I have been reading some posts about the Ljung-Box test and I am applying it to some of my databases. However, I am not really understanding the outputs, I think I am doing something wrong. I have a time series data every 5 minutes and I want to check if it is White Noise. The data has 800 rows and it is the following (mostly all 1):
[1 1 1 1 1 1 1 1 1 1 1 1 1 5 4 4 1 1 1 1 1 1 1 2
1 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 4 1 3 1 1 1 1 1 2 1 1 1 1 1 1 1 2 3 2 1 1 2
1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 2 1 3 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 11 7 1 1 1 1 1...1]
I am also plotting the ACF of statsmodels with 40 lags. The outputs of the function acf are:
[ 1. 0.40168385 0.17665485 -0.00746597 0.00272706 -0.02031781
0.00265903 0.01285206 0.01281804 0.00511375 0.066442 0.0459539
0.07660102 -0.02058992 -0.01688757 -0.00580984 0.00271113 -0.0024364
-0.00247042 -0.00506119 -0.02043578 -0.00768598 0.01784761 0.05872178
0.04875562 0.08707303 0.01299028 0.06153473 -0.0100886 -0.01523614
-0.02038367 -0.0127474 -0.01278142 0.00763866 0.0101614 0.06381938
0.06634212 0.08420544 0.01258211 0.01510486 0.00740056]
thus I can see that they are very close to 0 starting from lag 3, what gives me the idea of it being white noise. However, when I run the Ljung-Box test of statsmodels, it returns me the following data:
lb_stat lb_pvalue bp_stat bp_pvalue
1 144.570070 2.666584e-33 144.085478 3.403318e-33
2 172.562972 3.376189e-38 171.953272 4.579536e-38
3 172.613028 3.471591e-37 172.003048 4.701366e-37
4 172.619714 2.865290e-36 172.009689 3.873593e-36
5 172.991262 1.677989e-35 172.378331 2.267774e-35
6 172.997633 1.040093e-34 172.384645 1.403245e-34
7 173.146633 5.446860e-34 172.532147 7.341165e-34
8 173.295013 2.628478e-33 172.678869 3.539256e-33
9 173.318656 1.255253e-32 172.702221 1.687471e-32
10 177.314414 8.455177e-33 176.644405 1.164428e-32
... ... ... ...
31 202.825613 3.860873e-27 201.502716 6.810909e-27
32 202.977258 9.384704e-27 201.648600 1.654383e-26
33 203.031484 2.341230e-26 201.700706 4.117698e-26
34 203.127555 5.651189e-26 201.792912 9.923617e-26
35 206.921511 2.839503e-26 205.430023 5.319358e-26
36 211.026126 1.249621e-26 209.360364 2.515537e-26
37 217.646477 1.909240e-27 215.692230 4.339157e-27
38 217.794461 4.405961e-27 215.833601 9.997658e-27
39 218.007986 9.768113e-27 216.037345 2.215969e-26
40 218.059303 2.287945e-26 216.086253 5.172516e-26
Since the pvalues are so low, I reject the null hypothesis, what gives the result of it not being white noise while the ACF plot was indicating the opposite. Am I interpreting it correctly?
Thank you very much!!