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Basic Question 4 of 9
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: yt = eb0 + b1t, then the growth rate in the time series over two consecutive periods is eb1.
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: yt = eb0 + b1t, then the growth rate in the time series over two consecutive periods is eb1.
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 |
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Learning Outcome Statements
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;
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;
explain the requirement for a time series to be covariance stationary and describe the significance of a series that is not stationary;
CFA® 2025 Level II Curriculum, Volume 1, Module 5.