scholarly journals IV and GMM Estimation and Testing of Multivariate Stochastic Unit Root Models

2016 ◽  
Author(s):  
Offer Lieberman ◽  
Peter C. B. Phillips
Keyword(s):  
Unit Root ◽  
Gmm Estimation ◽  
Unit Root Models

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 Optimal jackknife for unit root models

2015 ◽  
Vol 99 ◽  
pp. 135-142 ◽  
Author(s):  
Ye Chen ◽  
Jun Yu
Keyword(s):  
Unit Root ◽  
Unit Root Models

Testing for Unit Roots in Models with Structural Change

1994 ◽  
Vol 10 (5) ◽  
pp. 917-936 ◽  
Author(s):  
Joon Y. Park ◽  
Jaewhan Sung
Keyword(s):  
Structural Change ◽  
Least Squares ◽  
Unit Root ◽  
Unit Roots ◽  
Generalized Least Squares ◽  
Testing Procedure ◽  
Unit Root Tests ◽  
Limiting Distributions ◽  
Independent Unit ◽  
Unit Root Models

This paper considers the unit root tests in models with structural change. Particular attention is given to their dependency on the limiting ratios of the subsample sizes between breaks. The dependency is analyzed in detail, and the invariant testing procedure based on a transformed model is developed. The required transformation is essentially identical to the generalized least-squares correction for heteroskedasticity. The limiting distributions of the new tests do not depend on the relative sizes of the subsamples and are shown to be simple mixtures of the limiting distributions of the corresponding tests from the independent unit root models without structural change.

scholarly journals IV AND GMM INFERENCE IN ENDOGENOUS STOCHASTIC UNIT ROOT MODELS

2017 ◽  
Vol 34 (5) ◽  
pp. 1065-1100 ◽  
Author(s):  
Offer Lieberman ◽  
Peter C.B. Phillips
Keyword(s):  
Stock Returns ◽  
Unit Root ◽  
Instrumental Variable ◽  
Nonlinear Least Squares ◽  
Asymptotic Distributions ◽  
Small Samples ◽  
Time Varying ◽  
Limit Theory ◽  
The One ◽  
Unit Root Models

Lieberman and Phillips (2017; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates of the associated covariance parameters. This paper develops a nonlinear instrumental variable (NLIV) as well as GMM estimators of the STUR parameter which conveniently addresses endogeneity. We derive the asymptotic distributions of the NLIV and GMM estimators and establish consistency under similar orthogonality and relevance conditions to those used in the linear model. An overidentification test and its asymptotic distribution are also developed. The results enable inference about structural STUR models and a mechanism for testing the local STUR model against a simple UR null, which complements usual UR tests. Simulations reveal that the asymptotic distributions of the NLIV and GMM estimators of the STUR parameter as well as the test for overidentifying restrictions perform well in small samples and that the distribution of the NLIV estimator is heavily leptokurtic with a limit theory which has Cauchy-like tails. Comparisons of STUR coefficient and standard UR coefficient tests show that the one-sided UR test performs poorly against the one-sided STUR coefficient test both as the sample size and departures from the null rise. The results are applied to study the relationships between stock returns and bond spread changes.

Priors for unit root models

1996 ◽  
Vol 75 (1) ◽  
pp. 99-111 ◽  
Author(s):  
Joseph B. Kadane ◽  
Ngai Hang Chan ◽  
Lara J. Wolfson
Keyword(s):  
Unit Root ◽  
Unit Root Models

NONSTATIONARY LINEAR PROCESSES WITH INFINITE VARIANCE GARCH ERRORS

2020 ◽  
pp. 1-34
Author(s):  
Rongmao Zhang ◽  
Ngai Hang Chan
Keyword(s):  
Unit Root ◽  
Ordinary Least Squares ◽  
Infinite Variance ◽  
Linear Processes ◽  
Limit Distributions ◽  
Root Model ◽  
Augmented Dickey Fuller ◽  
Short Memory ◽  
Unit Root Models ◽  
Adf Test

Recently, Cavaliere, Georgiev, and Taylor (2018, Econometric Theory 34, 302–348) (CGT) considered the augmented Dickey–Fuller (ADF) test for a unit-root model with linear noise driven by i.i.d. infinite variance innovations and showed that ordinary least squares (OLS)-based ADF statistics have the same distribution as in Chan and Tran (1989, Econometric Theory 5, 354–362) for i.i.d. infinite variance noise. They also proposed an interesting question to extend their results to the case with infinite variance GARCH innovations as considered in Zhang, Sin, and Ling (2015, Stochastic Processes and their Applications 125, 482–512). This paper addresses this question. In particular, the limit distributions of the ADF for random walk models with short-memory linear noise driven by infinite variance GARCH innovations are studied. We show that when the tail index $\alpha <2$ , the limit distributions are completely different from that of CGT and the estimator of the parameters of the lag terms used in the ADF regression is not consistent. This paper provides a broad treatment of unit-root models with linear GARCH noises, which encompasses the commonly entertained unit-root IGARCH model as a special case.

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