arXiv subjects

Haeran Cho

Publications and source records attributed to Haeran Cho.

At least 19 recordsLinked to original sources

arXiv2026

Detection and Mode-Identification of Multiple Change Points in Tensor Factor Models

We study the problems arising from modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model with multiple structural change points. First, we propose an algorithm for detecting the multiple change points, which utilizes the low-rank structure of the data for statistical and computational efficiency. Also, the multi-dimensional array setting poses unique challenges, as some changes are associated with a subset of the modes, and the changes in different modes may interact with one another. Recognizing these, we investigate the problem of identifying each change with the tensor modes post-segmentation. To this end, we formalize the mode-identifiability of each change and propose an algorithm for detecting the modes at which the data are undergoing a mode-identifiable shift. We establish the consistency of both change point detection and mode-identification methods under a weak moment condition, and demonstrate their good performance on simulated datasets where, in particular, it is shown that the mode-identification step can improve the post-segmentation estimation of the mode-wise loading space. Additionally we analyze the datasets on New York City taxi usage and Fama--French portfolio returns using the proposed suite of methods.

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arXiv2025

Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series

We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as well as their remaining interconnectedness using a sparse VAR model. To handle heavy tails, we propose an element-wise data truncation step followed by a two-stage estimation procedure for estimating the latent factors and the VAR parameter matrices. Assuming the existence of the $(2 + 2\epsilon)$-th moment only for some $\epsilon \in (0, 1)$, we derive the rates of estimation which, making explicit the effect of heavy tails through $\epsilon$, are comparable to the rates attainable in light-tailed settings as $\epsilon \to 1$. Numerically, we demonstrate the competitive performance of the proposed estimators on simulated datasets and in an application to forecasting macroeconomics indicators.

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arXiv2025

Covariance scanning for adaptively optimal change point detection in high-dimensional linear models

This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed by the sparsity of the covariance-weighted differential parameter. This form of "inherent sparsity" captures a delicate interplay between the covariance structure of the regressors and the change in regression coefficients on the detectability of a change point. Complementing the lower bounds, we introduce two covariance scanning-based methods, McScan and QcSan, which achieve minimax optimal performance (up to possible logarithmic factors) in the sparse and the dense regimes, respectively. In particular, QcScan is the first method shown to achieve consistency in the dense regime and further, we devise a combined procedure which is adaptively minimax optimal across sparse and dense regimes without the knowledge of the sparsity. Computationally, covariance scanning-based methods avoid costly computation of Lasso-type estimators and attain worst-case computation complexity that is linear in the dimension and sample size. Additionally, we consider the post-detection estimation of the differential parameter and the refinement of the change point estimator. Simulation studies support the theoretical findings and demonstrate the computational and statistical efficiency of the proposed covariance scanning methods.

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arXiv2024

Moving sum procedure for multiple change point detection in large factor models

This paper proposes a moving sum methodology for detecting multiple change points in high-dimensional time series under a factor model, where changes are attributed to those in loadings as well as emergence or disappearance of factors. We establish the asymptotic null distribution of the proposed test for family-wise error control, and show the consistency of the procedure for multiple change point estimation. Simulation studies and an application to a large dataset of volatilities demonstrate the competitive performance of the proposed method.

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arXiv2024

Tail-robust factor modelling of vector and tensor time series in high dimensions

We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce extreme observations with non-negligible probability. We propose to combine a two-step procedure for tensor decomposition with data truncation, which is easy to implement and does not require an iterative search for a numerical solution. Departing away from the light-tail assumptions often adopted in the time series factor modelling literature, we derive the consistency and asymptotic normality of the proposed estimators while assuming the existence of the $(2 + 2\epsilon)$-th moment only for some $\epsilon \in (0, 1)$. Our rates explicitly depend on $\eps$ characterising the effect of heavy tails, and on the chosen level of truncation. We also propose a consistent criterion for determining the number of factors. Simulation studies and applications to two macroeconomic datasets demonstrate the good performance of the proposed estimators.

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arXiv2024

Estimation and Inference for Change Points in Functional Regression Time Series

In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is computationally efficient as well as achieving consistency in multiple change point detection. This algorithm utilizes the predictive power of piece-wise constant functional linear regression models in the reproducing kernel Hilbert space framework. We further propose a refinement step that improves the localization rate of the initial estimator output by FRBS, and derive asymptotic distributions of the refined estimators for two different regimes determined by the magnitude of a change. To facilitate the construction of confidence intervals for underlying change points based on the limiting distribution, we propose a consistent block-type long-run variance estimator. Our theoretical justifications for the proposed approach accommodate temporal dependence and heavy-tailedness in both the functional covariates and the measurement errors. Empirical effectiveness of our methodology is demonstrated through extensive simulation studies and an application to the Standard and Poor's 500 index dataset.

