arXiv subjects

Tzung Hsuen Khoo

Publications and source records attributed to Tzung Hsuen Khoo.

3 recordsLinked to original sources

arXiv2026

Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data

The paper introduces a multivariate functional areal spatial principal component analysis (mfasPCA) framework, together with multivariate functional Moran's I statistics, to enable the assessment of spatial autocorrelation and dimension reduction for multivariate functional data observed over areal units. The proposed framework is spatial-functional in scope: the functional argument may represent time, age, wavelength, or another ordered continuum, while spatial dependence is introduced across areal units through a spatial weight matrix. The principal component method is defined through a Moran-type spatially weighted criterion. We propose eigenvalue-based permutation tests to assess the significance of spatially structured components. The testing framework includes omnibus tests, componentwise tests with Holm adjustment, and sequential rank-wise tests based on tail sums of eigenvalues. Simulation studies show that mfasPCA captures positive and negative spatial-functional structures and concentrates them in the leading components under the respective autocorrelation regimes. A real-data application illustrates how mfasPCA identifies spatially structured modes of multivariate functional variation.

stat.ME↗

arXiv2026

Generalized dynamic functional principal component analysis

In this paper, we explore dimension reduction for functional time series. We propose a generalized dynamic functional principal component analysis (GDFPCA) which does not rely on spectral density estimation and demonstrates strong empirical performance for both stationary and nonstationary functional time series. We define the generalized dynamic functional principal components (GDFPCs) as static factor time series in a functional dynamic factor model and obtain their multivariate representation from a truncation of the functional dynamic factor model. Estimation is based on a least-squares reconstruction criterion and implemented via a two-step procedure for the coefficient vectors of the loading curves under a basis expansion. We establish mean-square consistency of the reconstructed functional time series under weak stationarity. Simulation studies show that GDFPCA performs comparably to dynamic functional principal component analysis (DFPCA) for stationary data, while providing improved reconstruction accuracy in nonstationary settings, where both DFPCA and functional principal component analysis (FPCA) deteriorate. Applications to real datasets support the empirical advantages observed in the simulations.

stat.ME↗

arXiv2023

A Markov-switching spatio-temporal ARCH model

Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by sudden shocks that may lead to an overestimation of persistence, causing an upward bias in the estimates. Different regime-switching models that have abrupt regime-switching governed by a Markov chain were developed to model volatility in financial time series data. Volatility modelling was also extended to spatially interconnected time series, resulting in spatial variants of ARCH models. This inspired us to propose a Markov switching framework of the spatio-temporal log-ARCH model. In this article, we discuss the Markov-switching extension of the model, the estimation procedure and the smooth inferences of the regimes. The Monte-Carlo simulation studies show that the maximum likelihood estimation method for our proposed model has good finite sample properties. The proposed model was applied to 28 stock indices data that were presumably affected by the 2015-2016 Chinese stock market crash. The results showed that our model is a better fit compared to that of the one-regime counterpart. Furthermore, the smoothed inference of the data indicated the approximate periods where structural breaks occurred. This model can capture structural breaks that simultaneously occur in nearby locations.

stat.ME↗