Gaussian autoregressive process with dependent innovations. Some\n asymptotic results

2017/04/11 by Fabio Gobbi, Gobbi, Fabio, Sabrina Mulinacci +1
Economics, Econometrics and Finance · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1704.03262

openalex publication_date 2017/04/11 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a modified version of a gaussian standard\nfirst-order autoregressive process where we allow for a dependence structure\nbetween the state variable Y_t-1 and the next innovation \ξ_t. We call\nthis model dependent innovations gaussian AR(1) process (DIG-AR(1)). We analyze\nthe moment and temporal dependence properties of the new model. After proving\nthat the OLS estimator does not consistently estimate the autoregressive\nparameter, we introduce an infeasible estimator and we provide its\n\√(T)-asymptotic normality.\n

Citations

• Some Limit Theorems for Random Functions. II

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