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;

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;

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;

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;