arXiv subjects

Cristian F. Jiménez-Varón

Publications and source records attributed to Cristian F. Jiménez-Varón.

7 recordsLinked to original sources

arXiv2026

Multiscale Dynamic Dependence Estimation over Networks

In many settings, observed multivariate time series are often nonstationary in nature, i.e., their second order properties vary over time. An additional feature is that their cross-channel dependencies are structured by an underlying network. Together, they give rise to complex interactions between temporal dynamics and network topology. We propose Locally Stationary Wavelet processes on Networks (Net-LSW), a new framework for modelling multiscale, time-varying dependencies that explicitly incorporates the network structure. Unlike traditional multivariate approaches, the Net-LSW process encodes the graph directly in the covariance structure of its random increments. We introduce the concept of local partial correlation graph, mathematically connecting absent edges to zero entries in the time-scale dependent inverse wavelet spectral structure. For inference on the local cross-nodal (partial) dependence, we develop a novel subprocess-based estimation scheme and establish its consistency properties. This new pipeline for network-based nonstationary process modelling, complete with estimation and simulation capabilities that extend outside time-varying vector autoregressive models, is shown to accurately recover evolving dependence structures whilst respecting the underlying graph topology. The analysis of daily stock price volatilities across a global bank network captures multiscale, highly nonstationary dependencies and identifies time-varying systemic shifts during major financial shocks, including Brexit and the COVID-19 pandemic.

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arXiv2026

Interpretable models for forecasting high-dimensional functional time series

We study the modeling and forecasting of high-dimensional functional time series, which can be temporally dependent and cross-sectionally correlated. Central to our implementation is a functional analysis of variance by decomposing high-dimensional functional time series, such as subnational age- and sex-specific mortality observed over years, into two distinct components: a deterministic mean structure and a residual process varying over time. Unlike purely statistical dimensionality-reduction techniques, the functional analysis of variance decomposition provides an interpretable framework by partitioning the series into effects attributable to data-specific factors, such as regional and sex-level variations, and a grand functional mean. From the residual process, we implement a functional factor model to capture the remaining stochastic trends. By combining the forecasts of the residual component with the estimated deterministic structure, we obtain the forecasted curves for high-dimensional functional time series. Illustrated by the age-specific Japanese subnational mortality rates from 1975 to 2023, we evaluate and compare the accuracy of the point and interval forecasts across various forecast horizons. The results demonstrate that leveraging these interpretable components not only clarifies the underlying drivers of the data, but also improves point forecast accuracy by about 25% to 45% compared to an existing method, providing more transparent insights for evidence-based policy decisions, such as accurate modeling of financial costs of length of stay in the old-aged care facilities.

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arXiv2026

Modeling and forecasting subnational age distribution of death counts

Existing mortality forecasting methods focus on age-specific mortality rates, which lie in an unconstrained space and overlook the distributional nature of life-table death counts. Few studies have developed and compared forecasting methods that model the shape and dynamics of the age distribution of deaths, especially at the subnational level, where data quality varies greatly. This paper presents several forecasting methods to model and forecast the subnational age distribution of death counts. The age distribution of death counts has many similarities to probability density functions, which are non-negative and have a constrained integral, and thus live in a constrained nonlinear space. To address the nonlinear nature of objects, we implement a cumulative distribution function transformation that is scale-free and has additional monotonicity. Using subnational Japanese life-table death counts from the Japanese Mortality Database (2025), we evaluate the forecast accuracy of the transformation and forecasting methods. The improved forecast accuracy of life-table death counts implemented here will be of great interest to demographers in estimating regional age-specific survival probabilities and life expectancy, and to actuaries as a foundation for exploring potential applications in determining annuity prices for various ages and maturities.

