Pith Number

pith:7XJLY3U7

pith:2024:7XJLY3U7VIC6GHJZQ5LTRA5MWM

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A Distributed Lag Approach to the Generalised Dynamic Factor Model

Philipp Gersing

The dynamic common component in the GDFM equals a finite number of lags of contemporaneously pervasive factors obtained by static principal components.

arxiv:2410.20885 v3 · 2024-10-28 · econ.EM · stat.ME

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Claims

C1strongest claim

under reasonable conditions the dynamic common component can be represented in terms of a finite number of lags of contemporaneously pervasive factors. In this case the dynamic factor decomposition of the GDFM reduces to the OLS regression of observed variables on estimated factors and their lags, with factors obtained via static principal components.

C2weakest assumption

The assumption that the dynamic common component admits a finite-lag representation in terms of contemporaneously pervasive factors (the key theoretical insight that permits reduction to static PCA plus OLS).

C3one line summary

Introduces a lag-based OLS estimator for GDFM using static PCA factors, establishes consistency and asymptotic normality, and applies it to European macro data to identify sizeable weak common components.

Receipt and verification

First computed	2026-06-09T01:05:03.993867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdd2bc6e9faa05e31d3987573883acb3205a1b8c670d938068cf4d77832f7be9

Aliases

arxiv: 2410.20885 · arxiv_version: 2410.20885v3 · doi: 10.48550/arxiv.2410.20885 · pith_short_12: 7XJLY3U7VIC6 · pith_short_16: 7XJLY3U7VIC6GHJZ · pith_short_8: 7XJLY3U7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7XJLY3U7VIC6GHJZQ5LTRA5MWM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fdd2bc6e9faa05e31d3987573883acb3205a1b8c670d938068cf4d77832f7be9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78a45a614cc9bebe11517739f1f65b6189fdd225d142db5debaa1d0f9000dab6",
    "cross_cats_sorted": [
      "stat.ME"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "econ.EM",
    "submitted_at": "2024-10-28T10:07:06Z",
    "title_canon_sha256": "d997043c5b6a221c44ae3ad5274a74c3368cd6d6b3c77ca6a683ae382413a819"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.20885",
    "kind": "arxiv",
    "version": 3
  }
}