linear regression of time series with time index

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Hi, let us say we have a variable y and quarter index for 10 years. Let me use t to denote for time index. If i want to run linear regression of this kind:
y_t =beta_0 + beta_1 * y_{t-1} +beta_2 * t + error_t;
how will include the time index t in the regression?
I searched a lot, but could not find satisfying answer or solution.
thanks for the help.

Answers (1)

Ridwan Alam
Ridwan Alam on 6 Jan 2020
If you have a fixed equation like the one provided, I believe you are looking for parameter estimation methods to find beta_0, beta_1, beta_2. If this is the case, you can try cftool to fit y and t to your equation:

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