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Christis Katsouris

Publications and source records attributed to Christis Katsouris.

At least 19 recordsLinked to original sources
arXiv2024

Weak Convergence for Self-Normalized Partial Sum Processes in the Skorokhod M1 Topology with Applications to Regularly Varying Time Series

In this paper we study the weak convergence of self-normalized partial sum processes in the Skorokhod M1 topology for sequences of random variables which exhibit clustering of large values of the same sign. We show that for stationary regularly varying sequences with such properties, their corresponding properly centered self-normalized partial sums processes converge to a stable Levy process. The convergence is established in the space of cadlag functions endowed with Skorohod's M1 topology, which is more suitable especially for cases in which the standard J1 topology fails to induce weak convergence of joint stochastic functionals.

math.PR↗
arXiv2024

Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models

This paper develops an asymptotic distribution theory for an endogenous instrumentation approach in quantile predictive regressions when both generated covariates and persistent predictors are used. The generated covariates are obtained from an auxiliary quantile predictive regression model and the statistical problem of interest is the robust estimation and inference of the parameters that correspond to the primary quantile predictive regression in which this generated covariate is added to the set of nonstationary regressors. We find that the proposed doubly IVX corrected estimator is robust to the abstract degree of persistence regardless of the presence of generated regressor obtained from the first stage procedure. The asymptotic properties of the two-stage IVX estimator such as mixed Gaussianity are established while the asymptotic covariance matrix is adjusted to account for the first-step estimation error.

econ.EM↗
arXiv2024

Robust Estimation in Network Vector Autoregression with Nonstationary Regressors

This article studies identification and estimation for the network vector autoregressive model with nonstationary regressors. In particular, network dependence is characterized by a nonstochastic adjacency matrix. The information set includes a stationary regressand and a node-specific vector of nonstationary regressors, both observed at the same equally spaced time frequencies. Our proposed econometric specification correponds to the NVAR model under time series nonstationarity which relies on the local-to-unity parametrization for capturing the unknown form of persistence of these node-specific regressors. Robust econometric estimation is achieved using an IVX-type estimator and the asymptotic theory analysis for the augmented vector of regressors is studied based on a double asymptotic regime where both the network size and the time dimension tend to infinity.

econ.EM↗
arXiv2023

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.

econ.EM↗
arXiv2023

High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional dependent data which is relevant to covariance matrix structures as well as to dependent time series sequences. Second, we present main aspects of the asymptotic theory related to time series regression models with many covariates. Third, we discuss various applications of statistical learning methodologies for time series analysis purposes.

econ.EM↗
arXiv2023

Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models

In this article, we study the statistical and asymptotic properties of break-point estimators in nonstationary autoregressive and predictive regression models for testing the presence of a single structural break at an unknown location in the full sample. Moreover, we investigate aspects such as how the persistence properties of covariates and the location of the break-point affects the limiting distribution of the proposed break-point estimators.

econ.EM↗
arXiv2023

Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions

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.

econ.EM↗
arXiv2023

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.

econ.EM↗
arXiv2023

Predictability Tests Robust against Parameter Instability

We consider Wald type statistics designed for joint predictability and structural break testing based on the instrumentation method of Phillips and Magdalinos (2009). We show that under the assumption of nonstationary predictors: (i) the tests based on the OLS estimators converge to a nonstandard limiting distribution which depends on the nuisance coefficient of persistence; and (ii) the tests based on the IVX estimators can filter out the persistence under certain parameter restrictions due to the supremum functional. These results contribute to the literature of joint predictability and parameter instability testing by providing analytical tractable asymptotic theory when taking into account nonstationary regressors. We compare the finite-sample size and power performance of the Wald tests under both estimators via extensive Monte Carlo experiments. Critical values are computed using standard bootstrap inference methodologies. We illustrate the usefulness of the proposed framework to test for predictability under the presence of parameter instability by examining the stock market predictability puzzle for the US equity premium.

econ.EM↗
arXiv2023

Bootstrapping Nonstationary Autoregressive Processes with Predictive Regression Models

We establish the asymptotic validity of the bootstrap-based IVX estimator proposed by Phillips and Magdalinos (2009) for the predictive regression model parameter based on a local-to-unity specification of the autoregressive coefficient which covers both nearly nonstationary and nearly stationary processes. A mixed Gaussian limit distribution is obtained for the bootstrap-based IVX estimator. The statistical validity of the theoretical results are illustrated by Monte Carlo experiments for various statistical inference problems.

econ.EM↗
arXiv2023

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.

econ.EM↗
arXiv2023

Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors

In this paper, we study the estimation of the threshold predictive regression model with hybrid stochastic local unit root predictors. We demonstrate the estimation procedure and derive the asymptotic distribution of the least square estimator and the IV based estimator proposed by Magdalinos and Phillips (2009), under the null hypothesis of a diminishing threshold effect. Simulation experiments focus on the finite sample performance of our proposed estimators and the corresponding predictability tests as in Gonzalo and Pitarakis (2012), under the presence of threshold effects with stochastic local unit roots. An empirical application to stock return equity indices, illustrate the usefulness of our framework in uncovering regimes of predictability during certain periods. In particular, we focus on an aspect not previously examined in the predictability literature, that is, the effect of economic policy uncertainty.

econ.EM↗
arXiv2023

Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates

We propose an econometric environment for structural break detection in nonstationary quantile predictive regressions. We establish the limit distributions for a class of Wald and fluctuation type statistics based on both the ordinary least squares estimator and the endogenous instrumental regression estimator proposed by Phillips and Magdalinos (2009a, Econometric Inference in the Vicinity of Unity. Working paper, Singapore Management University). Although the asymptotic distribution of these test statistics appears to depend on the chosen estimator, the IVX based tests are shown to be asymptotically nuisance parameter-free regardless of the degree of persistence and consistent under local alternatives. The finite-sample performance of both tests is evaluated via simulation experiments. An empirical application to house pricing index returns demonstrates the practicality of the proposed break tests for regression quantiles of nonstationary time series data.

econ.EM↗
arXiv2023

Testing for Structural Change under Nonstationarity

This Appendix (dated: July 2021) includes supplementary derivations related to the main limit results of the econometric framework for structural break testing in predictive regression models based on the OLS-Wald and IVX-Wald test statistics, developed by Katsouris C (2021). In particular, we derive the asymptotic distributions of the test statistics when the predictive regression model includes either mildly integrated or persistent regressors. Moreover, we consider the case in which a model intercept is included in the model vis-a-vis the case that the predictive regression model has no model intercept. In a subsequent version of this study we reexamine these particular aspects in more depth with respect to the demeaned versions of the variables of the predictive regression.

econ.EM↗
arXiv2022

Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models

We revisit classical asymptotics when testing for a structural break in linear regression models by obtaining the limit theory of residual-based and Wald-type processes. First, we establish the Brownian bridge limiting distribution of these test statistics. Second, we study the asymptotic behaviour of the partial-sum processes in nonstationary (linear) time series regression models. Although, the particular comparisons of these two different modelling environments is done from the perspective of the partial-sum processes, it emphasizes that the presence of nuisance parameters can change the asymptotic behaviour of the functionals under consideration. Simulation experiments verify size distortions when testing for a break in nonstationary time series regressions which indicates that the Brownian bridge limit cannot provide a suitable asymptotic approximation in this case. Further research is required to establish the cause of size distortions under the null hypothesis of parameter stability.

econ.EM↗