scholarly journals Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model

Econometrics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 22 ◽  
Author(s):  
Pierre Perron ◽  
Yohei Yamamoto
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Structural Changes ◽  
Error Variance ◽  
Regression Coefficients ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Joint Approach ◽  
Size Distortions

In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients, possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the variance (or in the coefficients). In this note, we provide evidence that such procedures have poor finite sample properties when the changes in the first step are not correctly accounted for. In doing so, we show that testing for changes in the coefficients (or in the variance) ignoring changes in the variance (or in the coefficients) induces size distortions and loss of power. Our results illustrate a need for a joint approach to test for structural changes in both the coefficients and the variance of the errors. We provide some evidence that the procedures suggested by Perron et al. (2019) provide tests with good size and power.

scholarly journals Comparison study on the confidence intervals in linear regression models with restricted parameter space

2019 ◽  
Vol 52 (2) ◽  
pp. 115-127
Author(s):  
XIUQIN BAI ◽  
WEIXING SONG
Keyword(s):  
Linear Regression ◽  
Empirical Likelihood ◽  
Regression Models ◽  
Confidence Region ◽  
Estimation Procedure ◽  
Regression Coefficients ◽  
Comparison Study ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Confidence Estimation

This paper proposes an empirical likelihood confidence region for the regression coefficients in linear regression models when the regression coefficients are subjected to some equality constraints. The shape of the confidence set does not depend on the re-parametrization of the regression model induced by the equality constraint. It is shown that the asymptotic coverage rate attains the nominal confidence level and the Bartlett correction can successfully reduce the coverage error rate from $O(n^{-1})$ to $O(n^{-2})$, where n denotes the sample size. Simulation studies are conducted to evaluate the finite sample performance of the proposed empirical likelihood empirical confidence estimation procedure. Finally, a comparison study is conducted to compare the finite sample performance of the proposed and the classical ellipsoidal confidence sets based on normal theory.

scholarly journals Stochastic Restricted LASSO-Type Estimator in the Linear Regression Model

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Manickavasagar Kayanan ◽  
Pushpakanthie Wijekoon
Keyword(s):  
Linear Regression ◽  
Variable Selection ◽  
Regression Models ◽  
Prior Information ◽  
Estimation Procedure ◽  
Regression Coefficients ◽  
Linear Regression Models ◽  
Monte Carlo Simulation Study ◽  
Regression Parameters ◽  
Linear Restrictions

Among several variable selection methods, LASSO is the most desirable estimation procedure for handling regularization and variable selection simultaneously in the high-dimensional linear regression models when multicollinearity exists among the predictor variables. Since LASSO is unstable under high multicollinearity, the elastic-net (Enet) estimator has been used to overcome this issue. According to the literature, the estimation of regression parameters can be improved by adding prior information about regression coefficients to the model, which is available in the form of exact or stochastic linear restrictions. In this article, we proposed a stochastic restricted LASSO-type estimator (SRLASSO) by incorporating stochastic linear restrictions. Furthermore, we compared the performance of SRLASSO with LASSO and Enet in root mean square error (RMSE) criterion and mean absolute prediction error (MAPE) criterion based on a Monte Carlo simulation study. Finally, a real-world example was used to demonstrate the performance of SRLASSO.

Testing Impact Measures in Spatial Autoregressive Models

2019 ◽  
Vol 43 (1-2) ◽  
pp. 40-75 ◽  
Author(s):  
Giuseppe Arbia ◽  
Anil K. Bera ◽  
Osman Doğan ◽  
Süleyman Taşpınar
Keyword(s):  
Linear Regression ◽  
Spatial Data ◽  
Regression Models ◽  
Delta Method ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Spatial Panel Data Models ◽  
Spatial Panel Data ◽  
Spatial Autoregressive ◽  
The Impact

Researchers often make use of linear regression models in order to assess the impact of policies on target outcomes. In a correctly specified linear regression model, the marginal impact is simply measured by the linear regression coefficient. However, when dealing with both synchronic and diachronic spatial data, the interpretation of the parameters is more complex because the effects of policies extend to the neighboring locations. Summary measures have been suggested in the literature for the cross-sectional spatial linear regression models and spatial panel data models. In this article, we compare three procedures for testing the significance of impact measures in the spatial linear regression models. These procedures include (i) the estimating equation approach, (ii) the classical delta method, and (iii) the simulation method. In a Monte Carlo study, we compare the finite sample properties of these procedures.

scholarly journals SHRINKAGE ESTIMATION OF REGRESSION MODELS WITH MULTIPLE STRUCTURAL CHANGES

2015 ◽  
Vol 32 (6) ◽  
pp. 1376-1433 ◽  
Author(s):  
Junhui Qian ◽  
Liangjun Su
Keyword(s):  
Regression Models ◽  
Structural Changes ◽  
Equity Premium ◽  
Asymptotic Distributions ◽  
Regression Coefficients ◽  
Tuning Parameter ◽  
Linear Regression Models ◽  
Predictive Regression ◽  
Finite Samples ◽  
Fundamental Information

In this paper, we consider the problem of determining the number of structural changes in multiple linear regression models via group fused Lasso. We show that with probability tending to one, our method can correctly determine the unknown number of breaks, and the estimated break dates are sufficiently close to the true break dates. We obtain estimates of the regression coefficients via post Lasso and establish the asymptotic distributions of the estimates of both break ratios and regression coefficients. We also propose and validate a data-driven method to determine the tuning parameter. Monte Carlo simulations demonstrate that the proposed method works well in finite samples. We illustrate the use of our method with a predictive regression of the equity premium on fundamental information.

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