arXiv subjects

Anna Bykhovskaya

Publications and source records attributed to Anna Bykhovskaya.

9 recordsLinked to original sources

arXiv2026

Generalized Autoregressive Multivariate Models: From Binary to Poisson

This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics, accommodating nonlinearities, network interactions, and cross-sectional dependence in the multivariate case. Existence and uniqueness of a stationary solution is established via a coupling argument tailored to the discontinuities inherent in binary data. A key theoretical result, further supported by our empirical illustration on S&P 100 data, shows that, under a rare-events scaling, aggregates of such binary processes converge to a Poisson autoregression, providing a micro-foundation for this widely used count model. Maximum likelihood estimation is proposed and illustrated empirically.

econ.EM↗

arXiv2026

How weak are weak factors? Uniform inference for signal strength in signal plus noise models

The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The objective is to construct confidence intervals for the signal strength that are uniformly valid across all regimes - strong, weak, and critical signals. We demonstrate that traditional Gaussian approximations fail in the critical regime. Instead, we introduce a universal transitional distribution that enables valid inference across the entire spectrum of signal strengths. The approach is illustrated through applications in macroeconomics and finance.

stat.ME↗

arXiv2025

Estimation of a Dynamic Tobit Model with a Unit Root

This paper studies robust estimation in the dynamic Tobit model under local-to-unity (LUR) asymptotics. We show that both Gaussian maximum likelihood (ML) and censored least absolute deviations (CLAD) estimators are consistent, extending results from the stationary case where ordinary least squares (OLS) is inconsistent. The asymptotic distributions of MLE and CLAD are derived; for the short-run parameters they are shown to be Gaussian, yielding standard normal t-statistics. In contrast, although OLS remains consistent under LUR, its t-statistics are not standard normal. These results enable reliable model selection via sequential t-tests based on ML and CLAD, paralleling the linear autoregressive case. Applications to financial and epidemiological time series illustrate their practical relevance.

econ.EM↗

arXiv2025

Canonical Correlation Analysis: review

For over a century canonical correlations, variables, and related concepts have been studied across various fields, with contributions dating back to Jordan [1875] and Hotelling [1936]. This text surveys the evolution of canonical correlation analysis, a fundamental statistical tool, beginning with its foundational theorems and progressing to recent developments and open research problems. Along the way we introduce and review methods, notions, and fundamental concepts from linear algebra, random matrix theory, and high-dimensional statistics, placing particular emphasis on rigorous mathematical treatment. The survey is intended for technically proficient graduate students and other researchers with an interest in this area. The content is organized into five chapters, supplemented by six sets of exercises found in Chapter 6. These exercises introduce additional material, reinforce key concepts, and serve to bridge ideas across chapters. We recommend the following sequence: first, solve Problem Set 0, then proceed with Chapter 1, solve Problem Set 1, and so on through the text.

stat.ME↗

arXiv2025

Largevars: An R Package for Testing Large VARs for the Presence of Cointegration

Cointegration is a property of multivariate time series that determines whether its non-stationary, growing components have a stationary linear combination. Largevars R package conducts a cointegration test for high-dimensional vector autoregressions of order k based on the large N, T asymptotics of Bykhovskaya and Gorin (2022, 2025). The implemented test is a modification of the Johansen likelihood ratio test. In the absence of cointegration the test converges to the partial sum of the Airy_1 point process, an object arising in random matrix theory. The package and this article contain simulated quantiles of the first ten partial sums of the Airy_1 point process that are precise up to the first 3 digits. We also include two examples using Largevars: an empirical example on S&P100 stocks and a simulated VAR(2) example.

econ.EM↗

arXiv2025

High-Dimensional Canonical Correlation Analysis

This paper studies high-dimensional canonical correlation analysis (CCA) with an emphasis on the vectors that define canonical variables. The paper shows that when two dimensions of data grow to infinity jointly and proportionally, the classical CCA procedure for estimating those vectors fails to deliver a consistent estimate. This provides the first result on the impossibility of identification of canonical variables in the CCA procedure when all dimensions are large. As a countermeasure, the paper derives the magnitude of the estimation error, which can be used in practice to assess the precision of CCA estimates. Applications of the results to cyclical vs. non-cyclical stocks and to a limestone grassland data set are provided.

econ.EM↗

arXiv2024

The Local to Unity Dynamic Tobit Model

This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive. Surprisingly, despite the presence of censoring, the OLS estimators of the model parameters are consistent. We show that this allows OLS-based inferences to be drawn on the overall persistence of the process (as measured by the sum of the autoregressive coefficients), and for the null of a unit root to be tested in the presence of censoring. Our simulations illustrate that the conventional ADF test substantially over-rejects when the data is generated by a dynamic Tobit with a unit root, whereas our proposed test is correctly sized. We provide an application of our methods to testing for a unit root in the Swiss franc / euro exchange rate, during a period when this was subject to an occasionally binding lower bound.

econ.EM↗

arXiv2023

Asymptotics of Cointegration Tests for High-Dimensional VAR($k$)

The paper studies nonstationary high-dimensional vector autoregressions of order $k$, VAR($k$). Additional deterministic terms such as trend or seasonality are allowed. The number of time periods, $T$, and the number of coordinates, $N$, are assumed to be large and of the same order. Under this regime the first-order asymptotics of the Johansen likelihood ratio (LR), Pillai-Bartlett, and Hotelling-Lawley tests for cointegration are derived: the test statistics converge to nonrandom integrals. For more refined analysis, the paper proposes and analyzes a modification of the Johansen test. The new test for the absence of cointegration converges to the partial sum of the Airy$_1$ point process. Supporting Monte Carlo simulations indicate that the same behavior persists universally in many situations beyond those considered in our theorems. The paper presents empirical implementations of the approach for the analysis of S$\&$P$100$ stocks and of cryptocurrencies. The latter example has a strong presence of multiple cointegrating relationships, while the results for the former are consistent with the null of no cointegration.

econ.EM↗

arXiv2021

Cointegration in large VARs

The paper analyses cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, $N$, and the number of time periods, $T$, are large and of the same order. We propose a way to examine a VAR of order $1$ for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from over-rejection. This is achieved through novel asymptotic theorems for eigenvalues of matrices in the test statistic in the regime of proportionally growing $N$ and $T$. Our theoretical findings are supported by Monte Carlo simulations and an empirical illustration. Moreover, we find a surprising connection with multivariate analysis of variance (MANOVA) and explain why it emerges.

econ.EM↗