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##### Learning Outcome Statements
 1. Trend Modelsa. 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 Modelsd. 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 Rootsh. 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 Modelsk. 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 Modelsm. 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 Seriesn. 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.
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