Analytic derivatives for estimation of linear dynamic models

DOI10.1016/0898-1221(89)90106-5zbMath0684.62040OpenAlexW2739643621MaRDI QIDQ1825566

Peter A. Zadrozny

Publication date: 1989

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://www2.census.gov/ces/wp/1988/CES-WP-88-05.pdf

zbMATH Keywords

algorithmsasymptotic approximationmaximum likelihood estimatesNewton methodsHessian matrixCramér-Rao boundsasymptotic covariancesdiscrete-time, linear, dynamic models in state-space formexact Gaussian log-likelihood functionexact gradient vectorexact sample, information matrixlocal identifiability of parameters

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Applications of statistics (62P99) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Probabilistic methods, stochastic differential equations (65C99)

Related Items (12)

Kalman-filtering methods for computing information matrices for time- invariant, periodic, and generally time-varying VARMA models and samples ⋮ Evaluating the information matrix in linearized DSGE models ⋮ An algorithm for the exact Fisher information matrix of vector ARMAX time series ⋮ SVD-based state and parameter estimation approach for generalized Kalman filtering with application to GARCH-in-Mean estimation ⋮ The asymptotic and exact Fisher information matrices of a vector ARMA process ⋮ Computing the Exact Fisher Information Matrix of Periodic State-Space Models ⋮ Analytic derivatives of the matrix exponential for estimation of linear continuous-time models. ⋮ An algorithm for computing the asymptotic fisher information matrix for seasonal SISO models ⋮ Computation of the exact information matrix of Gaussian dynamic regression time series models ⋮ A generalization of Whittle's formula for the information matrix of vector-mixed time series ⋮ Construction of the exact Fisher information matrix of Gaussian time series models by means of matrix differential rules ⋮ A direct derivation of the exact Fisher information matrix of Gaussian vector state space models

Cites Work

• Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions
• Iterative solution of the Lyapunov matrix equation
• FIML estimation of the dynamic simultaneous equations model with ARMA disturbances
• Algorithm AS 197: A Fast Algorithm for the Exact Likelihood of Autoregressive-Moving Average Models
• A structured state space approach to computing the likelihood of an ARIMA process and its derivatives
• Numerical aspects of different Kalman filter implementations
• Computing the likelihood and its dierivatives for a gaussian ARMA model
• EXACT MAXIMUM LIKELIHOOD ESTIMATE AND LAGRANGE MULTIPLIER TEST STATISTIC FOR ARMA MODELS
• Estimation, Prediction, and Interpolation for ARIMA Models with Missing Data
• Analytic Derivatives for Estimation of Discrete-Time, Linear-Quadratic, Dynamic, Optimization Models
• Likelihood Function of Stationary Multiple Autoregressive Moving Average Models
• Maximum Likelihood Fitting of ARMA Models to Time Series with Missing Observations
• Derivative computations for the log likelihood function
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• Exact likelihood of vector autoregressive-moving average process with missing or aggregated data
• Maximum likelihood identification of Gaussian autoregressive moving average models
• Square-root algorithms for least-squares estimation
• A note on obtaining the theoretical autocovariances of an ARMA process
• Some new algorithms for recursive estimation in constant, linear, discrete-time systems
• The Theory of Parametric Identification
• Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix Products
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