Simple Time Series Models
- This is basic trend modeling.
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.
- 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.