arXiv subjects

Won-Ki Seo

Publications and source records attributed to Won-Ki Seo.

18 recordsLinked to original sources

arXiv2026

Anthropogenic Forcing, Climate Change, and the Shape of Warming: Statistical Inference for Distributional Cointegration

Anthropogenic forcing components follow different long-run paths, while persistent temperature change can involve distributional changes beyond the mean. Scalar regressions aggregate these components and retain only mean temperature, obscuring how distinct forcing paths relate to persistent distributional change. We develop new testing, estimation, and inference methods for long-run relations between an integrated predictor vector and a density-valued response. These comprise a residual-based test of between-cointegration (whether predictor trends account for all stochastic trends in the response density), a fully modified least-squares estimator of predictor-specific functional responses, and simulation-based inference for interpretable projections. We apply the methods to densities of observed local temperature anomalies and anthropogenic effective radiative forcing divided into CO$_2$ and non-CO$_2$ portfolios. The test results are consistent with persistent movements in these portfolios statistically accounting for the persistent evolution of the anomaly distribution, with no additional stochastic trend detected in the residual. A joint test rejects the common-response restriction imposed by aggregating the two portfolios. The fitted CO$_2$ response mainly shifts mass toward warmer anomalies and increases central concentration, whereas the non-CO$_2$ response produces a smaller shift but greater dispersion and off-center reshaping. Positive fitted mean responses for both portfolios conceal these contrasts, demonstrating the information lost through scalar aggregation.

stat.AP↗

arXiv2026

Inference on common trends in functional time series

We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the nonstationary subspace. We also consider tests of hypotheses on the nonstationary and stationary subspaces themselves. The Hilbert space can be of an arbitrarily large dimension, and our methods remain asymptotically valid even when the time series of interest takes values in a subspace of possibly unknown dimension. This has wide applicability in practice; for example, to cointegrated vector time series that are either high-dimensional or of finite dimension, to high-dimensional factor models that include a finite number of nonstationary factors, to cointegrated curve-valued (or function-valued) time series, and to nonstationary dynamic functional factor models. To illustrate our methods, we include two empirical examples.

econ.EM↗

arXiv2026

Identification-Robust Testing in Endogenous Functional Linear Regression with Weak or Irrelevant Auxiliary Variables

We develop dimension-reduction-free tests for the slope function in functional linear regression when the functional regressor may be endogenous or measured with error. The tests are based on a functional moment condition induced by an auxiliary functional variable and do not require estimation of the slope function, providing a functional analogue of Anderson--Rubin-type moment testing. They remain asymptotically valid under weak or even failed relevance of the auxiliary variable: such relevance affects power, not size. The trade-off is that power is confined to alternatives detectable through the moment operator, a subspace we characterize explicitly. We establish the asymptotic null distribution, consistency against detectable alternatives, and local power under drifting alternatives. We also derive the locally optimal test within a class of weighted test statistics. Feasible critical values for implementation of the tests are obtained from data. Simulations show reliable size control and competitive power, including under weak relevance. We illustrate the method using a functional regression analysis of residential electricity demand and temperature distributions in South Korea.

stat.ME↗

arXiv2026

Random trade timing and power-law tails in realized prices

This paper studies stochastic mechanisms under which light-tailed latent price dynamics yield realized prices with power-law tails. The realized price is modeled as $P_T=e^{X_T}$, where $X$ is a Markov-modulated Lévy process and $T$ is the random time of the next trade. We consider two trade-timing environments. In the intertrade-incidence model, trades occur on a discrete grid with type-dependent probabilities. In the intertrade-time model, the waiting time to the next trade is generalized Erlang, allowing for heterogeneous arrival rates and transaction-completion delays. We show that random trade timing can generate Pareto-type tails, possibly with a logarithmic correction, in realized prices even when the latent price process is light-tailed. In both models, the tail exponent is determined by the least frequent trading type, while the proportions of faster-trading types affect only the scale constant. We also provide sufficient conditions under which these Pareto-type tails sharpen to exact Paretian tails. These results identify random trade timing and heterogeneity in trading behavior as a general mechanism for generating power-law tails in realized prices.

math.PR↗

arXiv2026

Inversion of an analytic operator function through Fredholm quotients and its application

We characterize the inverse of an analytic Fredholm operator-valued function A(z) near an isolated singularity within a general Banach space framework. Our approach relies on the sequential factorization of A(z) via Fredholm quotient operators. By analyzing the properties of these quotient operators near an isolated singularity, we fully characterize the Laurent series expansion of the inverse of A(z) in terms of its Taylor coefficients around the singularity. These theoretical results are subsequently applied to characterize the solution of a general autoregressive law of motion in a Banach space.

