- CFA Exams
- CFA Exam: Level II 2021
- Study Session 2. Quantitative Methods (1)
- Reading 6. Time-Series Analysis
- Subject 1. Trend models

###
**CFA Practice Question**

Which statement(s) is (are) true?

II. Exponential growth should be modeled using log-linear trend models.

III. If we describe a time series by this equation: y

I. Exponential growth is growth by a constant amount from one period to the next.

II. Exponential growth should be modeled using log-linear trend models.

III. If we describe a time series by this equation: y

_{t}= e^{b0 + b1t}, then the growth rate in the time series over two consecutive periods is e^{b1}.Correct Answer: II

III. The growth rate should be e

I: It should be a constant growth rate from one period to the next.

III. The growth rate should be e

^{b1}- 1.###
**User Contributed Comments**
5

User |
Comment |
---|---|

Offboard |
Could someone explain the 3rd satement? how to get exp(b1)-1? |

VenkatB |
Y(T) = e^ (b0 + b1t) = e^ b0 * e ^ b1t For example let us assume b0 is some constant (=2) and b1=4 ________ when t =1 Y(1) = e^(2+4*1) = e^6 ______ when t=2 Y(2) = e^(2+4*2) = e^10 _____________ when t=3 Y(2) = e^(2+4*3) = e^14 _____________ So the growth rate is e^4 (=e^b1) , not sure how they are saying e^b1 -1 |

aravinda |
Here it is..... Y(t) = e^(b0 + b1t) and Y(t+1) = e^{ b0 + b1(t+1) } Growth Rate between 2 consecutive periods ==> Y(t+1) - Y(t) / Y(t)...just a HPR ==> { e^[ b0 + b1(t+1) ] - e^ ( b0 + b1t) } / e^ (b0 + b1t) ==> { e^ [b0 + b1(t+1)] / e^ (b0 + b1t) } - 1 ==> { e^ [b0 + b1(t+1) * e^ - (b0 + b1t) } - 1 ==> { e^ [b0 + b1t + b1 - b0 - b1t] } - 1 ==> e ^ ( b1) - 1 |

VenkatB |
Thanks aravinda |

StJohnDale |
Thanks Aravinda..good one |