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.

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 QML Estimators in Linear Regression Models with Functional Coefficient Autoregressive Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Hongchang Hu
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Models ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Autoregressive Processes ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Quasi Maximum Likelihood ◽  
Functional Coefficient

This paper studies a linear regression model, whose errors are functional coefficient autoregressive processes. Firstly, the quasi-maximum likelihood (QML) estimators of some unknown parameters are given. Secondly, under general conditions, the asymptotic properties (existence, consistency, and asymptotic distributions) of the QML estimators are investigated. These results extend those of Maller (2003), White (1959), Brockwell and Davis (1987), and so on. Lastly, the validity and feasibility of the method are illuminated by a simulation example and a real example.

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.

scholarly journals Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 793-813
Author(s):  
Mohamed Alahiane ◽  
Idir Ouassou ◽  
Mustapha Rachdi ◽  
Philippe Vieu
Keyword(s):  
Functional Data ◽  
Regression Models ◽  
Asymptotic Distributions ◽  
Link Function ◽  
Linear Regression Models ◽  
Single Index ◽  
Partially Linear ◽  
Generalize Linear Regression ◽  
Single Index Models ◽  
Non Parametric

Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) is an unknown univariate link function. In this article, we generalize these models to have a functional component, replacing the generalized partially linear single index models η0α0⊤X+β0⊤Z , where α is a vector in IRd, η0(·) and β0(·) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α0, the unknown functions β0(·) and η0(·) and establish their asymptotic distributions, and furthermore, a simulation study is carried out to evaluate the models and the effectiveness of the proposed estimation methodology.

scholarly journals The distributions of the J and Cox non-nested tests in regression models with weakly correlated regressors

2021 ◽  
Author(s):  
Leo Michelis
Keyword(s):  
Monte Carlo ◽  
Alternative Model ◽  
Regression Models ◽  
Population Distribution ◽  
Nuisance Parameter ◽  
Linear Regression Models ◽  
Null Distributions ◽  
Finite Samples ◽  
The Monte Carlo Method ◽  
Asymptotic Expressions

This paper examines the asymptotic null distributions of the <em>J</em> and Cox non-nested tests in the framework of two linear regression models with nearly orthogonal non-nested regressors. The analysis is based on the concept of near population orthogonality (NPO), according to which the non-nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn. New distributional results emerge under NPO. The <em>J</em> and Cox tests tend to two different random variables asymptotically, each of which is expressible as a function of a nuisance parameter, <em>c</em>, a N(0,1) variate and a <em>χ</em>2(<em>q</em>) variate, where <em>q</em> is the number of non-nested regressors in the alternative model. The Monte Carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under NPO by plugging consistent estimates of <em>c</em> into the relevant asymptotic expressions. An empirical example illustrates the ‘plug in’ procedure.

scholarly journals Assessment of spline functions for estimating growth curve parameters of FUNAABAlpha chickens

2020 ◽  
Vol 46 (5) ◽  
Author(s):  
H. A. Bashiru ◽  
S. O. Oseni ◽  
L. A. Omadime
Keyword(s):  
Regression Models ◽  
Selection Criteria ◽  
Goodness Of Fit ◽  
Information Criterion ◽  
Regression Coefficients ◽  
Spline Functions ◽  
Linear Regression Models ◽  
Male And Female ◽  
Spline Models ◽  
Best Fit

