quarter
2015 occupancy is related to 3 quarter 2015 as well as 4th
rd
quarter 2014 occupancy.

So how do we correct for this seasonality?