**Simple Time Series Models**

- This is basic trend modeling.

A simple trend model can be expressed as follows:

y_{t} = b_{0} + b_{1}t+ ε_{t}

- b
_{0}= the y-intercept; where t = 0. - b
_{1}= the slope coefficient of the time trend. - t = the time period.
- ŷ
_{t}= the estimated value for time t based on the model. - e
_{i}= 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 R
^{2}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 y
_{t}= b_{0}+ b_{1}t+ e_{t}; or - y
_{t }= e^{b}_{0}^{ + b}_{1t}^{ + }^{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.

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