Time Series Analysis: Simple and Log-linear Trend Models
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Simple Time Series Models
This is basic trend modeling.
A simple trend model can be expressed as follows:
- = the y-intercept; where t = 0.
- = the slope coefficient of the time trend.
- t = the time period.
- = the estimated value for time t based on the model.
- = 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:
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.