arXiv subjects

Jonas Krampe

Publications and source records attributed to Jonas Krampe.

9 recordsLinked to original sources

arXiv2024

Decomposing Global Bank Network Connectedness: What is Common, Idiosyncratic and When?

We propose a novel approach to estimate high-dimensional global bank network connectedness in both the time and frequency domains. By employing a factor model with sparse VAR idiosyncratic components, we decompose system-wide connectedness (SWC) into two key drivers: (i) common component shocks and (ii) idiosyncratic shocks. We also provide bootstrap confidence bands for all SWC measures. Furthermore, spectral density estimation allows us to disentangle SWC into short-, medium-, and long-term frequency responses to these shocks. We apply our methodology to two datasets of daily stock price volatilities for over 90 global banks, spanning the periods 2003-2013 and 2014-2023. Our empirical analysis reveals that SWC spikes during global crises, primarily driven by common component shocks and their short term effects. Conversely, in normal times, SWC is largely influenced by idiosyncratic shocks and medium-term dynamics.

econ.EM↗

arXiv2024

Frequency Domain Statistical Inference for High-Dimensional Time Series

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence or the partial coherence, encode comprehensively the complex linear relations between the component processes of the multivariate system. In this paper, we develop inference procedures for such parameters in a high-dimensional, time series setup. Towards this goal, we first focus on the derivation of consistent estimators of the coherence and, more importantly, of the partial coherence which possess manageable limiting distributions that are suitable for testing purposes. Statistical tests of the hypothesis that the maximum over frequencies of the coherence, respectively, of the partial coherence, do not exceed a prespecified threshold value are developed. Our approach allows for testing hypotheses for individual coherences and/or partial coherences as well as for multiple testing of large sets of such parameters. In the latter case, a consistent procedure to control the false discovery rate is developed. The finite sample performance of the inference procedures introduced is investigated by means of simulations and applications to the construction of graphical interaction models for brain connectivity based on EEG data are presented.

stat.ME↗

arXiv2022

Inverse covariance operators of multivariate nonstationary time series

For multivariate stationary time series many important properties, such as partial correlation, graphical models and autoregressive representations are encoded in the inverse of its spectral density matrix. This is not true for nonstationary time series, where the pertinent information lies in the inverse infinite dimensional covariance matrix operator associated with the multivariate time series. This necessitates the study of the covariance of a multivariate nonstationary time series and its relationship to its inverse. We show that if the rows/columns of the infinite dimensional covariance matrix decay at a certain rate then the rate (up to a factor) transfers to the rows/columns of the inverse covariance matrix. This is used to obtain a nonstationary autoregressive representation of the time series and a Baxter-type bound between the parameters of the autoregressive infinite representation and the corresponding finite autoregressive projection. The aforementioned results lay the foundation for the subsequent analysis of locally stationary time series. In particular, we show that smoothness properties on the covariance matrix transfer to (i) the inverse covariance (ii) the parameters of the vector autoregressive representation and (iii) the partial covariances. All results are set up in such a way that the constants involved depend only on the eigenvalue of the covariance matrix and can be applied in the high-dimensional settings with non-diverging eigenvalues.

math.ST↗

arXiv2022

Factor Models with Sparse VAR Idiosyncratic Components

We reconcile the two worlds of dense and sparse modeling by exploiting the positive aspects of both. We employ a factor model and assume {the dynamic of the factors is non-pervasive while} the idiosyncratic term follows a sparse vector autoregressive model (VAR) {which allows} for cross-sectional and time dependence. The estimation is articulated in two steps: first, the factors and their loadings are estimated via principal component analysis and second, the sparse VAR is estimated by regularized regression on the estimated idiosyncratic components. We prove the consistency of the proposed estimation approach as the time and cross-sectional dimension diverge. In the second step, the estimation error of the first step needs to be accounted for. Here, we do not follow the naive approach of simply plugging in the standard rates derived for the factor estimation. Instead, we derive a more refined expression of the error. This enables us to derive tighter rates. We discuss the implications of our model for forecasting, factor augmented regression, bootstrap of factor models, and time series dependence networks via semi-parametric estimation of the inverse of the spectral density matrix.

