dorsal/arxiv
View SchemaDeriving the sampling errors of correlograms for general white noise
| Authors | T. D. Carozzi, A. M. Buckley |
|---|---|
| Categories | |
| ArXiv ID | physics/0505145 |
| URL | https://arxiv.org/abs/physics/0505145 |
Abstract
We derive the second-order sampling properties of certain autocovariance and autocorrelation estimators for sequences of independent and identically distributed samples. Specifically, the estimators we consider are the classic lag windowed correlogram, the correlogram with subtracted sample mean, and the fixed-length summation correlogram. For each correlogram we derive explicit formulas for the bias, covariance, mean square error and consistency for generalised higher-order white noise sequences. In particular, this class of sequences may have non-zero means, be complexed valued and also includes non-analytical noise signals. We find that these commonly used correlograms exhibit lag dependent covariance despite the fact that these processes are white and hence by definition do not depend on lag.
{
"annotation_id": "29b4bd33-422d-4c4d-ad95-fce2e55b52fc",
"date_created": "2026-03-02T18:00:57.282000Z",
"date_modified": "2026-03-02T18:00:57.282000Z",
"file_hash": "b85251a5c8abb4f415ae7b2be1808454936939a62ae53c556b5cdb807cdebcf0",
"private": false,
"record": {
"abstract": "We derive the second-order sampling properties of certain autocovariance and\nautocorrelation estimators for sequences of independent and identically\ndistributed samples. Specifically, the estimators we consider are the classic\nlag windowed correlogram, the correlogram with subtracted sample mean, and the\nfixed-length summation correlogram. For each correlogram we derive explicit\nformulas for the bias, covariance, mean square error and consistency for\ngeneralised higher-order white noise sequences. In particular, this class of\nsequences may have non-zero means, be complexed valued and also includes\nnon-analytical noise signals. We find that these commonly used correlograms\nexhibit lag dependent covariance despite the fact that these processes are\nwhite and hence by definition do not depend on lag.",
"arxiv_id": "physics/0505145",
"authors": [
"T. D. Carozzi",
"A. M. Buckley"
],
"categories": [
"physics.data-an"
],
"title": "Deriving the sampling errors of correlograms for general white noise",
"url": "https://arxiv.org/abs/physics/0505145"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a70d21f7-bc32-4207-9193-69ad7b2061a0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}