math.SP↗

arXiv2026

Testing for integer integration in functional time series

We develop a statistical testing procedure to examine whether the curve-valued time series of interest is integrated of order d for an integer d. The proposed procedure can distinguish between integer-integrated time series and fractionally-integrated ones, and it has broad applicability in practice. Monte Carlo simulation experiments show that the proposed testing procedure performs reasonably well. We apply our methodology to Canadian yield curve data and French sub-national age-specific mortality data. We find evidence that these time series are mostly integrated of order one, while some have fractional orders exceeding or falling below one.

stat.ME↗

arXiv2025

Functional Regression with Nonstationarity and Error Contamination: Application to the Economic Impact of Climate Change

This paper studies a regression model with functional dependent and explanatory variables, both of which exhibit nonstationary dynamics. The model assumes that the nonstationary stochastic trends of the dependent variable are explained by those of the explanatory variables, and hence that there exists a stable long-run relationship between the two variables despite their nonstationary behavior. We also assume that the functional observations may be error-contaminated. We develop novel autocovariance-based estimation and inference methods for this model. The methodology is broadly applicable to economic and statistical functional time series with nonstationary dynamics. To illustrate our methodology and its usefulness, we apply it to evaluating the global economic impact of climate change, an issue of intrinsic importance.

stat.ME↗

arXiv2025

Optimal linear prediction with functional observations: Why you can use a simple post-dimension reduction estimator

We study the optimal linear prediction of a random function that takes values in an infinite dimensional Hilbert space. We begin by characterizing the mean square prediction error (MSPE) associated with a linear predictor and discussing the minimal achievable MSPE. This analysis reveals that, in general, there are multiple non-unique linear predictors that minimize the MSPE, and even if a unique solution exists, consistently estimating it from finite samples is generally impossible. Nevertheless, we can define asymptotically optimal linear operators whose empirical MSPEs approach the minimal achievable level as the sample size increases. We show that, interestingly, standard post-dimension reduction estimators, which have been widely used in the literature, attain such asymptotic optimality under minimal conditions.

math.ST↗

arXiv2025

Functional Linear Projection and Impulse Response Analysis

This paper proposes econometric methods for studying how economic variables respond to function-valued shocks. Our methods are developed based on linear projection estimation of predictive regression models with a function-valued predictor and other control variables. We show that the linear projection coefficient associated with the functional variable allows for the impulse response interpretation in a functional structural vector autoregressive model under a certain identification scheme, similar to well-known Sims' (1972) causal chain, but with nontrivial complications in our functional setup. A novel estimator based on an operator Schur complement is proposed and its asymptotic properties are studied. We illustrate its empirical applicability with two examples involving functional variables: economy sentiment distributions and functional monetary policy shocks.

econ.EM↗

arXiv2025

Nonlinear Temperature Sensitivity of Residential Electricity Demand: Evidence from a Distributional Regression Approach

We estimate the temperature sensitivity of residential electricity demand during extreme temperature events using the distribution-to-scalar regression model. Rather than relying on simple averages or individual quantile statistics of raw temperature data, we construct distributional summaries, such as probability density, hazard rate, and quantile functions, to retain a more comprehensive representation of temperature variation. This approach not only utilizes richer information from the underlying temperature distribution but also enables the examination of extreme temperature effects that conventional models fail to capture. Additionally, recognizing that distribution functions are typically estimated from limited discrete observations and may be subject to measurement errors, our econometric framework explicitly addresses this issue. Empirical findings from the hazard-to-demand model indicate that residential electricity demand exhibits a stronger nonlinear response to cold waves than to heat waves, while heat wave shocks demonstrate a more pronounced incremental effect. Moreover, the temperature quantile-to-demand model produces largely insignificant demand response estimates, attributed to the offsetting influence of two counteracting forces.

econ.EM↗

arXiv2024

Fractionally integrated curve time series with cointegration

We introduce methods and theory for fractionally cointegrated curve time series. We develop a variance-ratio test to determine the dimensions associated with the nonstationary and stationary subspaces. For each subspace, we apply a local Whittle estimator to estimate the long-memory parameter and establish its consistency. A Monte Carlo study of finite-sample performance is included, along with two empirical applications.

math.ST↗

arXiv2023

Functional instrumental variable regression with an application to estimating the impact of immigration on native wages

