A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case Without an Intercept

Econometrica ◽  
1991 ◽  
Vol 59 (1) ◽  
pp. 211 ◽  
Author(s):  
Pierre Perron
Keyword(s):  
Continuous Time ◽  
Autoregressive Process ◽  
Time Approximation ◽  
First Order

A Continuous Time Approximation to the Stationary First-Order Autoregressive Model

1991 ◽  
Vol 7 (2) ◽  
pp. 236-252 ◽  
Author(s):  
Pierre Perron
Keyword(s):  
Asymptotic Distribution ◽  
Continuous Time ◽  
Autoregressive Model ◽  
Sampling Interval ◽  
Finite Sample ◽  
Sample Distribution ◽  
Time Approximation ◽  
First Order ◽  
Percentage Points ◽  
Autoregressive Parameter

We consider the least-squares estimator in a strictly stationary first-order autoregression without an estimated intercept. We study its continuous time asymptotic distribution based on an asymptotic framework where the sampling interval converges to zero as the sample size increases. We derive a momentgenerating function which permits the calculation of percentage points and moments of this asymptotic distribution and assess the adequacy of the approximation to the finite sample distribution. In general, the approximation is excellent for values of the autoregressive parameter near one. We also consider the behavior of the power function of tests based on the normalized leastsquares estimator. Interesting nonmonotonic properties are uncovered. This analysis extends the study of Perron [15] and helps to provide explanations for the finite sample results established by Nankervis and Savin [13].

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.

An Exact Discrete Analog to a Closed Linear First-Order Continuous-Time System with Mixed Sample

1987 ◽  
Vol 3 (1) ◽  
pp. 143-149 ◽  
Author(s):  
Terence D. Agbeyegbe
Keyword(s):  
Continuous Time ◽  
Discrete Model ◽  
Moving Average ◽  
Discrete Analog ◽  
Time System ◽  
First Order ◽  
Exact Discrete Model ◽  
Asymptotically Efficient ◽  
Order Continuous ◽  
Continuous Time System

This article deals with the derivation of the exact discrete model that corresponds to a closed linear first-order continuous-time system with mixed stock and flow data. This exact discrete model is (under appropriate additional conditions) a stationary autoregressive moving average time series model and may allow one to obtain asymptotically efficient estimators of the parameters describing the continuous-time system.

scholarly journals Robust Trend Estimation for AR(1) Disturbances

2016 ◽  
Vol 34 (2) ◽  
Author(s):  
Roland Fried ◽  
Ursula Gather
Keyword(s):  
Robust Estimation ◽  
Linear Trend ◽  
Autoregressive Process ◽  
Trend Estimation ◽  
First Order ◽  
Repeated Median

We discuss the robust estimation of a linear trend if the noise follows an autoregressive process of first order. We find the ordinary repeated median to perform well except for negative correlations. In this case it can be improved by a Prais-Winsten transformation using a robust autocorrelation estimator.

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