Timeline for Non-Correlated errors from Generalized Least Square model (GLS)
Current License: CC BY-SA 3.0
10 events
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| Apr 14, 2014 at 18:41 | comment | added | B_Miner | Here is what I was wondering - what is the difference between the two models gls and arima? Although they provide the same coefficients, log lik etc. if you observe the acf() of the residuals of each, only the arima model residuals have been "corrected". | |
| Apr 14, 2014 at 18:06 | comment | added | jbowman | @B_Miner - yes, you are correct, GLS estimates the model and the covariance structure of the residuals, and the residuals from the model will not be homoskedastic. If you have a general arima model, the gls estimates will be of the covariance matrix, not of the arima parameters. As for model specification and white noise residuals - that applies to situations where the covariance matrix of the disturbances ("true residuals") is $\sigma^2 I$. If you've misspecified the model, the odds are pretty good that the residuals won't have that covariance matrix. | |
| Apr 14, 2014 at 2:04 | comment | added | B_Miner | jBowman, may I asked two follow-ups to this rather old question (I was just logging in to ask the same as this OP)? 1) I assume the same holds for heteroskedasticity - i.e. the residuals from GLS still wont look homoscedastic? 2) Is the situation different for regression with arima errors (your arima example)? I have always read that to see if you have the model specified properly, the residuals should be white noise? | |
| Jul 22, 2012 at 16:12 | comment | added | jbowman |
I've appended some prediction example stuff to the response, but the short version is yes, for time series data predict.arima() will give you better prediction than predict.gls().
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| Jul 22, 2012 at 16:11 | history | edited | jbowman | CC BY-SA 3.0 |
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| Jul 22, 2012 at 15:30 | comment | added | Anand | Bowman, thank you sir for such a concise and clear explanation. So, in short using residuals structure at the end of data series instead of Covariance matrix will be a better approach in prediction. What that means is predict.arima() will give you better prediction than predict.gls() correct? | |
| Jul 21, 2012 at 17:19 | history | edited | jbowman | CC BY-SA 3.0 |
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| Jul 21, 2012 at 16:57 | comment | added | Michael R. Chernick | Also the ARMA modeling approach fit the correlation structure in the residuals rather than specifying it in the covariance matrix. | |
| Jul 21, 2012 at 16:50 | comment | added | Michael R. Chernick | Applying an arma structure to the residuals would I think be a little different from the result the gls gives regarding the regression parameters. | |
| Jul 21, 2012 at 15:22 | history | answered | jbowman | CC BY-SA 3.0 |