{"paper":{"title":"Stability and the Lyapounov exponent of threshold AR-ARCH Models","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daren B. H. Cline, Huay-min H. Pu","submitted_at":"2005-03-24T14:53:52Z","abstract_excerpt":"The Lyapounov exponent and sharp conditions for geometric ergodicity are determined of a time series model with both a threshold autoregression term and threshold autoregressive conditional heteroscedastic (ARCH) errors.\n The conditions require studying or simulating the behavior of a bounded, ergodic Markov chain. The method of proof is based on a new approach, called the piggyback method, that exploits the relationship between the time series and the bounded chain. The piggyback method also provides a means for evaluating the Lyapounov exponent by simulation and provides a new perspective on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503547","kind":"arxiv","version":1},"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"}