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Basic Question 1 of 11
Which equation(s) represent(s) an AR time-series model?
II. yt = b0 + b1t + εt.
III. lnyt = b0 + b1t + εt.
IV. xt = b0 + b1xt-1 + b2xt-2 + ... + bpxt-p +εt.
I. xt = b0 + b1xt-1 + εt.
II. yt = b0 + b1t + εt.
III. lnyt = b0 + b1t + εt.
IV. xt = b0 + b1xt-1 + b2xt-2 + ... + bpxt-p +εt.
User Contributed Comments 5
| User | Comment |
|---|---|
| MasterD | Am I mistaken or does II and III not have any t-1 values, only t. If so, then what's all this about all options relating to PREVIOUS period values? |
| ucsbdan | II and III are special cases: check the text book. |
| ericczhang | I got it wrong too, but I'm guessing since t = (t-1)+1 you can rewrite the regression equation in terms of t-1 and thus it's an AR model since then you can rewrite the regression equation in terms of y-1. |
| sahilb7 | In II and III, y is dependent upon b1t which is also related to (t-1)... i.e. b1[(t-1)+1] |
| sahilb7 | II is a Linear trend model III is a Log-Linear trend model |
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Learning Outcome Statements
describe the structure of an autoregressive (AR) model of order p and calculate one- and two-period-ahead forecasts given the estimated coefficients;
explain how autocorrelations of the residuals can be used to test whether the autoregressive model fits the time series;
explain mean reversion and calculate a mean-reverting level;
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;
CFA® 2025 Level II Curriculum, Volume 1, Module 5.