linear regression of time series with time index

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.

Answer 1

[Ridwan Alam]

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:

https://www.mathworks.com/help/curvefit/custom-nonlinear-models.html