- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 6. Time-Series Analysis
- Subject 2. Autoregressive (AR) Time-Series Models

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**CFA Practice Question**

Which equation(s) represent(s) an AR time-series model?

II. y

III. lny

IV. x

I. x

_{t}= b_{0}+ b_{1}x_{t-1}+ ε_{t}.II. y

_{t}= b_{0}+ b_{1}t + ε_{t}.III. lny

_{t}= b_{0}+ b_{1}t + ε_{t}.IV. x

_{t}= b_{0}+ b_{1}x_{t-1}+ b_{2}x_{t-2}+ ... + b_{p}x_{t-p}+ε_{t}.Correct Answer: I, II, III and IV

A key feature of an autoregressive model is that the current period values are related to previous period values. The 4 equations all presents the relationship.

I is called AR(1) model and IV is called AR(p) model. Notice that II, a linear trend model, and III, a log-linear trend model, are special cases of AR models.

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**User Contributed Comments**
5

User |
Comment |
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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 |