Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models

Econometrica ◽  
1993 ◽  
Vol 61 (1) ◽  
pp. 139 ◽  
Author(s):  
Donald W. K. Andrews
Keyword(s):  
Unit Root ◽  
Unbiased Estimation ◽  
First Order ◽  
Median Unbiased Estimation ◽  
Unit Root Models

scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

PATH INTEGRAL METHOD FOR LIMITING DISTRIBUTION OF AN ESTIMATOR ARISING FROM AN AR(1)-PROCESS WITH A UNIT ROOT

2013 ◽  
Vol 16 (04) ◽  
pp. 1350029
Author(s):  
SHIH-FENG HUANG ◽  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
Characteristic Function ◽  
Path Integral ◽  
Unit Root ◽  
Autoregressive Model ◽  
Integral Method ◽  
Unit Root Test ◽  
Random Variable ◽  
Limiting Distribution ◽  
First Order ◽  
Path Integral Method

We propose the path-integral technique to derive the characteristic function of the limiting distribution of the unit root test in a first order autoregressive model. Our results provide a new and useful approach to obtain the closed form of the characteristic function of a random variable associated with the limiting distribution, which is realized as a ratio of Brownian functionals on the classical Wiener space.

scholarly journals UNIFORM ASYMPTOTIC NORMALITY IN STATIONARY AND UNIT ROOT AUTOREGRESSION

2011 ◽  
Vol 27 (6) ◽  
pp. 1117-1151 ◽  
Author(s):  
Chirok Han ◽  
Peter C. B. Phillips ◽  
Donggyu Sul
Keyword(s):  
Normal Distribution ◽  
Rate Of Convergence ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Signal Strength ◽  
Rates Of Convergence ◽  
Moment Conditions ◽  
First Order ◽  
The Cost ◽  
Artificial Shrinkage

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution that holds uniformly in the autoregressive coefficient ρ, including stationary and unit root cases. The rate of convergence is $\root \of n $ when $\left| \rho \right| < 1$ and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when ρ = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator (FAE) is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases, which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. Confidence intervals constructed from the FAE using local asymptotic theory around unity also lead to improvements over the MLE.

AN INVARIANCE PRINCIPLE FOR SIEVE BOOTSTRAP IN TIME SERIES

2002 ◽  
Vol 18 (2) ◽  
pp. 469-490 ◽  
Author(s):  
Joon Y. Park
Keyword(s):  
Time Series ◽  
Invariance Principle ◽  
Unit Root ◽  
Autoregressive Process ◽  
Linear Process ◽  
Linear Processes ◽  
Testing Procedures ◽  
Sieve Bootstrap ◽  
Model Driven ◽  
Unit Root Models

This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form and holds almost surely for all sample realizations. Our development relies upon the strong approximation and the Beveridge–Nelson representation of linear processes. For illustrative purposes, we apply our results and show the asymptotic validity of the sieve bootstrap for Dickey–Fuller unit root tests for the model driven by a general linear process with independent and identically distributed innovations. We thus provide a theoretical justification on the use of the bootstrap Dickey–Fuller tests for general unit root models, in place of the testing procedures by Said and Dickey and by Phillips.

scholarly journals Optimal jackknife for unit root models

2015 ◽  
Vol 99 ◽  
pp. 135-142 ◽  
Author(s):  
Ye Chen ◽  
Jun Yu
Keyword(s):  
Unit Root ◽  
Unit Root Models
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