On the bias of the least squares estimator for the first order autoregressive process

Breton, Alain; Pham, Dinh-Tuan

doi:10.1007/bf00050668

Cited by 35 publications

(7 citation statements)

References 13 publications

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“…Using relation (A.6) of the Appendix, the expression can be simplified to Definition (2.2) was reproduced at the beginning of the expression to remind us that this is a formula for b T as well as n T -Formula (3.2) gives an infinite polynomial in l/T. The first term in the asymptotic expansion for b T (obtained by repeatedly applying (A.4) to (3.2)) was derived by Shenton and Johnson [24] and Le Breton and Pham [18] in a different context. They give…”

Section: The Approximationmentioning

confidence: 99%

Ols Bias in a Nonstationary Autoregression

Abadir

1993

Econom. Theory

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An analytical formula is derived to approximate the finite sample bias of the ordinary least-squares (OLS) estimator of the autoregressive parameter when the underlying process has a unit root. It is found that the bias is expressible in terms of parabolic cylinder functions which are easy to compute. Numerical evaluation of the formula reveals that the approximation is very accurate. The derived formula inspires a heuristic approximation, obtained by leastsquares fitting of the asymptotic bias. More importantly, the formula proves analytically that the bias declines at a rate which is slower than the consistency rate, thus explaining some previous simulation findings. A case where the bias increases with the sample size is also given.

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Section: The Approximationmentioning

confidence: 99%

Ols Bias in a Nonstationary Autoregression

Abadir

1993

Econom. Theory

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“…It is well known that the LS estimator is biased in finite samples. Its mean is to order 1/n 3 given by (White 1961; for earlier results see Bartlett 1946;Hurwicz 1950;Kendall 1954;Marriott and Pope 1954; for the unstable case see Le Breton and Pham 1989). Assuming that the bias is approximately proportional to 1/n, Quenouille (1949) proposed to reduce the bias to order 1/n 2 simply by calculating the sample correlation coefficient not only for the whole sample but also for the first and second half separately.…”

Section: Bias Correctionmentioning

confidence: 99%

Heteroscedasticity-robust estimation of autocorrelation

Reschenhofer

2018

Communications in Statistics - Simulation and Computation

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This paper proposes estimators of the first-order autocorrelation that are based on suitably transformed ratios of successive observations. The new estimators are given by simple functions of the observations. Numerical optimization is not required. Simulations show that they are highly robust against extreme values and clusters of high volatility and are therefore particularly useful for the estimation of serial correlation in return series. Besides, the results of the simulation study also call into question the common practice of correcting the small-sample bias of conventional estimators.

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“…Fellag and Zieliński (1996) studied the bias of the least-squares estimator in a contaminated Gaussian model. Breton and Pham (1989) determined the bias of the least-squares estimator under Gaussian white noise and provided asymptotic results.…”

Section: Tablementioning

confidence: 99%

Inference About the First-Order Autoregressive Coefficient

Provost¹,

Sanjel²

2005

Communications in Statistics - Theory and Methods

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Several estimators of the coefficient of an AR(1) process can be expressed as the ratio of two quadratic forms. In this article, we are considering the ordinary leastsquares, a modified least-squares, the Yule-Walker, and Burg's estimators. It will be shown that the modified least-squares estimator is the least biased and that the ordinary least-squares and Burg's estimators share very similar distributional properties. An integral representation of the moments of these estimators is provided and a methodology is proposed for correcting their bias. Bounds for the supports of the Yule-Walker and Burg's estimators are determined and the density functions of those estimators are then approximated in terms of Jacobi polynomials. Finally, confidence intervals for the autoregressive coefficient are determined from replicated series.

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On the bias of the least squares estimator for the first order autoregressive process

Abstract: Autoregressive process, asymptotic bias, explosive, least squares estimator, stable, unstable,

Cited by 35 publications

References 13 publications

Ols Bias in a Nonstationary Autoregression

Ols Bias in a Nonstationary Autoregression

Heteroscedasticity-robust estimation of autocorrelation

Inference About the First-Order Autoregressive Coefficient

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