A class of partially adaptive one-step m-estimators for the non-linear regression model with dependent observations

Pötscher, Benedikt M.; Prucha, Ingmar R.

doi:10.1016/0304-4076(86)90039-4

Cited by 37 publications

(7 citation statements)

References 38 publications

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“…On the other hand, partially adaptive estimation is a more practical goal because it avoids the dif culty of nonparametric estimation of score functions. (also see similar arguments in Potscher and Prucha (1986), Hogg and Lenth (1984), McDonald and Newey (1988), and Phillips (1994)). …”

Section: Introductionsupporting

confidence: 58%

“…The student-t distribution is an important class of distributions (see more discussion in, say, Hall and Joiner 1982) that contains the Cauchy distribution as a special case and the normal distribution as a limit case, and has wide applications in economic analysis. Its adaptation parameter depends on the scale and thickness parameters, which can be easily estimated from the data using the approach proposed by Potscher and Prucha (1986). Partially adaptive estimator based on this class of distribution is reasonably robust.…”

Section: A Unit Root Test Based On Partially Adaptive Estimationmentioning

confidence: 98%

“…The family of student-t represents an important dimension of the space of distributions, including the normal distribution as a limiting case and the Cauchy distribution as a special case. Its adaptation parameter will depend on the scale and thickness parameters, which can be easily estimated from the data using the approach proposed by Potscher and Prucha (1986). There is no doubt that other classes of distributions can also be analyzed similarly.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Testing Unit Root Based on Partially Adaptive Estimation

Lima¹,

Zhang²

2010

Journal of Time Series Econometrics

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This paper proposes unit root tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adaptive estimation using nonparametric methods. Taking into account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, which includes the normal distribution as a limiting case. Monte Carlo experiments indicate that, in the presence of heavy tail distributions, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit root is not found in real exchange rate and nominal interest rate even when heavy-tail is taken into account.

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Section: Introductionsupporting

confidence: 58%

Section: A Unit Root Test Based On Partially Adaptive Estimationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Testing Unit Root Based on Partially Adaptive Estimation

Lima¹,

Zhang²

2010

Journal of Time Series Econometrics

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“…In practice, even if the exact distribution of the innovations is unknown, as long as the data have similar tail behavior as the density function used in the estimation, inferences based on these methods still have good sampling performance. Thus, we may consider adaptive (Hansen and Lee, 1994;Seo, 1996;Beelders, 1998) or partially adaptive (Bickel, 1982, p. 664;Potscher and Prucha, 1986;Xiao, 1999) estimation methods so that the data density can be approximated. For example, to capture the feature of heavy tails in economic and financial data, we may consider a partially adaptive estimator based on the Student-t distributions, which has wide applications in economic analysis.…”

Section: Asymptotic Analysis Of the M-estimatorsmentioning

confidence: 99%

Likelihood-Based Inference in Trending Time Series With a Root Near Unity

Zhang

2001

Econom. Theory

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This paper studies likelihood-based estimation and tests for autoregressive time series models with deterministic trends and general disturbance distributions. In particular, a joint estimation of the trend coefficients and the autoregressive parameter is considered. Asymptotic analysis on the M-estimators is provided. It is shown that the limiting distributions of these estimators involve nonlinear equation systems of Brownian motions even for the simple case of least squares regression. Unit root tests based on M-estimation are also considered, and extensions of the Neyman–Pearson test are studied. The finite sample performance of these estimators and testing procedures is examined by Monte Carlo experiments.

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“…In most of these results, the predictors are assumed to be non-random. M-estimates in the regression context have been studied among others by Bustos (1982), Pötscher and Prucha (1986), Jurečkova (1989), Liese and Vajda (1994) and Koul (1996).…”

Section: Introductionmentioning

confidence: 99%