The objective of this study was to fit four spline linear regression models to describe the growth of FUNAAB-Alpha Chickens (FAC). Body weight records of 300 FAC raised from day old till the 20th week were used to fit spline models of 3 (SP3), 4 (SP4), 5 (SP5) and 6 knots (SP6) using the REG procedure of SAS®. The data were first plotted to determine the most appropriate location of knots and they were placed at 4th, 10 th and 16 th week of age for SP3; 4th, 8th, 12th and 16th week for SP4; 4th, 7th, 10th, 14th and 18th week for SP5 and 3rd, 6th, 9th, 12th, 15 th and 18 th week for SP6, respectively. The hatch weight predicted by SP3 was observed to be highest while SP6 predicted the lowest hatch weight for male and female FAC. Regression coefficients ranged from -38.47 to 47.46 and -39.40 to 40.47 for the male and female, respectively. For all the models, the highest magnitude of these coefficients were estimated at early ages after hatching (at 3 to 10 weeks of age). Based on Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) as the goodness-of-fit selection criteria, SP3 had the lowest value for AIC and BIC for male FAC while SP4 had the lowest value of AIC and BIC for the female FAC. It was concluded that spline models of lower knots (SP3 and SP4) were the best fit to describe the growth of male and female FAC respectively, and that growth rate at early stages of life of FAC may be good predictors of later growth performance.

Forecasting Economic Indicators of Transport Activity

2021 ◽  
pp. 70-78
Author(s):  
D. Biryukov ◽  
O. Rod'kina ◽  
Ruslan Vakulenko ◽  
D. Lapaev
Keyword(s):  
Correlation Analysis ◽  
Economic Activity ◽  
Regression Models ◽  
Economic Indicators ◽  
Transport Sector ◽  
Linear Regression Models ◽  
Transport Activity ◽  
Statistical Accuracy ◽  
Predictive Regression ◽  
And Storage

The article discusses the methodological and practical aspects of forecasting the economic indicators of the transport sector at the level of a transport company and the type of economic activity. The development of forecasting methodology at the present time is analyzed. The necessity, features and main directions of development of the forecasting methodology for the type of economic activity are revealed. The methodological basis for forecasting the development of the transport sector is investigated and characterized. A method for forecasting transportation and storage as a type of economic activity under conditions of uncertainty is proposed and tested. Based on the results of the correlation analysis, subsets of predicted indicators and factors were formed that were optimal for constructing the corresponding linear regression models. Predictive regression models have been developed, their significance and statistical accuracy have been confirmed.

Accounting for Endogeneity in Regression Models Using Copulas: A Step-by-Step Guide for Empirical Studies

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alecos Papadopoulos
Keyword(s):  
Regression Models ◽  
Empirical Studies ◽  
Gaussian Copula ◽  
Supplementary File ◽  
Linear Regression Models ◽  
Finite Samples ◽  
Endogenous Regressors ◽  
Proposed Model ◽  
Present Simulation ◽  
Detailed Presentation

Abstract We provide a detailed presentation and guide for the use of Copulas in order to account for endogeneity in linear regression models without the need for instrumental variables. We start by developing the model from first principles of likelihood inference, and then focus on the Gaussian Copula. We discuss its merits and propose diagnostics to assess its validity. We analyze in detail and provide solutions to the various issues that may arise in empirical applications for applying the method. We treat the cases of both continuous and discrete endogenous regressors. We present simulation evidence for the performance of the proposed model in finite samples, and we illustrate its application by a short empirical study. A Supplementary File contains additional simulations and another empirical illustration.

MALLIAVIN CALCULUS FOR THE ESTIMATION OF TIME-VARYING REGRESSION MODELS USED IN FINANCIAL APPLICATIONS

2007 ◽  
Vol 10 (05) ◽  
pp. 771-800 ◽  
Author(s):  
AHMED ABUTALEB ◽  
MICHAEL G. PAPAIOANNOU
Keyword(s):  
Malliavin Calculus ◽  
Regression Models ◽  
Closed Form Solution ◽  
Form Solution ◽  
Regression Coefficients ◽  
Time Varying ◽  
Linear Regression Models ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Estimation Of Time

The paper introduces a new method for the estimation of time-varying regression coefficients employed in financial modeling. We use Malliavin calculus (stochastic calculus of variations) to estimate the time-varying regression coefficients that appear in linear regression models, and the generalized Clark–Ocone formula to derive a closed-form solution for the estimates of the time-varying coefficients. While this approach can be applied to any signal model, we present its application to signals modeled as a Brownian motion and an Ornstein–Uhlenbeck process. Simulation results prove the superiority of the proposed method, as compared to conventional methods.

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