Page 60 - FINAL CFA II SLIDES JUNE 2019 DAY 3

LOS 9.o: Determine an appropriate time-series model to
analyze a given investment problem and justify that choice. READING 9: TIME SERIES ANALYSIS

Which model best suits are needs?

Determine your goal first –Are You Modelling:
1.1 Relationship of a variable to other variables (e.g., cointegrated, cross-sectional multiple regression)? OR
1.2 The variable over time (e.g., trend model)?

Once decided, plot the variable over time and look for non-stationarity (e.g. non-constant variance or mean, seasonality, or structural change).

Structural change : significant shift in the plotted data at a point in time that seems to divide the data into 2+ distinct patterns (see point a.)
Scenario 1: NO seasonality or structural shift. If data plots:
1. on a straight line with an upward or downward slope, use a linear trend model.
2. in a curve, use a log-linear trend model.

Scenario 2: Run trend analysis, compute residuals, & test for serial correlation (SC) via DW test. If:
1. No SC, you can use the model.
2. SC present, you must use another model (e.g., an AR).

Scenario 3: If 2.2 above, reexamine for stationarity before running an AR model. If not stationary, treat
the data for use in an AR model as follows:
1. If it has a linear trend, first-difference the data;
2. If the data has an exponential trend, first-difference the natural log of the data;
3. If there is a structural shift, run two separate models;
4. If the data has a seasonal component, incorporate the seasonality in the AR model.

Scenario 4: After first-differencing in 5, if series is covariance stationary, run an AR(1) model and test for
You must run two different models SC and seasonality:
(before and after this point) and test 1. If No remaining SC, use the model;
whether the time series has actually shifted. 2. If SC, incorporate lagged values of the variable (for seasonality—e.g., for monthly data, add the 12th
lag) until you have removed (i.e., modeled) any SC.
If the time series has shifted significantly, a Scenario 5: Test for ARCH and whether the resulting coefficient is significantly different from zero. If:
single time series encompassing the entire 1. Not significantly different from zero, you can use the model.
period will likely produce unreliable results. 2. Significantly different from zero, ARCH is present -correct it using generalized least squares.
6 key scenarios… Scenario 6: If you have developed two statistically reliable models and want to determine which is better
at forecasting, calculate their out-of-sample RMSE.