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.