Functional linear regression gets its popularity as a statistical tool to study the relationship between function-valued response and exogenous explanatory variables. However, in practice, it is hard to expect that the explanatory variables of interest are perfectly exogenous, due to, for example, the presence of omitted variables and measurement error. Despite its empirical relevance, it was not until recently that this issue of endogeneity was studied in the literature on functional regression, and the development in this direction does not seem to sufficiently meet practitioners' needs; for example, this issue has been discussed with paying particular attention on consistent estimation and thus distributional properties of the proposed estimators still remain to be further explored. To fill this gap, this paper proposes new consistent FPCA-based instrumental variable estimators and develops their asymptotic properties in detail. Simulation experiments under a wide range of settings show that the proposed estimators perform considerably well. We apply our methodology to estimate the impact of immigration on native wages.

econ.EM↗

arXiv2023

Functional Principal Component Analysis for Cointegrated Functional Time Series

Functional principal component analysis (FPCA) has played an important role in the development of functional time series analysis. This note investigates how FPCA can be used to analyze cointegrated functional time series and proposes a modification of FPCA as a novel statistical tool. Our modified FPCA not only provides an asymptotically more efficient estimator of the cointegrating vectors, but also leads to novel FPCA-based tests for examining essential properties of cointegrated functional time series.

stat.ME↗

arXiv2023

Fredholm inversion around a singularity: application to autoregressive time series in Banach space

This paper consider inverting a holomorphic Fredholm operator pencil. Specifically, we provide necessary and sufficient conditions for the inverse of a holomorphic Fredholm operator pencil to have a simple pole and a second order pole. Based on those results, a closed-form expression of the Laurent expansion of the inverse around an isolated singularity is obtained in each case. As an application of the results, we obtain a suitable extension of the Granger-Johansen representation theory for random sequences taking values in a separable Banach space. Due to our closed-form expression of the inverse, we may fully characterize I(1) and I(2) solutions except a term that depends on initial values.

math.FA↗

arXiv2021

Cointegration and Representation of Cointegrated Autoregressive Processes in Banach Spaces

We extend the notion of cointegration for time series taking values in a potentially infinite dimensional Banach space. Examples of such time series include stochastic processes in C[0,1] equipped with the supremum distance and those in a finite dimensional vector space equipped with a non-Euclidean distance. We then develop versions of the Granger-Johansen representation theorems for I(1) and I(2) autoregressive (AR) processes taking values in such a space. To achieve our goal, we first note that an AR(p) law of motion can be characterized by a linear operator pencil via the companion form representation, and then study the spectral properties of a linear operator pencil to obtain a necessary and sufficient condition for a given AR(p) law of motion to admit I(1) or I(2) solutions. These operator-theoretic results form a fundamental basis for our representation theorems. Furthermore, it is shown that our operator-theoretic approach is in fact a closely related extension of the conventional approach taken in a Euclidean space setting. Our theoretical results may be especially relevant in a recently growing literature on functional time series analysis in Banach spaces.

math.FA↗

arXiv2020

Tail behavior of stopped Lévy processes with Markov modulation

This article concerns the tail probabilities of a light-tailed Markov-modulated Lévy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of the spectral abscissa of a certain matrix-valued function. We illustrate the use of our results with an application to the stationary distribution of wealth in a simple economic model in which agents with constant absolute risk aversion are subject to random mortality and income fluctuation.

math.PR↗

arXiv2019

Representation of I(1) and I(2) autoregressive Hilbertian processes

We extend the Granger-Johansen representation theorems for I(1) and I(2) vector autoregressive processes to accommodate processes that take values in an arbitrary complex separable Hilbert space. This more general setting is of central relevance for statistical applications involving functional time series. We first obtain a range of necessary and sufficient conditions for a pole in the inverse of a holomorphic index-zero Fredholm operator pencil to be of first or second order. Those conditions form the basis for our development of I(1) and I(2) representations of autoregressive Hilbertian processes. Cointegrating and attractor subspaces are characterized in terms of the behavior of the autoregressive operator pencil in a neighborhood of one.

math.ST↗

arXiv2018

Cointegrated Density-Valued Linear Processes

In data rich environments we may sometimes deal with time series that are probability density-function valued, such as observations of cross-sectional income distributions over time. To apply the methods of functional time series analysis to such observations, we should first embed them in a linear space in which the essential properties of densities are preserved under addition and scalar multiplication. Bayes Hilbert spaces provide one way to achieve this embedding. In this paper we investigate the use of Bayes Hilbert spaces to model cointegrated density-valued linear processes. We develop an I(1) representation theory for cointegrated linear processes in a Bayes Hilbert space, and adapt existing statistical procedures for estimating the corresponding attractor space to a Bayes Hilbert space setting. We revisit empirical applications involving earnings and wage densities to illustrate the utility of our approach.

math.ST↗