Autoregressive Processes

A p-order autoregressive process, denoted AR(p), takes the form

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Thinking of the subscripts i as representing time, we see that the value of y at time i is a linear function of y at earlier times plus a fixed constant and a random error term. Similar to the ordinary linear regression model, we assume that the error terms are independently distributed based on a normal distribution with zero mean and a constant variance σ2 and that the error terms are independent of the y values.

Topics

References

Greene, W. H. (2002) Econometric analysis. 5th Ed. Prentice-Hall
https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/reference/referencespapers.aspx?referenceid=1243286

Gujarati, D. & Porter, D. (2009) Basic econometrics. 5th Ed. McGraw Hill
http://www.uop.edu.pk/ocontents/gujarati_book.pdf

Hamilton, J. D. (1994) Time series analysis. Princeton University Press
https://press.princeton.edu/books/hardcover/9780691042893/time-series-analysis

Wooldridge, J. M. (2009) Introductory econometrics, a modern approach. 5th Ed. South-Western, Cegage Learning
https://cbpbu.ac.in/userfiles/file/2020/STUDY_MAT/ECO/2.pdf

7 thoughts on “Autoregressive Processes”

  1. Hi Charles, Thank you very much for this site. It is extremely helpful. I would like to find out how you determine the error terms for the ARIMA model (ei).

    Kind regards,
    Kyle

    Reply
    • Kyle,
      The formula is of form y_i = [linear combination of y_j terms and coefficients] + e_i. If you know the values of the coefficients and the y_j terms, then the error term is simply e_i = y_i – [linear combination of y_j terms and coefficients].
      Charles

      Reply

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