# Four contributions to statistical inference in econometrics

This study includes 4 sections and is targeted on 3 topics: discriminating between stationary and nonstationary time series, examining the constancy of the error covariance matrix of a vector model, and estimating density functions over bounded domains using kernel techniques.
In Section One, “Testing the unit root hypothesis versus the logistic smooth transition autoregressive model”, and Section Two, “A nonlinear option to the unit root hypothesis”, the joint hypothesis of unit root and linearity enables one to differentiate between random walk processes, without or with drift, and stationary nonlinear processes of the smooth transition autoregressive type. This is significant in applications due to the fact steps taken in modelling a time series could possibly be drastically different based on whether or not the unit root hypothesis is rejected. In Section One the nonlinearity is based on the logistic function, whereas Section Two looks at the second-order logistic function. Monte Carlo simulations reveal that the proposed tests have comparable or higher power than the standard Dickey-Fuller unit root tests when the alternative exhibits nonlinear behavior…

## Contents: Four contributions to statistical inference in econometrics

I Summary of Thesis
II The chapters
1 Testing the unit root hypothesis against the logistic smooth
transition autoregressive model
1.1 Introduction
1.2 Model, null hypothesis and auxiliary regression
1.3 Limit results and the asymptotic tests
1.4 Small sample properties of the tests
1.4.1 Size simulations
1.4.2 Bootstrapping the critical values
1.4.3 Power simulations
1.5 Application
1.6 Conclusions
A Proof of Theorem 1
B Proof of Theorem 2
2 A nonlinear alternative to the unit root hypothesis
2.1 Introduction
2.2 Model and joint unit root and linearity hypothesis
2.3 Limit results and critical values
2.4 Small san1ple properties of the tests
2.4.1 Size simulations
2.5
2.6
2.4.2 Bootstrapping the p-values
2.4.3 Power simulations
Empirical application
2.5.1 A short introduction to the PPP literature
2.5.2 Testing the PPP hypothesis in practice Conclusions
A Proof of Theorem 1
3 Testing the constancy of the error covariance matrix in vector models
3.1 Introduction
3.2 The model
3.3 The test statistic
3.4 Bivariate illustration
3.5 Testing against smoothly changing variances
3.5.1 Assumptions
3.5.2 The identification problem and a solution
3.5.3 Smooth and deterministically time-varying variances
3.6 Small sample properties of the test
3.6.1 Size simulations
3.6.2 Violating Assun1ption 1: time-varying correlations
3.6.3 Power simulations
3.7 Conclusions
A Proof of Lemma 1
B Tables
4 Estimating confidence regions over bounded domains…

Source: Stockholm School of Economics