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    ARIMA estimation technique




    Hello, I am using SAS to forecast with ARIMA.
    I need to choose between two methods, conditional least Squares and MLE.
    Which technique do you recommend and why?

    Thanks in advance!

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    Re: ARIMA estimation technique

    Do you want to tell us more about your model?


    MLE is always a work horse, though I don't know if it is just a naming thing but what is conditional least squares referencing, is it conditional on past values?
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    Re: ARIMA estimation technique

    Quote Originally Posted by hlsmith View Post
    Do you want to tell us more about your model?


    MLE is always a work horse, though I don't know if it is just a naming thing but what is conditional least squares referencing, is it conditional on past values?
    Thank you for your reply. The data is the Swedish nominal interest rate from 1995 to 2015 (quarterly data).

    Im not an expert, but to the best of my knowledge ARIMA models cant be estimated purely by OLS, due to the inclusion of the MA term. Thus, first some MLE method is used for the MA terms, then this is used to give the best fit for an ARIMA model, with OLS for the "remaining part", thus, "conditional" least Squares.

    Furthermore, the ADF test with intercept gives a p-value of 0.2144 but the ADF test without intercept gives a p-value of 0.01, thus the first test says that the nominal interest rate is nonstationary but the second says that it is, however, ive Heard from a teacher that the ADF test without intercept should not be used unless its used on residuals (with a mean of 0). The series does not look fully stationary either, but is not a clear cut case of nonstationarity.

    When fitting models, with the AR and MA Component at a maximum of 4 and the I Component at 0 or 1, the RMSE for insample forecasts is generally lower for the models with I=1. However, the best performing model (looking at both AIC and RMSE) is a (4,0,4) model. Can this still be used, even if the "entering variable" was not stationary according to the adf test? the model does perform better afterall.

    Thanks in advance.

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    Re: ARIMA estimation technique

    OLS would not work with time series because of autocorrelation. I had not heard you actually had a choice in your ARIMA estimator before now.
    The ADF test is a different issue than how you estimate the results. It deals with non-Stationarity, an entirely different issue. ADF with and without an intercept is making different assumptions about the nature of the time series so its not surprising that you get different results. If you don't have a theoretical basis for choosing one then there are a series of decision rules by different analyst which to start with. Commonly you start with one, then based on the results you move on to another (there are actually three versions of the ADF of which you noted two).

    I will see if I can find the decision rule but its buried in a massive document so it might be a few days.

    You don't judge what the I is by performance. Performance, be that prediction or AIC, is done only after you decide on the order of Stationarity. A time series is either stationary or its not, I have never heard a better predicting model used as a basis for deciding on the order of integration. Note that the ADF has serious power issues. Its recommended that you try one of the Stationarity test that uses the reverse null hypothesis than ADF to see if you come to the same conclusion as the ADF.
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    Re: ARIMA estimation technique

    A side note, I believe the use of standard OLS or other options as not appropriate in that without correction they will not address increased uncertainty in forecast values further out into the future.


    noetsi,


    Can you provide a little info in the ADF tests available in SAS and in which options will elicit them.
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    Re: ARIMA estimation technique

    I have not worked with that in about 3 years (I ended up using exponential smoothing rather than ARIMA). I will try to find that material. I do know that the test exist I believe in both PROC ARIMA and PROC AUTOREG.
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    Re: ARIMA estimation technique

    I guess, is the test just the Dickey, etc. tests? I was just thinking those were for autocorrelation not directly for stationary assessment.
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    Re: ARIMA estimation technique

    ADF is how you use this process in SAS. I believe the three types of ADF is called ,Zero Mean, Single Mean, and Trend by SAS although I am not certain of this. You can see an example of that in the code below.

    This paper helps some with unit roots https://support.sas.com/resources/pa.../3294-2015.pdf

    If you go to the section of this that deals with the Stationarity option, it shows all the SAS Stationarity test.
    http://support.sas.com/documentation...eg_sect014.htm
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    Re: ARIMA estimation technique


    Thank you all for your answers!

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