Timeline for non-normal residuals in ARIMA
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Sep 27, 2015 at 15:03 | answer | added | kjetil b halvorsen♦ | timeline score: 2 | |
| Sep 27, 2015 at 13:02 | answer | added | IrishStat | timeline score: 1 | |
| Mar 25, 2015 at 16:49 | comment | added | Richard Hardy | I got a short comment by Rob J. Hyndman where he says MLE with a Gaussian likelihood is asymptotically equivalent to least squares estimation. Minimizing the sum of squared errors should work ok for almost all distributions here. So perhaps you were right all along. | |
| Mar 25, 2015 at 16:49 | comment | added | Richard Hardy | Actually, I was referring to stationary ARMA as well (the integratedness was not my concern, although perhaps it should have been?). Would you say (or at least guess) that MLE should work fine as a quasi-MLE when applied on a stationary ARMA? | |
| Mar 25, 2015 at 9:43 | comment | added | Christoph Hanck | You are right about arIma, and indeed Fuller's theorem is about stationary time series. At least, White's (1982 Ecma) paper does not cover this case directly, but then, his are not necessary conditions. In short, I do not know. My hunch would be that it should also work, given that coefficients are typically estimated superconsistently in nonstationary time series models, but that really is just a guess. | |
| Mar 25, 2015 at 9:39 | comment | added | Richard Hardy | I understand that. My main worry is whether quasi-MLE works for ARIMA. As you just noted, MLEs are often also quasi-MLEs, so I wonder if ARIMA belongs to the case where the normal MLE is a quasi-MLE. Would only the true erorr distribution matter when answering this question (I suspect a skewed error distribution would be a killer), or does it also depend on the model (like ARIMA, multiple linear regression etc)? | |
| Mar 25, 2015 at 9:29 | comment | added | Christoph Hanck | @RichardHardy, I'd first say it sure is true that asymptotics are often better guide in finite samples when errors are normal than if they come from, say, some weird skewed distribution. Second, I meant to refer to that MLEs are often also quasi-MLEs in that they often consistently estimate parameters of interest (with also a large-sample normal approximation) even if the likelihood is misspecified in that a wrong error distribution is chosen. A reference would be Fuller (1996), Theorem 8.4.1 (p. 432). | |
| Mar 25, 2015 at 1:08 | history | tweeted | twitter.com/#!/StackStats/status/580536747089666050 | ||
| Mar 24, 2015 at 17:18 | comment | added | Richard Hardy | @ChristophHanck, your statements about asymptotics make sense in a linear regression setting. However, ARIMA models may be more sensitive to non-normality since the normality assumption is used in the maximum likelihood estimation (but not in OLS) and the ARIMA likelihood is quite complicated. Could you give an explanation or a reference supporting your opinion? I share the doubts of m3d1v0... | |
| Mar 24, 2015 at 17:16 | comment | added | Richard Hardy | I found two conflicting opinions here on Cross Validated: Aksakal says that MLE is not reliable if the normality assumption is violated. Rob J. Hyndman says that non-normality is not that big of a problem. I am sure Rob J. Hyndman is very experienced and authoritative, I just wonder what the explanation for his observation is. | |
| Mar 24, 2015 at 14:15 | comment | added | Christoph Hanck | Under very strict conditions, normality of the errors is important to get that t-statistics are indeed t-distributed. These are not met here anyhow, so that you need to rely on asymptotics to get a distribution for your t-statistics. Now, if you rely on asymptotics, normality of the errors is not (that) important anymore. | |
| Mar 24, 2015 at 13:49 | comment | added | m3div0 | I have read in some works, that the normality of the residuals is imortant so that the t-statistics of the AR and MA terms are valid. As I understood, if the residuals wont be normally distributed I may mistakenly exclude some significant term or include some insignificant one. But I am not sure and therefore I came here to ask :) | |
| Mar 24, 2015 at 13:41 | comment | added | Christoph Hanck | Why do you expect that errors should be normally distributed, whether or not the other checks you mention look good? There is no particular reason they should be. | |
| Mar 24, 2015 at 6:42 | answer | added | ccsv | timeline score: 1 | |
| S Mar 24, 2015 at 6:40 | history | edited | Glen_b | CC BY-SA 3.0 |
corrected spellings & added tags
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| S Mar 24, 2015 at 6:40 | history | suggested | Learner | CC BY-SA 3.0 |
corrected spellings & added tags
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| Mar 24, 2015 at 5:21 | review | Suggested edits | |||
| S Mar 24, 2015 at 6:40 | |||||
| Mar 23, 2015 at 21:04 | history | asked | m3div0 | CC BY-SA 3.0 |