Sequential estimation of the autoregressive parameter in a first order autoregressive process

DOI10.1080/07474948808836142zbMath0669.62074OpenAlexW1586633499MaRDI QIDQ3823021

T. N. Sriram

Publication date: 1988

Published in: Sequential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07474948808836142

zbMATH Keywords

asymptotic normalitysecond order approximationstopping timeuniform integrabilitystopping ruleleast squares estimatorbest predictorfinite second momentnonlinear renewal theoryreverse martingaleBurkholder inequalityasymptotically risk efficientmean squared error losscost of estimation errorfirst order, non-explosive autoregressive model

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Sequential estimation (62L12)

Related Items (30)

Sequential point estimation of parameters in a threshold AR(1) model ⋮ Sequential point estimation for branching processes i, subcritical case ⋮ Sequential estimation for time series regression models ⋮ On uniform asymptotic normality of sequential least squares estimators for the parameters in a stable AR(\(p\)) ⋮ \(L_ p\) convergence of reciprocals of sample means with applications to sequential estimation in linear regression ⋮ On asymptotic normality of sequential LS-estimate for unstable autoregressive process \(AR(2)\) ⋮ Sequential estimation of the mean of a first-order autoregressive process ⋮ Sequential estimation for the parameters of a stationary auto regressive model ⋮ Estimators with prescribed Precision in Stochastic regression models ⋮ Sequential estimation for dependent oberservations with an application to non-standard autoregressive processes ⋮ Unnamed Item ⋮ Sequential estimation of ratio of normal parameters ⋮ Risk-efficient sequential estimation of multivariate random coefficient autoregressive process ⋮ Unnamed Item ⋮ Sequential estimation of the autoregressive parameters in ar(p) model ⋮ Sequential Generlized Least squares Estimator For An Autoressive parameter ⋮ On Sequential Least Squares Estimates of Autoregressive Parameters ⋮ Risk efficient estimation of fully dependent random coefficient autoregressive models of general order ⋮ Editor's Special Invited Paper: Sequential Estimation for Time Series Models ⋮ Fixed size confidence regions for parameters of threshold AR(1) models ⋮ Approximations to expected stopping times with applications to sequential estimation ⋮ Second-order analysis of regret for sequential estimation of the autoregressive parameter in a first-order autoregressive model ⋮ On Uniform Asymptotic Normality of Sequential Estimators for the Parameters in a Stable AR(1) ⋮ Fixed precision estimator of the offspring mean in branching processes ⋮ The sequential estimation in stochastic regression model with random coefficients ⋮ Optimal index estimation of heavy-tailed distributions ⋮ On sequential estimation of parameters in semimartingale regression models with continuous time parameter. ⋮ On Optimal Adaptive Prediction of Multivariate Autoregression ⋮ Guaranteed parameter estimation in a first order autoregressive progress with infinite variance ⋮ Two-stage procedure in a first-order autoregressive process and comparison with a purely sequential procedure

Cites Work

• Unnamed Item
• Unnamed Item
• Sequential determination of estimator as well as sample size
• Fixed accuracy estimation of an autoregressive parameter
• Second order approximation to the risk of a sequential procedure
• Sequential estimation of the mean of a first-order stationary autoregressive process
• The performance of a sequential procedure for the estimation of the mean
• On the expansion for expected sample size in nonlinear renewal theory
• Bounded regret of a sequential procedure for estimation of the mean
• A nonlinear renewal theory with applications to sequential analysis. I
• A nonlinear renewal theory with applications to sequential analysis II
• On Asymptotic Distributions of Estimates of Parameters of Stochastic Difference Equations
• A Frequentistic Approach to Sequential Estimation in the General Linear Model
• Sequential point estimation of the mean when the distribution is unspecified
• On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean

This page was built for publication: Sequential estimation of the autoregressive parameter in a first order autoregressive process