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We mention Borodin and Ibragimov (1995), Park and Phillips (1999), de Jong (2004), Jeganathan (2004), P\\\"{o}tscher (2004), de Jong and Whang (2005), Berkes and Horvath (2006), and Christopeit (2009) which study weak convergence results for such expressions under various conditions on $x_{t}$ and the function $f$. Of course, these result"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.3902","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-20T13:43:55Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"c00537c6aff26072b5652580c8ec04a849ca0b381feb7f7c1bf7b4c5e32c0fe3","abstract_canon_sha256":"1fef74fb90f8e6f8f1bf0623ebe8726be2a35f11aca223827afde8775f56d310"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:22.825553Z","signature_b64":"Ce6DXJppKAaggJnX6u4gkXaRdcQopQ7sFFsy5+Mup+YAJ365CEhTsAS4Vjr1YMBa52hjjqS6MbKc0/tbFIK0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ae5213743db502201241d595b322afabb480c3c99860aa56f9332a3c43d2713","last_reissued_at":"2026-05-18T02:32:22.825157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:22.825157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Order of Magnitude of Sums of Negative Powers of Integrated Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Benedikt M. P\\\"otscher","submitted_at":"2011-01-20T13:43:55Z","abstract_excerpt":"The asymptotic behavior of expressions of the form $% \\sum_{t=1}^{n}f(r_{n}x_{t})$ where $x_{t}$ is an integrated process, $r_{n}$ is a sequence of norming constants, and $f$ is a measurable function has been the subject of a number of articles in recent years. We mention Borodin and Ibragimov (1995), Park and Phillips (1999), de Jong (2004), Jeganathan (2004), P\\\"{o}tscher (2004), de Jong and Whang (2005), Berkes and Horvath (2006), and Christopeit (2009) which study weak convergence results for such expressions under various conditions on $x_{t}$ and the function $f$. 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