2019/04/15 by Mika Meitz, Meitz, Mika, Pentti Saikkonen +1
Economics, Econometrics and Finance · Mathematics · #Autoregressive model #Classical mechanics #Econometrics (econ.EM) #Ergodic theory #Ergodicity #FOS: Economics and business #FOS: Mathematics #Invariant measure #Markov Chains and Monte Carlo Methods #Markov chain #Mathematical analysis #Mathematics #Mixing (physics) #Moment (physics) #Physics #Point processes and geometric inequalities #Probability (math.PR) #Quantum mechanics #Stationary ergodic process #Statistical physics #Statistics #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #econ.EM #math.PR #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1904.07103
v2 updated reference to Meitz and Saikkonen (2019)
openalex publication_date 2019/04/15 · arxiv created 2019/04/16 · arxiv updated 2019/04/17 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
It is well known that stationary geometrically ergodic Markov chains are β-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies β-mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies β-mixing with subgeometrically decaying mixing coefficients. Although this result is simple it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity can not be established. To illustrate our results we derive new subgeometric ergodicity and β-mixing results for the self-exciting threshold autoregressive model.