Asymptotic theory for LAD estimation of moderate deviations from a unit root

2014 ◽  
Vol 90 ◽  
pp. 25-32 ◽  
Author(s):  
Zhiyong Zhou ◽  
Zhengyan Lin
Keyword(s):  
Unit Root ◽  
Asymptotic Theory ◽  
Moderate Deviations ◽  
Lad Estimation

scholarly journals ASYMPTOTIC THEORY FOR KERNEL ESTIMATORS UNDER MODERATE DEVIATIONS FROM A UNIT ROOT, WITH AN APPLICATION TO THE ASYMPTOTIC SIZE OF NONPARAMETRIC TESTS

2019 ◽  
Vol 36 (4) ◽  
pp. 559-582
Author(s):  
James A. Duffy
Keyword(s):  
Unit Root ◽  
Regression Models ◽  
Asymptotic Theory ◽  
Kernel Density ◽  
Nonparametric Tests ◽  
Moderate Deviations ◽  
Autoregressive Processes ◽  
Predictive Regression ◽  
Asymptotic Size ◽  
Rejection Probability

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled uniformly in the degree of persistence of the regressor. This provides a rigorous justification for the validity of the usual nonparametric inferential procedures, even in cases where regressors may be highly persistent.

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.

LSTUR regression theory and the instability of the sample correlation coefficient between financial return indices

2020 ◽  
Author(s):  
Tim Ginker ◽  
Offer Lieberman
Keyword(s):  
Correlation Coefficient ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Financial Return ◽  
Spurious Regression ◽  
Root Model ◽  
Sampling Window ◽  
Sample Correlation ◽  
Underlying Processes ◽  
Regression Theory

Summary It is well known that the sample correlation coefficient between many financial return indices exhibits substantial variation on any reasonable sampling window. This stylised fact contradicts a unit root model for the underlying processes in levels, as the statistic converges in probability to a constant under this modeling scheme. In this paper, we establish asymptotic theory for regression in local stochastic unit root (LSTUR) variables. An empirical application reveals that the new theory explains very well the instability, in both sign and scale, of the sample correlation coefficient between gold, oil, and stock return price indices. In addition, we establish spurious regression theory for LSTUR variables, which generalises the results known hitherto, as well as a theory for balanced regression in this setting.

REGIME-SWITCHING AUTOREGRESSIVE COEFFICIENTS AND THE ASYMPTOTICS FOR UNIT ROOT TESTS

2008 ◽  
Vol 24 (4) ◽  
pp. 1137-1148
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Sample Size ◽  
Unit Root ◽  
Regime Switching ◽  
Asymptotic Theory ◽  
Unit Roots ◽  
Stationary Regime ◽  
Unit Root Tests ◽  
Asymptotic Results ◽  
Switching Models ◽  
Root Model

Most of the asymptotic results for Markov regime-switching models with possible unit roots are based on specifications implying that the number of regime switches grows to infinity as the sample size increases. Conversely, in this note we derive some new asymptotic results for the case of Markov regime switches that are infrequent in the sense that their number is bounded in probability, even asymptotically. This is achieved by (inversely) relating the probability of regime switching to the sample size. The proposed asymptotic theory is applied to a well-known stochastic unit root model, where the dynamics of the observed variable switches between a unit root regime and a stationary regime.

Unit Root Tests Based on M Estimators

1995 ◽  
Vol 11 (2) ◽  
pp. 331-346 ◽  
Author(s):  
André Lucas
Keyword(s):  
Linear Combination ◽  
Unit Root ◽  
Asymptotic Theory ◽  
Simulation Experiment ◽  
Unit Root Test ◽  
Ordinary Least Squares ◽  
Asymptotic Distributions ◽  
Unit Root Tests ◽  
Nuisance Parameters ◽  
M Estimator

This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation of this result is discussed. A simulation experiment is described, illustrating the level and power of different unit root tests for several sample sizes and data generating processes. The tests based on M estimators turn out to be more powerful than the OLS-based tests if the innovations are fat-tailed.

scholarly journals Limit theory for moderate deviations from a unit root

2007 ◽  
Vol 136 (1) ◽  
pp. 115-130 ◽  
Author(s):  
Peter C.B. Phillips ◽  
Tassos Magdalinos
Keyword(s):  
Unit Root ◽  
Moderate Deviations ◽  
Limit Theory
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