Log-Linear Trend Models

[CY_Analyst]

I have a question regarding the Linear and Log-Liner Trend Models.
The descriptions for both are:
Linear Trend Models are appropriate if the data points appear to be equally distributed above and below the regression line.
Log Linear Trend Models are more suitable when the date plots with a non linear (curved) shape, then the residuals will be persistently positive or negative for a period of time.
However the models in Schweser Pg 200 show the opposite. Can someone explain why?
The models in the CFAI book Reading 11 Figures 6 and 8 have the same concept as in Schweser.
Any help would be appreciated.

 

[krokodilizm]

I checked both figures and they are consistent with what you said: residuals ARE consistently above or below the trend line. It’s all correct. Log linear models are used when growth is in the form of a curve.
Think: When an economic phenomenon follows a curve and you try to to draw a best fit line you will experience serial correlation, i.e. the residuals are predominantly below or above your line. Draw a curve and then strike a straight line through it to see what I mean. Log linear models avoid this by taking logs of the data, as opposed to raw data. That’s all there is to it.
Simplify the complicated side, don’t complify the….

 

[tickersu]

krokodilizm wrote:
Think: When an economic phenomenon follows a curve and you try to to draw a best fit line you will experience serial correlation, i.e. the residuals are predominantly below or above your line.

I would just add that this would be an example of positive serial correlation– if a negative error is typically followed by a negative error or if a positive error is typically followed by a positive error. Negative serial correlation of the errors would be a case where a negative (positive) error is typically followed by a positive (negative) error.

 

[S2000magician]

tickersu wrote:

krokodilizm wrote:Think: When an economic phenomenon follows a curve and you try to to draw a best fit line you will experience serial correlation, i.e. the residuals are predominantly below or above your line.

I would just add that this would be an example of positive serial correlation– if a negative error is typically followed by a negative error or if a positive error is typically followed by a positive error. Negative serial correlation of the errors would be a case where a negative (positive) error is typically followed by a positive (negative) error.

I was thinking about mentioning the same thing, which is certainly true if an economic phenomenon follows an exponential curve.
However, because all he stipulated was that the phenomenon follows a curve, you could conceivably get positive serial correlation or negative serial correlation, depending on the nature of the curve (consider, for example, a high-frequency sine wave).

 

[tickersu]

S2000magician wrote:

tickersu wrote:

krokodilizm wrote:Think: When an economic phenomenon follows a curve and you try to to draw a best fit line you will experience serial correlation, i.e. the residuals are predominantly below or above your line.

I would just add that this would be an example of positive serial correlation– if a negative error is typically followed by a negative error or if a positive error is typically followed by a positive error. Negative serial correlation of the errors would be a case where a negative (positive) error is typically followed by a positive (negative) error.

I was thinking about mentioning the same thing, which is certainly true if an economic phenomenon follows an exponential curve.
However, because all he stipulated was that the phenomenon follows a curve, you could conceivably get positive serial correlation or negative serial correlation, depending on the nature of the curve (consider, for example, a high-frequency sine wave).

That’s a good point, and I hadn’t thought about that before replying. I think it is still good to differentiate the difference between positive and negative autocorrelation, but overall, you definitely have it.

 

[CY_Analyst]

Thank you all!

 

[S2000magician]

My pleasure.