{"paper":{"title":"Long and Short Memory in Economics: Fractional-Order Difference and Differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.MF","q-fin.ST"],"primary_cat":"q-fin.EC","authors_text":"Valentina V. Tarasova, Vasily E. Tarasov","submitted_at":"2016-12-23T08:37:05Z","abstract_excerpt":"Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov fractional differences of non-integer order d. Equations of ARIMA(p,d,q) and ARFIMA(p,d,q) models are the fractional-order difference equations with the Grunwald-Letnikov differences of order d. We prove that the long and short memory with power law should be described by the exact fractional-order differences, for which the Fourier transform demonstrates the po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07903","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}