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arXiv2024

Detection and inference of changes in high-dimensional linear regression with non-sparse structures

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised maximum likelihood-type estimation and then contrast them for change point detection. Contrary to this common practice, we show that the exact sparsity of neither regression parameters nor their differences, a.k.a.\ differential parameters, is necessary for consistency in multiple change point detection. In fact, both statistically and computationally, better efficiency is attained by a simple strategy that scans for large discrepancies in local covariance between the regressors and the response. We go a step further and propose a suite of tools for directly inferring about the differential parameters post-segmentation, which are applicable even when the regression parameters themselves are non-sparse. Theoretical investigations are conducted under general conditions permitting non-Gaussianity, temporal dependence and ultra-high dimensionality. Numerical results from simulated and macroeconomic datasets demonstrate the competitiveness and efficacy of the proposed methods. Implementation of all methods is provided in the R package \texttt{inferchange} on GitHub.

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arXiv2023

Nonparametric data segmentation in multivariate time series via joint characteristic functions

Modern time series data often exhibit complex dependence and structural changes which are not easily characterised by shifts in the mean or model parameters. We propose a nonparametric data segmentation methodology for multivariate time series termed NP-MOJO. By considering joint characteristic functions between the time series and its lagged values, NP-MOJO is able to detect change points in the marginal distribution, but also those in possibly non-linear serial dependence, all without the need to pre-specify the type of changes. We show the theoretical consistency of NP-MOJO in estimating the total number and the locations of the change points, and demonstrate the good performance of NP-MOJO against a variety of change point scenarios. We further demonstrate its usefulness in applications to seismology and economic time series.

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arXiv2023

fnets: An R Package for Network Estimation and Forecasting via Factor-Adjusted VAR Modelling

The package fnets for the R language implements the suite of methodologies proposed by Barigozzi et al. (2022) for the network estimation and forecasting of high-dimensional time series under a factor-adjusted vector autoregressive model, which permits strong spatial and temporal correlations in the data. Additionally, we provide tools for visualising the networks underlying the time series data after adjusting for the presence of factors. The package also offers data-driven methods for selecting tuning parameters including the number of factors, vector autoregressive order and thresholds for estimating the edge sets of the networks of interest in time series analysis. We demonstrate various features of fnets on simulated datasets as well as real data on electricity prices.

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arXiv2022

High-dimensional data segmentation in regression settings permitting temporal dependence and non-Gaussianity

We propose a data segmentation methodology for the high-dimensional linear regression problem where regression parameters are allowed to undergo multiple changes. The proposed methodology, MOSEG, proceeds in two stages: first, the data are scanned for multiple change points using a moving window-based procedure, which is followed by a location refinement stage. MOSEG enjoys computational efficiency thanks to the adoption of a coarse grid in the first stage, and achieves theoretical consistency in estimating both the total number and the locations of the change points, under general conditions permitting serial dependence and non-Gaussianity. We also propose MOSEG.MS, a multiscale extension of MOSEG which, while comparable to MOSEG in terms of computational complexity, achieves theoretical consistency for a broader parameter space where large parameter shifts over short intervals and small changes over long stretches of stationarity are simultaneously allowed. We demonstrate good performance of the proposed methods in comparative simulation studies and in an application to predicting the equity premium.

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arXiv2022

Capturing usage patterns in bike sharing system via multilayer network fused Lasso

Data collected from a bike-sharing system exhibit complex temporal and spatial features. We analyze shared-bike usage data collected in three large cities at the level of individual stations, accounting for station-specific behavior and covariate effects. For this, we adopt a penalized regression approach with a multilayer network fused Lasso penalty. These fusion penalties are imposed on networks which embed spatio-temporal linkages, and capture the homogeneity in bike usage that is attributed to intricate spatio-temporal features without arbitrarily partitioning the data. On the real-life datasets, we demonstrate that the proposed approach yields competitive predictive performance and provides a new interpretation of the data.

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arXiv2022

Moving sum procedure for change point detection under piecewise linearity

We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. Theoretically, it controls the family-wise error rate at a given significance level asymptotically and achieves consistency in multiple change point detection, as well as matching the minimax optimal rate of estimation when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is $O(n)$ which, combined with its good performance on simulated datasets, making it highly attractive in comparison with the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics.

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arXiv2022

Robust multiscale estimation of time-average variance for time series segmentation

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often required in order to distinguish genuine changes from random fluctuations due to the noise. When serial dependence is present, using a single estimator of the noise level may not be appropriate. Instead, it is proposed to adopt a scale-dependent time-average variance constant that depends on the length of the data section in consideration, to gauge the level of the noise therein. Accordingly, an estimator that is robust to the presence of multiple mean shifts is developed. The consistency of the proposed estimator is shown under general assumptions permitting heavy-tailedness, and its use with two widely adopted data segmentation algorithms, the moving sum and the wild binary segmentation procedures, is discussed. The performance of the proposed estimator is illustrated through extensive simulation studies and on applications to the house price index and air quality data sets.

