# Time Series Analysis: Simple and Log-linear Trend Models

Simple Time Series Models

• This is basic trend modeling.

A simple trend model can be expressed as follows:

yt = b0 + b1t+ εt

• b0 = the y-intercept; where t = 0.

• b1 = the slope coefficient of the time trend.

• t = the time period.

• ŷt = the estimated value for time t based on the model.

• ei = the random error of the time trend.

• The big validity pit-fall for simple trend models is serial correlation; if this problem is present, then you will see an artificially high R2 and your slope coefficient may falsely appear to be significant.

• There is a visual way to detect serial correlation (not shown) or you can perform a Dubin-Watson test.

Log-linear Trend Models

• This applies to non-linear time series trends.

The structure is:

• ln yt = b0 + b1t+ et; or

• yt \= e b0 + b1t + et

• Again, like the simple trend model, use a graph or Durbin Watson test to check for serial correlation, as this will be a big threat to validity.