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arXiv2026

Frequency-Domain Analysis of Time Series with Network-Structured Dependence: Application to Global Bank Connectedness

Financial spillovers in interconnected systems, such as global banking networks, require tools that capture temporal and frequency dynamics, while incorporating the underlying network topology. While current network time series models are developed in the time-domain, frequency-domain approaches, which reveal how cross-nodal dependencies vary across different cycles, remain under-explored. This paper develops a spectral analysis framework that accommodates flexible forms of network dependence, including interactions mediated through intermediate nodes. This ensures that inter-nodal relationships are not restricted to direct connections, a feature crucial for capturing indirect financial spillovers. We define the network time series spectral density, alongside coherence and partial coherence, and propose both parametric and network-constrained nonparametric methods for their estimation. Simulations and theoretical results demonstrate the strong performance of the parametric approach when the data-generating process aligns with the model structure, whereas the nonparametric alternative provides robustness against model misspecification. An application to global bank connectedness shows that the proposed spectral measures capture inter-bank frequency-specific spillover effects, yielding results consistent with existing measures while additionally uncovering richer patterns of volatility transmission that are intimately connected to the network topology.

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arXiv2025

Forecasting density-valued functional panel data

We introduce a statistical method for modeling and forecasting functional panel data represented by multiple densities. Density functions are nonnegative and have a constrained integral and thus do not constitute a linear vector space. We implement a center log-ratio transformation to transform densities into unconstrained functions. These functions exhibit cross-sectional correlation and temporal dependence. Via a functional analysis of variance decomposition, we decompose the unconstrained functional panel data into a deterministic trend component and a time-varying residual component. To produce forecasts for the time-varying component, a functional time series forecasting method, based on the estimation of the long-run covariance, is implemented. By combining the forecasts of the time-varying residual component with the deterministic trend component, we obtain $h$-step-ahead forecast curves for multiple populations. Illustrated by age- and sex-specific life-table death counts in the United States, we apply our proposed method to generate forecasts of the life-table death counts for 51 states.

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arXiv2024

A semi-parametric estimation method for quantile coherence with an application to bivariate financial time series clustering

In multivariate time series analysis, spectral coherence measures the linear dependency between two time series at different frequencies. However, real data applications often exhibit nonlinear dependency in the frequency domain. Conventional coherence analysis fails to capture such dependency. The quantile coherence, on the other hand, characterizes nonlinear dependency by defining the coherence at a set of quantile levels based on trigonometric quantile regression. This paper introduces a new estimation technique for quantile coherence. The proposed method is semi-parametric, which uses the parametric form of the spectrum of a vector autoregressive (VAR) model to approximate the quantile coherence, combined with nonparametric smoothing across quantiles. At a given quantile level, we compute the quantile autocovariance function (QACF) by performing the Fourier inverse transform of the quantile periodograms. Subsequently, we utilize the multivariate Durbin-Levinson algorithm to estimate the VAR parameters and derive the estimate of the quantile coherence. Finally, we smooth the preliminary estimate of quantile coherence across quantiles using a nonparametric smoother. Numerical results show that the proposed estimation method outperforms nonparametric methods. We show that quantile coherence-based bivariate time series clustering has advantages over the ordinary VAR coherence. For applications, the identified clusters of financial stocks by quantile coherence with a market benchmark are shown to have an intriguing and more informative structure of diversified investment portfolios that may be used by investors to make better decisions.

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arXiv2024

Forecasting high-dimensional functional time series: Application to sub-national age-specific mortality

We study the modeling and forecasting of high-dimensional functional time series (HDFTS), which can be cross-sectionally correlated and temporally dependent. We introduce a decomposition of the HDFTS into two distinct components: a deterministic component and a residual component that varies over time. The decomposition is derived through the estimation of two-way functional analysis of variance. A functional time series forecasting method, based on functional principal component analysis, is implemented to produce forecasts for the residual component. By combining the forecasts of the residual component with the deterministic component, we obtain forecast curves for multiple populations. We apply the model to age- and sex-specific mortality rates in the United States, France, and Japan, in which there are 51 states, 95 departments, and 47 prefectures, respectively. The proposed method is capable of delivering more accurate point and interval forecasts in forecasting multi-population mortality than several benchmark methods considered.

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