Learning Outcome Statements

1. Trend models

a. calculate and evaluate the predicted trend value for a time series, modeled as either a linear trend or a log-linear trend, given the estimated trend coefficients;

b. describe factors that determine whether a linear or a log-linear trend should be used with a particular time series and evaluate limitations of trend models;

c. explain the requirement for a time series to be covariance stationary and describe the significance of a series that is not stationary;

2. Autoregressive (AR) time-series models

d. describe the structure of an autoregressive (AR) model of order p and calculate one- and two-period-ahead forecasts given the estimated coefficients;

e. explain how autocorrelations of the residuals can be used to test whether the autoregressive model fits the time series;

f. explain mean reversion and calculate a mean-reverting level;

g. contrast in-sample and out-of-sample forecasts and compare the forecasting accuracy of different time-series models based on the root mean squared error criterion;

3. Random walks and unit roots

h. explain the instability of coefficients of time-series models;

i. describe characteristics of random walk processes and contrast them to covariance stationary processes;

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;

4. Seasonality in time-series models

k. describe the steps of the unit root test for nonstationarity and explain the relation of the test to autoregressive time-series models;

l. explain how to test and correct for seasonality in a time-series model and calculate and interpret a forecasted value using an AR model with a seasonal lag;

5. Autoregressive conditional heteroskedasticity models

m. explain autoregressive conditional heteroskedasticity (ARCH) and describe how ARCH models can be applied to predict the variance of a time series;

6. Regressions with more than one time series

n. explain how time-series variables should be analyzed for nonstationarity and/or cointegration before use in a linear regression;

o. determine an appropriate time-series model to analyze a given investment problem and justify that choice.