stat.ME↗

arXiv2021

Structural Inference in Sparse High-Dimensional Vector Autoregressions

We consider statistical inference for impulse responses in sparse, structural high-dimensional vector autoregressive (SVAR) systems. We introduce consistent estimators of impulse responses in the high-dimensional setting and suggest valid inference procedures for the same parameters. Statistical inference in our setting is much more involved since standard procedures, like the delta-method, do not apply. By using local projection equations, we first construct a de-sparsified version of regularized estimators of the moving average parameters associated with the VAR system. We then obtain estimators of the structural impulse responses by combining the aforementioned de-sparsified estimators with a non-regularized estimator of the contemporaneous impact matrix, also taking into account the high-dimensionality of the system. We show that the distribution of the derived estimators of structural impulse responses has a Gaussian limit. We also present a valid bootstrap procedure to estimate this distribution. Applications of the inference procedure in the construction of confidence intervals for impulse responses as well as in tests for forecast error variance decomposition are presented. Our procedure is illustrated by means of simulations.

stat.ME↗

arXiv2021

Estimation of the Distribution of the Individual Reproduction Number: The Case of the COVID-19 Pandemic

We investigate the problem of estimating the distribution of the individual reproduction number governing the COVID-19 pandemic. Under the assumption that this random variable follows a Negative Binomial distribution, we focus on constructing estimators of the parameters of this distribution using reported infection data and taking into account issues like under-reporting or the time behavior of the infection and of the reporting processes. To this end, we extract information from regionally dissaggregated data reported by German health authorities, in order to estimate not only the mean but also the variance of the distribution of the individual reproduction number. In contrast to the mean, the latter parameter also depends on the unknown under-reporting rate of the pandemic. The estimates obtained allow not only for a better understanding of the time-varying behavior of the expected value of the individual reproduction number but also of its dispersion, for the construction of bootstrap confidence intervals and for a discussion of the implications of different policy interventions. Our methodological investigations are accompanied by an empirical study of the development of the COVID-19 pandemic in Germany, which shows a strong overdispersion of the individual reproduction number.

stat.AP↗

arXiv2020

Statistical Estimation of High-Dimensional Vector Autoregressive Models

High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for fitting sparse VAR models to such time series. Attention is paid to the different sparsity assumptions imposed on the VAR parameters and how these sparsity assumptions are related to the particular consistency properties of the estimators established. A sparsity scheme for high-dimensional VAR models is proposed which is found to be more appropriate for the time series setting considered. Furthermore, it is shown that, under this sparsity setting, threholding extents the consistency properties of regularized estimators to a wide range of matrix norms. Among other things, this enables application of the VAR parameters estimators to different inference problems, like forecasting or estimating the second-order characteristics of the underlying VAR process. Extensive simulations compare the finite sample behavior of the different regularized estimators proposed using a variety of performance criteria.

stat.ML↗

arXiv2019

Time Series Modeling on Dynamic Networks

This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled by a multivariate doubly stochastic time series framework, that is we assume linear processes for which the coefficient matrices are stochastic processes themselves. We explicitly allow for dependence in the dynamics of the coefficient matrices as well as between these two stochastic processes. This framework allows for a separate modeling of the attributes and the underlying network. In this setting, we define network autoregressive models and discuss their stationarity conditions. Furthermore, an estimation approach is discussed in a low- and high-dimensional setting and how this can be applied to forecasting. The finite sample behavior of the forecast approach is investigated. This approach is applied to real data whereby the goal is to forecast the GDP of 33 economies.

stat.ME↗

arXiv2017

EstimatedWold Representation and Spectral Density-Driven Bootstrap for Time Series

The second-order dependence structure of purely nondeterministic stationary process is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process. This relation together with some spectral density estimator is used in order to obtain consistent estimators of these coefficients. A spectral density-driven bootstrap for time series is then developed which uses the entire sequence of estimated MA coefficients together with appropriately generated pseudo innovations in order to obtain a bootstrap pseudo time series. It is shown that if the underlying process is linear and if the pseudo innovations are generated by means of an i.i.d. wild bootstrap which mimics, to the necessary extent, the moment structure of the true innovations, this bootstrap proposal asymptotically works for a wide range of statistics. The relations of the proposed bootstrap procedure to some other bootstrap procedures, including the autoregressive-sieve bootstrap, are discussed. It is shown that the latter is a special case of the spectral density-driven bootstrap, if a parametric autoregressive spectral density estimator is used. Simulations investigate the performance of the new bootstrap procedure in finite sample situations. Furthermore, a real-life data example is presented.

math.ST↗