Formal statistical test for whether a process is a white noise

Question

Is there a formal statistical test to test if process is a white noise?

1

against what alternative ? – user603 Feb 11 '11 at 15:03

score 14 · Accepted Answer · edited Apr 13 '17 at 12:44

14

In time-series analysis usually Ljung-Box test is used. Note though that it tests the correlations. If the correlations are zero, but variance varies, then the process is not white noise, but Ljung-Box test will fail to reject the null-hypothesis. Here is an example in R:

> Box.test(c(rnorm(100,0,1),rnorm(100,0,10)),type="Ljung-Box")

    Box-Ljung test

data:  c(rnorm(100, 0, 1), rnorm(100, 0, 10)) 
X-squared = 0.4771, df = 1, p-value = 0.4898

Here is the plot of the process: enter image description here

Here is more discussion about this test.

edited Apr 13 '17 at 12:44

Community

1

answered Feb 11 '11 at 07:47

mpiktas

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Ouliers in the error series will "deflate the ACF" thus yielding an ALICE IN WINDERKlAND effect. All ACF's are subject to this thus one must ensure no anomalies – IrishStat Mar 21 '11 at 23:44

score 0 · Answer 2 · edited Dec 02 '18 at 08:21

The R library hwwntest (Haar Wavelet White Noise test) seems to work pretty well. It offers a number of functions. It does require the amount of data to be a power of 2.

hywavwn.test() seems to work the best for me.

> hywavwn.test(rnorm(128, 0, 1))

    Hybrid Wavelet Test of White Noise

data:  
p-value = 0.542

> hywavwn.test(rnorm(128, 0, 10))

    Hybrid Wavelet Test of White Noise

data:  
p-value = 1

Formal statistical test for whether a process is a white noise

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