scholarly journals GAUSSIAN INFERENCE IN AR(1) TIME SERIES WITH OR WITHOUT A UNIT ROOT

2008 ◽  
Vol 24 (3) ◽  
pp. 631-650 ◽  
Author(s):  
Peter C.B. Phillips ◽  
Chirok Han
Keyword(s):  
Time Series ◽  
Central Limit ◽  
Unit Root ◽  
Initial Conditions ◽  
Finite Sample ◽  
Linear Processes ◽  
Limit Theory ◽  
Sample Bias ◽  
Dynamic Panels ◽  
Finite Sample Bias

This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform $\sqrt{n}$ rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, Annals of Statistics, 20, 971–1001). The approach also has useful extensions to dynamic panels.

FINITE-SAMPLE MOMENTS OF THE COEFFICIENT OF VARIATION

2009 ◽  
Vol 25 (1) ◽  
pp. 291-297 ◽  
Author(s):  
Yong Bao
Keyword(s):  
Coefficient Of Variation ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
General Distribution ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Finite Sample Bias ◽  
Sample Coefficient Of Variation

We study the finite-sample bias and mean squared error, when properly defined, of the sample coefficient of variation under a general distribution. We employ a Nagar-type expansion and use moments of quadratic forms to derive the results. We find that the approximate bias depends on not only the skewness but also the kurtosis of the distribution, whereas the approximate mean squared error depends on the cumulants up to order 6.

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 UNIT ROOT AND COINTEGRATING LIMIT THEORY WHEN INITIALIZATION IS IN THE INFINITE PAST

2009 ◽  
Vol 25 (6) ◽  
pp. 1682-1715 ◽  
Author(s):  
Peter C.B. Phillips ◽  
Tassos Magdalinos
Keyword(s):  
Normal Distribution ◽  
Least Squares ◽  
Rate Of Convergence ◽  
Unit Root ◽  
Initial Conditions ◽  
Cauchy Distribution ◽  
Least Squares Estimator ◽  
Initial Condition ◽  
Limit Theory ◽  
Regression Theory

It is well known that unit root limit distributions are sensitive to initial conditions in the distant past. If the distant past initialization is extended to the infinite past, the initial condition dominates the limit theory, producing a faster rate of convergence, a limiting Cauchy distribution for the least squares coefficient, and a limit normal distribution for the t-ratio. This amounts to the tail of the unit root process wagging the dog of the unit root limit theory. These simple results apply in the case of a univariate autoregression with no intercept. The limit theory for vector unit root regression and cointegrating regression is affected but is no longer dominated by infinite past initializations. The latter contribute to the limiting distribution of the least squares estimator and produce a singularity in the limit theory, but do not change the principal rate of convergence. Usual cointegrating regression theory and inference continue to hold in spite of the degeneracy in the limit theory and are therefore robust to initial conditions that extend to the infinite past.

Measuring Group Differences in High‐Dimensional Choices: Method and Application to Congressional Speech

Econometrica ◽  
2019 ◽  
Vol 87 (4) ◽  
pp. 1307-1340 ◽  
Author(s):  
Matthew Gentzkow ◽  
Jesse M. Shapiro ◽  
Matt Taddy
Keyword(s):  
Machine Learning ◽  
High Dimensional ◽  
Group Differences ◽  
Finite Sample ◽  
Sample Bias ◽  
The Past ◽  
Recent Advances ◽  
Finite Sample Bias ◽  
Choice Set

We study the problem of measuring group differences in choices when the dimensionality of the choice set is large. We show that standard approaches suffer from a severe finite‐sample bias, and we propose an estimator that applies recent advances in machine learning to address this bias. We apply this method to measure trends in the partisanship of congressional speech from 1873 to 2016, defining partisanship to be the ease with which an observer could infer a congressperson's party from a single utterance. Our estimates imply that partisanship is far greater in recent years than in the past, and that it increased sharply in the early 1990s after remaining low and relatively constant over the preceding century.

Adjusting finite sample bias in traffic safety modeling

2019 ◽  
Vol 131 ◽  
pp. 112-121 ◽  
Author(s):  
Huiying Mao ◽  
Xinwei Deng ◽  
Dominique Lord ◽  
Gerardo Flintsch ◽  
Feng Guo
Keyword(s):  
Traffic Safety ◽  
Finite Sample ◽  
Sample Bias ◽  
Finite Sample Bias
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