non normal residuals in VAR

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raj
Posts: 2
Joined: Mon Mar 02, 2009 2:12 pm

non normal residuals in VAR

Postby raj » Mon Mar 02, 2009 2:39 pm

Hi,

I have formed a VAR equation consisting of 16 variables going upto lag 1.

1. All the roots of the characteristic polynomial are within unit circle => VAR specification is stationary. GOOD
2. Its residuals are extremely non-normal with p-values 0.0000 when looking at the Jarque Bera statistic after View -> Residual Test -> Normality test .. POOR
3. It shows autocorrelation on applying Portmanteau Autocorrelation Test and Autocorrelation LM Test again with p value close to 0.0000 ... POOR

I tried playing with different variables and changed their lags. However non-normality and autocorrelation persists. I think autocorrelation is not a big problem as it just means there is some missing variable and VAR is not specified perfectly. Given this shortcoming, still its possible to use this VAR specification for forecasting purposes. I think bigger problem is non-normality of residuals and I don't know how it affects the VAR specification and what can be done to mitigate the non-normality effect.

Does anyone has some experience in dealing with such issues and give me some direction.

Thanks,
Raj

startz
Non-normality and collinearity are NOT problems!
Posts: 3775
Joined: Wed Sep 17, 2008 2:25 pm

Re: non normal residuals in VAR

Postby startz » Mon Mar 02, 2009 3:58 pm

raj wrote:Hi,

I have formed a VAR equation consisting of 16 variables going upto lag 1.

1. All the roots of the characteristic polynomial are within unit circle => VAR specification is stationary. GOOD
2. Its residuals are extremely non-normal with p-values 0.0000 when looking at the Jarque Bera statistic after View -> Residual Test -> Normality test .. POOR
3. It shows autocorrelation on applying Portmanteau Autocorrelation Test and Autocorrelation LM Test again with p value close to 0.0000 ... POOR

I tried playing with different variables and changed their lags. However non-normality and autocorrelation persists. I think autocorrelation is not a big problem as it just means there is some missing variable and VAR is not specified perfectly. Given this shortcoming, still its possible to use this VAR specification for forecasting purposes. I think bigger problem is non-normality of residuals and I don't know how it affects the VAR specification and what can be done to mitigate the non-normality effect.

Does anyone has some experience in dealing with such issues and give me some direction.

Thanks,
Raj

A VAR is just a bunch of least squares regressions. Non-normality is not very important. And if you have a large sample you can get a highly significant Jarque Bera statistic even though the residuals are not very far from normality.

The autocorrelation may be more of a problem for good forecasts. Perhaps you should allow a second lag.

raj
Posts: 2
Joined: Mon Mar 02, 2009 2:12 pm

Re: non normal residuals in VAR

Postby raj » Mon Mar 02, 2009 4:46 pm

Hi Startz,

Your point of J-B statistic being highly significant makes sense (my sample is like 1500 data points).

For autocorrelation, I find p values of 0.0000 for autocorrelation up to lags 8. So incorporating 2nd lag will not really remove autocorrelation. Can you suggest something

Thanks
Raj

startz
Non-normality and collinearity are NOT problems!
Posts: 3775
Joined: Wed Sep 17, 2008 2:25 pm

Re: non normal residuals in VAR

Postby startz » Mon Mar 02, 2009 5:01 pm

raj wrote:Hi Startz,

Your point of J-B statistic being highly significant makes sense (my sample is like 1500 data points).

For autocorrelation, I find p values of 0.0000 for autocorrelation up to lags 8. So incorporating 2nd lag will not really remove autocorrelation. Can you suggest something

Thanks
Raj

Try a second lag and see what happens. If it doesn't do it, add more lags. No guarantee, but it might work

QSnakecharmer
Posts: 13
Joined: Mon Mar 30, 2009 11:57 am

Re: non normal residuals in VAR

Postby QSnakecharmer » Mon Mar 30, 2009 12:53 pm

First try lag-length and order selection criteria to establish the lag-length order of the VAR model. The problem could be that you’re using too few lags (1) to capture the relationship between your variabless so there’s information left in the residuals (that’s what autocorrelation and non-normality is reflecting, remember that no-auto correlated residuals with Gaussian –normal- distribution are “pure” noise with no usable information).

From the affirmation that you’re using 1500 data points, I could infer that you’re using high frequency data? Like daily? If this is the case, then the origins of your problem is the high frequency of your data. You will need a lot of lags to erase the non-normality and the autocorrelation of high-frequency data, and eventually this would lead to another problem: multicollinearity (and even a singular matrix). The solution for this previous problem is fairly simple: make a low-to-high frequency conversion of your data, and try estimating the VAR with the converted data.


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