Quantile Time Series Regression Models Revisited

This article discusses recent developments in the literature of quantile time series models in the cases of stationary and nonstationary underline stochastic processes

Structural Analysis of Vector Autoregressive Models

This set of lecture notes discuss key concepts for the Structural Analysis of Vector Autoregressive models for the teaching of a course on Applied Macroeconometrics with Advanced Topics.Comment: arXiv admin note: text overlap with arXiv:1609.06029 by other author

Optimal Estimation Methodologies for Panel Data Regression Models

This survey study discusses main aspects to optimal estimation methodologies for panel data regression models. In particular, we present current methodological developments for modeling stationary panel data as well as robust methods for estimation and inference in nonstationary panel data regression models. Some applications from the network econometrics and high dimensional statistics literature are also discussed within a stationary time series environment

Unified Inference for Dynamic Quantile Predictive Regression

This paper develops unified asymptotic distribution theory for dynamic quantile predictive regressions which is useful when examining quantile predictability in stock returns under possible presence of nonstationarity.Comment: arXiv admin note: text overlap with arXiv:2308.0661

Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models

This paper considers the specification of covariance structures with tail estimates. We focus on two aspects: (i) the estimation of the VaR-CoVaR risk matrix in the case of larger number of time series observations than assets in a portfolio using quantile predictive regression models without assuming the presence of nonstationary regressors and; (ii) the construction of a novel variable selection algorithm, so-called, Feature Ordering by Centrality Exclusion (FOCE), which is based on an assumption-lean regression framework, has no tuning parameters and is proved to be consistent under general sparsity assumptions. We illustrate the usefulness of our proposed methodology with numerical studies of real and simulated datasets when modelling systemic risk in a network

Limit Theory under Network Dependence and Nonstationarity

These lecture notes represent supplementary material for a short course on time series econometrics and network econometrics. We give emphasis on limit theory for time series regression models as well as the use of the local-to-unity parametrization when modeling time series nonstationarity. Moreover, we present various non-asymptotic theory results for moderate deviation principles when considering the eigenvalues of covariance matrices as well as asymptotics for unit root moderate deviations in nonstationary autoregressive processes. Although not all applications from the literature are covered we also discuss some open problems in the time series and network econometrics literature.Comment: arXiv admin note: text overlap with arXiv:1705.08413 by other author

Asymptotic Theory for Moderate Deviations from the Unit Boundary in Quantile Autoregressive Time Series

We establish the asymptotic theory in quantile autoregression when the model parameter is specified with respect to moderate deviations from the unit boundary of the form (1 + c / k) with a convergence sequence that diverges at a rate slower than the sample size n. Then, extending the framework proposed by Phillips and Magdalinos (2007), we consider the limit theory for the near-stationary and the near-explosive cases when the model is estimated with a conditional quantile specification function and model parameters are quantile-dependent. Additionally, a Bahadur-type representation and limiting distributions based on the M-estimators of the model parameters are derived. Specifically, we show that the serial correlation coefficient converges in distribution to a ratio of two independent random variables. Monte Carlo simulations illustrate the finite-sample performance of the estimation procedure under investigation

Aspects of estimation and inference for predictive regression models

This PhD thesis presents three essays on nonstationary time series econometrics which are grouped into three chapters. The chapters cover aspects of estimation and inference for predictive regression models through the lens of moderate deviation principles from the unit root boundary in a class of stable but nearly-unstable processes which exhibit high persistence. The first chapter presents an overview of the research background which includes the persistence classes and the main asymptotic properties of estimators for nonstationary autoregressive processes. The persistence properties of time series is modelled via the local-to-unity parametrization which implies that the autoregressive coefficient is specified such that it approaches the unit boundary as the sample size increases. The second part of the chapter summarizes the structure of the thesis and the main contributions to the literature. The second chapter, proposes an econometric framework for predictability testing in linear predictive regression models robust against parameter instability. In particular, the asymptotic theory for the proposed sup-Wald test statistics when regressors are assumed to be mildly integrated and persistent stochastic processes is established. The asymptotic theory of OLS and IVX based estimators and test statistics presented in this thesis is developed based on standard local-to-unity asymptotics and the limit theory of triangular arrays of martingales. The third chapter, addresses the aspect of structural break detection for nonstationary time series when a conditional quantile specification form is used. In particular, the proposed econometric framework is suitable for testing for a structural break at unknown time in nonstationary quantile predictive regression models and can be further employed for investigating the aspect of quantile predictability against parameter instability. The fourth chapter, proposes a novel estimation and inference methodology in systems of quantile predictive regressions with generated regressors. This econometric framework allows to address the issue of modelling systemic risk in financial networks when considering the interplay between network-type of dependence and time series non stationarity

Treatment effect validation via a permutation test in Stata

In this paper we describe the testing procedure for assessing the statistical significance of treatment effect under the experimental conditions of baseline imbalance across covariates and attrition from the survey, using the permutation tests proposed by Freedman and Lane (1983) and Romano and Wolf (2016). We discuss the testing procedure for these hypotheses based on a linear regression model and introduce the new Stata command [R] permtest for the implementation of the permutation test in Stata. Moreover, we investigate the finite-sample performance as well as the statistical validity of the test with a Monte Carlo simulation study in which we examine the empirical size and power properties under the conditions of baseline imbalance and attrition for a fixed number of permutation steps

Forecast evaluation in large cross-sections of realized volatility

In this paper, we consider the forecast evaluation of realized volatility measures under cross-section dependence using equal predictive accuracy testing procedures. We evaluate the predictive accuracy of the model based on the augmented cross-section when forecasting Realized Volatility. Under the null hypothesis of equal predictive accuracy the benchmark model employed is a standard HAR model while under the alternative of non-equal predictive accuracy the forecast model is an augmented HAR model estimated via the LASSO shrinkage. We study the sensitivity of forecasts to the model specification by incorporating a measurement error correction as well as cross-sectional jump component measures. The out-of-sample forecast evaluation of the models is assessed with numerical implementations