Fluorite | Level 6

## Default estimation method for arima models

Hi SAS community,

I've noticed that univariate ARIMA models are typically estimated by default using the maximum likelihood method. However, in SAS, the default method is CLS. According to the SAS manual, "Maximum likelihood estimates are more computationally expensive than conditional least squares estimates." SAS offers three options for estimation methods: CS, MLS, and ULS. Generally, which option would be preferable to use if all three methods converge and take the same computation time? Thank you.

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SAS Employee

## Re: Default estimation method for arima models

Hello @sasalex2024

I am not aware of an absolute answer to the question of which estimation method is preferred always, but you may find the following information and/or references helpful to you to decide which method you want to use:

(1). In PROC ARIMA documentation you are referencing, the following statement follows:

SAS Help Center: Estimation Details

...Maximum likelihood estimates are more expensive to compute than the conditional least squares estimates; however, they may be preferable in some cases (Ansley and Newbold 1980; Davidson 1981).

You may want to check the two references mentioned above to see the cases discussed where ML is preferable.

(2). SAS for Forecasting Time Series, third edition, by Brocklebank, Dickey, and Choi:

"Although CLS, ULS, and ML should give similar results for reasonably large data sets, studies comparing the three methods indicate that ML is the most accurate."

(3). Forecasting with Univariate Box-Jenkins Models, by Pankratz:

"Box and Jenkins (ref.) favor estimates chosen according to the maximum likelihood criterion. Mathematical statisticians frequently prefer the ML approach to estimation problems because the resulting estimates often have attractive statistical properties. ....."

"However, finding exact ML estimates of ARIMA models can be cumbersome and may require relatively large amounts of computer time. For this reason, Box and Jenkins suggest using the least-squares(LS) criterion. ....."

I hope this helps.

Wen

SAS Employee

## Re: Default estimation method for arima models

Hello @sasalex2024

I am not aware of an absolute answer to the question of which estimation method is preferred always, but you may find the following information and/or references helpful to you to decide which method you want to use:

(1). In PROC ARIMA documentation you are referencing, the following statement follows:

SAS Help Center: Estimation Details

...Maximum likelihood estimates are more expensive to compute than the conditional least squares estimates; however, they may be preferable in some cases (Ansley and Newbold 1980; Davidson 1981).

You may want to check the two references mentioned above to see the cases discussed where ML is preferable.

(2). SAS for Forecasting Time Series, third edition, by Brocklebank, Dickey, and Choi:

"Although CLS, ULS, and ML should give similar results for reasonably large data sets, studies comparing the three methods indicate that ML is the most accurate."

(3). Forecasting with Univariate Box-Jenkins Models, by Pankratz:

"Box and Jenkins (ref.) favor estimates chosen according to the maximum likelihood criterion. Mathematical statisticians frequently prefer the ML approach to estimation problems because the resulting estimates often have attractive statistical properties. ....."

"However, finding exact ML estimates of ARIMA models can be cumbersome and may require relatively large amounts of computer time. For this reason, Box and Jenkins suggest using the least-squares(LS) criterion. ....."

I hope this helps.

Wen

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