Autoregressive vs. trend model

Hello,

Reading the book I am confused on what exactly is the difference between an autoregressive model vs. a trend model in their respective equations? I know that autoregressive models better account for serial correlation, but what is exactly is the difference in terms of their regression1 models and equations?

Thank you!

In a trend model you regress an independent variable such as sales based on depended variables such as say historical price. In autoregressive models, you regress sales in t1 based on historical sales (in say t-1).

Sorry, this is incorrect. A trend model is based using a fictitious variable that increase 1 by 1, say 1,2,3,4,5,6,7,…,n

The idea of using this independent variable is to find a fixed pace the dependent variable would describe. For example, the salary income of a professional of 15 years experience. If you get the monthly income of this subject since 15 years ago you may find this figure:

Y1 = US$ 2,000

Y2 = US$ 2,500

Y3 = US$ 3,500

Y4 = US$ 4,000

Y5 = US$ 6,600

Y14 = US$ 12,500

Y15 = US$ 14,000

If you regress the salary income on a trend variable, you may find that the trend variable (1,2,3,4,5,…,14,15) is a good explainer (statistically significant).

The equation would be Monthly Salary = a + b*Trend + error

“a” and “b” are probably statistically significant.

This is correct.

To OP Keep_running,

AR models are good for time-series variables that are likely to depend on its own past or its past is the best data available for any forecast of this variable (for example Currencies Exchange Rates)

Ok, but don’t AR models also increase by one unit (like normal trend models)? How do AR models get rid of serial correlation?