{
  "annotation_id": "cd708c85-e254-46ae-ad32-74d651cd2f08",
  "date_created": "2026-02-17T05:53:23.545000Z",
  "date_modified": "2026-02-17T05:53:23.545000Z",
  "file_hash": "5aece2a50e843460b83fee4f1b102b54f079a6a1e8efaa38ee2d01f893643e9d",
  "private": false,
  "record": {
    "abstract": "The ability to assess ex-ante whether a time series is likely to be accurately forecast is important for forecasting practice because it informs the degree of modelling effort warranted. We define forecastability as a property of a time series (given a declared information set), and measure horizon-specific forecastability as the reduction in uncertainty provided by the past, using auto-mutual information (AMI) at lag h. AMI is estimated from training data using a k-nearest-neighbour estimator and evaluated against out-of-sample forecast error (sMAPE) on a filtered, balanced sample of 1,350 M4 series across six sampling frequencies. Seasonal Naive, ETS, and N-BEATS are used as probes of out-of-sample forecast performance. Training-only AMI provides a frequency-conditional diagnostic for forecast difficulty: for Hourly, Weekly, Quarterly, and Yearly series, AMI exhibits consistently negative rank correlation with sMAPE across probes. Under N-BEATS, the correlation is strongest for Hourly (p= -0.52) and Weekly (p= -0.51), with Quarterly (p= -0.42) and Yearly (p = -0.36) also substantial. Monthly is probe-dependent (Seasonal Naive p= -0.12; ETS p = -0.26; N-BEATS p = -0.24). Daily shows notably weaker AMI-sMAPE correlation under this protocol, suggesting limited ability to discriminate between series despite the presence of temporal dependence. The findings support within-frequency triage and effort allocation based on measurable signal content prior to forecasting, rather than between-frequency comparisons of difficulty.",
    "arxiv_id": "2601.10006",
    "authors": [
      "Peter Maurice Catt"
    ],
    "categories": [
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The Knowable Future: Mapping the Decay of Past-Future Mutual Information Across Forecast Horizons",
    "url": "https://arxiv.org/abs/2601.10006",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e2cf928b-4b59-44a4-91f6-0910009afa7f",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}