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  • Can ARIMA be directly used for non-stationary time series?

    Dear Statalist,

    I have a question about whether -arima- can be directly used for non-stationary time series (non-stationary even at first difference).

    In theory, ARIMA will firstly difference the original series, and then use the differenced series. I have tested the stationarity of the US Wholesale Price Index (WPI) used in the Stata manual of -arima-. Neither the original WPI series nor the first-differenced WPI is stationary. But the Stata manual still uses it (in the first-differenced form) to demonstrate -arima-.

    The data source of WPI is http://www.stata-press.com/data/r13/wpi1

    So does it mean that I can directly apply -arima- to non-stationary data (non-stationary even at first difference)?

    Thank you very much!

  • #2
    Any suggestions would be appreciated!

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    • #3
      Any suggestions would be appreciated, many thanks!

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      • #4
        The notion of ARIMA(n,p,q) is to specify the order of integration of an ARMA model (via p). So in essence, ARIMA is used to specifically model non-stationary time series data, for which order of integration is known (p). So if p=2, series has to be differenced twice etc. It is not clear what your question means, as ARIMA is used on non-stationary series by definition.

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        • #5
          Originally posted by Chinmay Sharma View Post
          The notion of ARIMA(n,p,q) is to specify the order of integration of an ARMA model (via p). So in essence, ARIMA is used to specifically model non-stationary time series data, for which order of integration is known (p). So if p=2, series has to be differenced twice etc. It is not clear what your question means, as ARIMA is used on non-stationary series by definition.
          Thank you very much! I see your point and it just solves my problem. May I ask if my use of ARIMA to estimate the following difference-stationary trend model is correct?

          I have a difference-stationary model D.ln(y)=b+u that is the first-difference form of the trend-stationary model ln(y)=a+bt+u, where b is the growth rate and t is the time variable.

          So in the difference-stationary model, the growth rate of y is regressed on a constant and an error term with an ARMA specification.

          So is it correct to use ARIMA to estimate this difference-stationary model (e.g. arima y, arima(1, 1, 1))?

          Thank you very much again!
          Last edited by Alex Mai; 27 Jun 2018, 11:06.

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