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arXiv2022

High-dimensional time series segmentation via factor-adjusted vector autoregressive modelling

Vector autoregressive (VAR) models are popularly adopted for modelling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modelling, the number of parameters grow quadratically with the dimensionality which necessitates the sparsity assumption in high dimensions. However, it is debatable whether such an assumption is adequate for handling datasets exhibiting strong serial and cross-sectional correlations. We propose a piecewise stationary time series model that simultaneously allows for strong correlations as well as structural changes, where pervasive serial and cross-sectional correlations are accounted for by a time-varying factor structure, and any remaining idiosyncratic dependence between the variables is handled by a piecewise stationary VAR model. We propose an accompanying two-stage data segmentation methodology which fully addresses the challenges arising from the latency of the component processes. Its consistency in estimating both the total number and the locations of the change points in the latent components, is established under conditions considerably more general than those in the existing literature. We demonstrate the competitive performance of the proposed methodology on simulated datasets and an application to US blue chip stocks data.

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arXiv2022

FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series

We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by {\it common} factors, models the remaining {\it idiosyncratic} dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i) factor-adjustment via dynamic principal component analysis, (ii) estimation of the latent VAR process via $\ell_1$-regularised Yule-Walker estimator, and (iii) estimation of partial correlation and long-run partial correlation matrices. In doing so, we learn three networks underpinning the VAR process, namely a directed network representing the Granger causal linkages between the variables, an undirected one embedding their contemporaneous relationships and finally, an undirected network that summarises both lead-lag and contemporaneous linkages. In addition, FNETS provides a suite of methods for forecasting the factor-driven and the idiosyncratic VAR processes. Under general conditions permitting tails heavier than the Gaussian one, we derive uniform consistency rates for the estimators in both network estimation and forecasting, which hold as the dimension of the panel and the sample size diverge. Simulation studies and real data application confirm the good performance of FNETS.

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arXiv2021

Bootstrap confidence intervals for multiple change points based on moving sum procedures

The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum statistics is derived, where the limit distributions differ depending on whether the corresponding size of changes is local, i.e. tends to zero as the sample size increases, or fixed. A bootstrap procedure for confidence interval generation is proposed which adapts to the unknown magnitude of changes and guarantees asymptotic validity both for local and fixed changes. Simulation studies show good performance of the proposed bootstrap procedure, and some discussions about how it can be extended to serially dependent errors is provided.

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arXiv2021

High-dimensional GARCH process segmentation with an application to Value-at-Risk

Models for financial risk often assume that underlying asset returns are stationary. However, there is strong evidence that multivariate financial time series entail changes not only in their within-series dependence structure, but also in the cross-sectional dependence among them. In particular, the stressed Value-at-Risk of a portfolio, a popularly adopted measure of market risk, cannot be gauged adequately unless such structural breaks are taken into account in its estimation. We propose a method for consistent detection of multiple change points in high-dimensional GARCH panel data set where both individual GARCH processes and their correlations are allowed to change over time. We prove its consistency in multiple change point estimation, and demonstrate its good performance through simulation studies and an application to the Value-at-Risk problem on a real dataset. Our methodology is implemented in the R package segMGarch, available from CRAN.

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arXiv2020

Data segmentation algorithms: Univariate mean change and beyond

Data segmentation a.k.a. multiple change point analysis has received considerable attention due to its importance in time series analysis and signal processing, with applications in a variety of fields including natural and social sciences, medicine, engineering and finance. In the first part of this survey, we review the existing literature on the canonical data segmentation problem which aims at detecting and localising multiple change points in the mean of univariate time series. We provide an overview of popular methodologies on their computational complexity and theoretical properties. In particular, our theoretical discussion focuses on the separation rate relating to which change points are detectable by a given procedure, and the localisation rate quantifying the precision of corresponding change point estimators, and we distinguish between whether a homogeneous or multiscale viewpoint has been adopted in their derivation. We further highlight that the latter viewpoint provides the most general setting for investigating the optimality of data segmentation algorithms. Arguably, the canonical segmentation problem has been the most popular framework to propose new data segmentation algorithms and study their efficiency in the last decades. In the second part of this survey, we motivate the importance of attaining an in-depth understanding of strengths and weaknesses of methodologies for the change point problem in a simpler, univariate setting, as a stepping stone for the development of methodologies for more complex problems. We illustrate this with a range of examples showcasing the connections between complex distributional changes and those in the mean. We also discuss extensions towards high-dimensional change point problems where we demonstrate that the challenges arising from high dimensionality are orthogonal to those in dealing with multiple change points.

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