Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors

DOI10.1214/aos/1030563979zbMath0932.62103OpenAlexW1988552646MaRDI QIDQ1807062

Shiqing Ling, Wai Keung Li

Publication date: 9 November 1999

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1030563979

zbMATH Keywords

maximum likelihood estimatorunstable ARMA modelslimiting distributionstochastic integralGARCH modelsbivariate Brownian motion

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Asymptotic distribution theory in statistics (62E20) Functional limit theorems; invariance principles (60F17)

Related Items (44)

On the choice of test for a unit root when the errors are conditionally heteroskedastic ⋮ Regression quantiles for unstable autoregressive models ⋮ Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticity ⋮ Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root ⋮ Delay times of sequential procedures for multiple time series regression models ⋮ Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence ⋮ Nearly nonstationary processes under infinite variance GARCH noises ⋮ ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL ⋮ ASYMPTOTIC INFERENCE FOR UNIT ROOT PROCESSES WITH GARCH(1,1) ERRORS ⋮ On a Partially Non-Stationary Vector AR Model with Vector GARCH Noises: Estimation and Testing ⋮ Rank test of unit‐root hypothesis with AR‐GARCH errors ⋮ Marked empirical processes for non-stationary time series ⋮ On adaptive estimation in nonstationary ARMA models with GARCH errors ⋮ Testing for a unit root under errors with just barely infinite variance ⋮ Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors ⋮ A note on testing for nonstationarity in autoregressive processes with level dependent conditional heteroskedasticity ⋮ Test for parameter change in ARMA models with GARCH innovations ⋮ Wavelet Improvement of the Over-Rejection of Unit Root Test Under GARCH Errors: An Application to Swedish Immigration Data ⋮ Residual empirical processes for long and short memory time series ⋮ LEAST ABSOLUTE DEVIATION ESTIMATION FOR UNIT ROOT PROCESSES WITH GARCH ERRORS ⋮ The asymptotic convexity of the negative likelihood function of GARCH models ⋮ Estimation and Testing Stationarity for Double-Autoregressive Models ⋮ A note on unit root tests with heavy-tailed GARCH errors ⋮ On regression-based tests for seasonal unit roots in the presence of periodic heteroscedasticity ⋮ Statistical Adequacy and the Testing of Trend Versus Difference Stationarity ⋮ Testing for reduction to random walk in autoregressive conditional heteroskedasticity models ⋮ A Note on Unit Root Tests and GARCH Errors: A Simulation Experiment ⋮ A frequentist approach to Bayesian asymptotics ⋮ Residual empirical processes for nearly unstable long-memory time series ⋮ A note on the self-normalized Dickey-Fuller test for unit roots in autoregressive time series with GARCH errors ⋮ ASYMPTOTICS OF THE QMLE FOR A CLASS OF ARCH(q) MODELS ⋮ UNIT ROOT TESTING IN THE PRESENCE OF HEAVY-TAILED GARCH ERRORS ⋮ NEAR-INTEGRATED RANDOM COEFFICIENT AUTOREGRESSIVE TIME SERIES ⋮ Estimation and Asymptotic Inference in the AR-ARCH Model ⋮ Bootstrap-based unit root tests for higher order autoregressive models with GARCH(1, 1) errors ⋮ PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS ⋮ EMPIRICAL LIKELIHOOD FOR GARCH MODELS ⋮ Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density ⋮ A PRIMER ON BOOTSTRAP TESTING OF HYPOTHESES IN TIME SERIES MODELS: WITH AN APPLICATION TO DOUBLE AUTOREGRESSIVE MODELS ⋮ A computationally convenient unit root test with covariates, conditional heteroskedasticity and efficient detrending ⋮ Asymptotic laws of successive least squares estimates for seasonal arima models and application ⋮ Asymptotic theory for multivariate GARCH processes. ⋮ Semi-nonparametric cointegration testing ⋮ Joint modeling of cointegration and conditional heteroscedasticity with applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Highly symmetric expanders
• Asymptotic properties of multivariate nonstationary processes with applications to autoregressions
• Asymptotic inference for nearly nonstationary AR(1) processes
• Limiting distributions of least squares estimates of unstable autoregressive processes
• Fractionally integrated generalized autoregressive conditional heteroskedasticity
• Estimation for autoregressive processes with unit roots
• Weak limit theorems for stochastic integrals and stochastic differential equations
• Testing for unit roots in autoregressive moving average models. An instrumental variable approach
• ARCH modeling in finance. A review of the theory and empirical evidence
• Distribution of the Estimators for Autoregressive Time Series With a Unit Root
• Maximum-Likelihood Estimation of Parameters Subject to Restraints
• Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models
• Multiple Time Series Regression with Integrated Processes
• Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
• Time Series Regression with a Unit Root
• Estimation and Testing for Unit Roots in a Partially Nonstationary Vector Autoregressive Moving Average Model
• RESULTS ON ESTIMATION AND TESTING FOR A UNIT ROOT IN THE NONSTATIONARY AUTOREGRESSIVE MOVING-AVERAGE MODEL
• Testing for Unit Roots in Seasonal Time Series
• ON THE PARTIAL SUMS OF RESIDUALS IN AUTOREGRESSIVE AND MOVING AVERAGE MODELS

This page was built for publication: Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors