Tuesday, Aug 4: 4:00 PM - 5:50 PM
6040
Contributed Papers
Thomas M. Menino Convention & Exhibition Center
Room: CC-156B
Main Sponsor
Business and Economic Statistics Section
Presentations
In this paper, we investigate the asymptotic distribution of a change-point
estimator for piecewise stationary time series across different magnitudes of
break sizes. Specifically, we examine break sizes of order O(1/n^α) for 0 <
α < 1/2, α = 1/2, and α > 1/2, corresponding to large, moderate, and small
break sizes, respectively, where n denotes the sample size. Our results reveal
that the asymptotic distributions in these three regimes differ but are all linked
to the maximizer of certain functions of a two-sided drifted Brownian motion.
To address the practical challenge of unknown break sizes, we introduce an
asymptotically pivotal statistic that is robust across the whole range of break
size regimes on α ∈ [0,∞). This statistic provides a unified approach for
constructing confidence intervals for the change-point without requiring prior
knowledge of the break size. Simulation studies show that the asymptotic
inference performs well under different break sizes, while the pivotal statistic
demonstrates better performance in most scenarios. Applications to financial
time series further highlight the practical relevance of the proposed inference
methods.
Keywords
piecewise stationary time series models
structural break
pivotal statistic
This paper studies quasi-maximum likelihood estimation for ARMA(p,q) models under weakly dependent innovation structures, with emphasis on CLT-based inference and its practical behavior across different shock designs. The classical i.i.d. innovation setting is used only as a benchmark for validating the estimation and simulation framework. The main focus is on nontrivial innovation structures, including conditionally heteroskedastic and other weakly dependent cases, together with boundary designs that violate key assumptions. Within this framework, we examine the asymptotic normal approximation for the QMLE and the role of robust covariance estimation for inference. Monte Carlo results show that when the underlying innovation conditions are compatible with the inferential framework, standardized estimators are close to normal and coverage improves with sample size. In contrast, when key assumptions fail, bias persists and interval performance deteriorates even when dispersion is adjusted. The study provides a focused view of how CLT-based inference for ARMA QMLE behaves under benchmark, admissible, and failure cases, and clarifies the practical limits of the methodology.
Keywords
ARMA models
Quasi-maximum likelihood estimation
central limit theorem
HAC inference
Monte Carlo simulation
Innovation mixing with summable coefficients
We study one particular type of multivariate spatial autoregression (MSAR) model with diverging dimensions in both responses and covariates. This makes the usual MSAR models no longer applicable due to the high computational cost. To address this issue, we propose a factor-augmented spatial autoregression (FSAR) model. FSAR is a special case of MSAR but with a novel factor structure imposed on the high-dimensional random error vector. The latent factors of FSAR are assumed to be of a fixed dimension. Therefore, they can be estimated consistently by the diversified projections method, as long as the dimension of the multivariate response is diverging. Once the fixed-dimensional latent factors are consistently estimated, they are then fed back into the original SAR model and serve as exogenous covariates. This leads to a novel FSAR model. Thereafter, different components of the high-dimensional response can be modeled separately. To handle the high-dimensional feature, a smoothly clipped absolute deviation (SCAD) type penalized estimator is developed for each response component. We show theoretically that the resulting SCAD estimator is uniformly selection consistent, as long as the tuning parameter is selected appropriately. For practical selection of the tuning parameter, a novel BIC method is developed. Extensive numerical studies are conducted to demonstrate the finite sample performance of the proposed method.
Keywords
Diversified Projections
Factor-Augmented Maximum Likelihood Estimator
High-Dimensional Spatial Data
Latent Factor Model
A novel methodology is developed and justified to consistently test for long-horizon
return predictability based on realized variance. To accomplish this, a parametric
transaction-level model is proposed for the continuous-time log price process based
on a pure-jump point process. The model determines the returns and realized variance
at any level of aggregation with properties shown to be consistent with the stylized
facts in empirical finance. Under the model, the long-memory parameter propagates
unchanged from the transaction-level drift to the calendar-time returns and the realized
variance, leading endogenously to a balanced predictive regression equation. An
asymptotic framework using power-law aggregation is also proposed in the predictive
regression. Within this framework, a hypothesis test is proposed for long-horizon return
predictability which is asymptotically correctly sized and consistent.
Keywords
Return predictability
Long memory
Predictive regression
Point process
High frequency
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional difficulty is summarizing the estimated evolving dependence structure for downstream decision-making tasks. We propose a Bayesian approach based on a low-rank factor representation, with latent states evolving under a dynamic shrinkage prior and observation errors following a multivariate factor stochastic volatility model. This specification allows locally adaptive regularization of the estimated correlation structure over time and informative uncertainty quantification. We establish, to our knowledge, a first-of-its-kind posterior contraction result for dynamically regularized Bayesian models, showing contraction around the true model parameters at an explicit rate under averaged Hellinger distance. To summarize the estimated correlation matrices, we build on the information-theoretic concept of total correlation to obtain a scalar measure of cross-sectional dependence. Simulation studies show improved accuracy and responsiveness relative to competing methods in a range of challenging scenarios. We then apply our method to monitoring the correlation evolution of equity portfolios during periods of financial market stress, providing an ex post framework for assessing the changing benefits of diversification in backtesting analyses.
Keywords
Bayesian time series
dynamic shrinkage prior
posterior contraction
financial risk management
backtesting
Speaker
Daniel Coulson, Cornell University
Co-Author(s)
Martin Wells, Department of Statistics and Data Science, Cornell University
David Matteson, Cornell University & National Institute of Statistical Sciences
Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in scale-free networks often lack a strong theoretical foundation. In this paper, we introduce a new framework for analyzing the asymptotic distribution of estimators for degree tail indices in scale-free inhomogeneous random graphs. Our framework leverages the relationship between the large weights and large degrees of Norros-Reittu and Chung-Lu random graphs. In particular, we determine a growth rate for the number of nodes k(n) such that for all nodes i ranging from 1 to k(n), the node with the i-th largest weight will have the i-th largest degree with high probability. Such alignment of upper-order statistics is then employed to establish the asymptotic normality of three different tail index estimators based on the upper degrees.
Keywords
Inhomogeneous random graphs
Tail estimation
Extreme value statistics
Central limit theorem
This paper studies linear mixed models for longitudinal data when covariates may be correlated with the idiosyncratic error and/or the random effects, biasing both fixed-effect estimates and random-effect predictions. We propose a two-stage linear mixed model instrumental variables estimator (LMMIV) that uses valid instruments to correct endogeneity while preserving the mixed-model structure. Its key novelty is the ability to quantify heterogeneity in all regression parameters, that is, both intercepts and slopes, even when endogeneity is present, rather than focusing only on mean effects or assuming random effects are uncorrelated with regressors. Under standard instrument exogeneity conditions, LMMIV yields consistent fixed effects and unbiased empirical BLUP-style predictions of random effects. Simulations confirm these theoretical results. Applied to a panel of 37 metro systems (1994–2019), we find substantial heterogeneity in demand elasticities: fare −0.86 to 0.12 (mean −0.29), income −0.07 to 0.57 (mean 0.18), and quality of service −0.03 to 0.91 (mean 0.32), with mean effects in line with the literature.
Keywords
Slope heterogeneity
linear mixed models
endogeneity
instrumental variables