arXiv subjects

Kejin Wu

Publications and source records attributed to Kejin Wu.

11 recordsLinked to original sources

arXiv2026

Prediction Inference of Time Series with Standard ReLU Deep Neural Networks

We propose a methodology based on the standard ReLU Deep Neural Networks (DNN) to make predictions and quantify their uncertainty. Classically, people rely on linear, non-linear, or non-parametric kernel methods to fit and then predict the time series. As the universal approximation ability was revealed for DNN, its application has become more and more popular for prediction tasks in various scientific areas. However, the corresponding uncertainty quantification has not been studied thoroughly. Particularly, the uncertainty in prediction will consist of two parts: (1) the future variability; (2) the estimation variability within training data. To capture both variabilities, we build the so-called pertinent prediction interval (PPI) with the DNN model estimator. We first explore the consistency property of the DNN estimator with beta-mixing dependent data. Subsequently, we show that the implied forward bootstrap series is still beta-mixing and possesses the same stationary distribution as the original time series in probability, which is a key condition to enable the PPI. Lastly, the desired PPI is built after imposing minimal conditions on the limiting distribution of predictive roots. Simulations and real-data analysis are deployed to challenge our approach with standard non-parametric methods.

stat.ML↗

arXiv2026

Distributional Conformal Prediction for Markov Processes

We introduce the Markov Distributional Conformal Prediction (MDCP) method that extends the distributional conformal prediction (previously developed for regression) to the setting of a strictly stationary Markov process. Instead of relying on a specific model structure to do prediction, the idea of distributional conformal prediction interval aligns with the Model-Free (MF) Prediction Principle. In analogy to MF prediction of Markov processes, our method exploits the probability integral transform based on estimated transition distribution functions to transform the Markov data to an i.i.d.~dataset. We show a non-asymptotic error bound of MDCPs unconditional coverage rate under a $\beta$-mixing condition and other standard assumptions on the kernel estimators. The asymptotic validity of the conditional prediction interval is also verified. In addition, we show that our conditional prediction interval is still asymptotically valid with Markov processes being $L^p$-$m$-approximable instead of satisfying the mixing property. Numerical simulations and real data experiments are deployed to empirically illustrate the finite-sample performance of MDCP, and compare it with the MF bootstrap prediction method.

stat.ME↗

arXiv2026

Mixed Time Series Quasi-Likelihood Models for Uncovering Covid-19 Viral Load and Mortality Dynamics

Accurate real-time monitoring of disease transmission is crucial for epidemic control, which has conventionally relied on reported cases or hospital admissions. Such metrics are frequently susceptible to delays in reporting, various forms of bias, and under-ascertainment. Cycle threshold values obtained from reverse transcription quantitative polymerase chain reaction offer a promising alternative, serving as a proxy for viral load. In this paper, we aim to jointly model the viral load and the number of deaths (mortality), which involves a continuous bounded and a count time series, and therefore, a proper mixed-type model is needed. This is the motivation to introduce a new mixed-valued time series quasi-likelihood (MixTSQL) model capable of analyzing multivariate time series of different types, like continuous, discrete, bounded, and continuous positive. The MixTSQL model only requires a mean-variance specification with no distributional assumptions needed, and allows for testing Granger causality. Statistical guarantees are provided to ensure consistency and asymptotic normality of the proposed quasi-maximum likelihood estimators. We analyze weekly viral load and Covid-19 death counts in S\~ao Paulo, Brazil, using our MixTSQL model, which not only establishes the temporal order in which viral load Granger-causes mortality but also offers a comprehensive joint statistical analysis.

stat.ME↗

arXiv2025

Calibration Prediction Interval for Non-parametric Regression and Neural Networks

Accurate conditional prediction in the regression setting plays an important role in many real-world problems. Typically, a point prediction often falls short since no attempt is made to quantify the prediction accuracy. Classically, under the normality and linearity assumptions, the Prediction Interval (PI) for the response variable can be determined routinely based on the $t$ distribution. Unfortunately, these two assumptions are rarely met in practice. To fully avoid these two conditions, we develop a so-called calibration PI (cPI) which leverages estimations by Deep Neural Networks (DNN) or kernel methods. Moreover, the cPI can be easily adjusted to capture the estimation variability within the prediction procedure, which is a crucial error source often ignored in practice. Under regular assumptions, we verify that our cPI has an asymptotically valid coverage rate. We also demonstrate that cPI based on the kernel method ensures a coverage rate with a high probability when the sample size is large. Besides, with several conditions, the cPI based on DNN works even with finite samples. A comprehensive simulation study supports the usefulness of cPI, and the convincing performance of cPI with a short sample is confirmed with two empirical datasets.

stat.ME↗

arXiv2024

GARCHX-NoVaS: A Model-free Approach to Incorporate Exogenous Variables

In this work, we explore the forecasting ability of a recently proposed normalizing and variance-stabilizing (NoVaS) transformation with the possible inclusion of exogenous variables. From an applied point-of-view, extra knowledge such as fundamentals- and sentiments-based information could be beneficial to improve the prediction accuracy of market volatility if they are incorporated into the forecasting process. In the classical approach, these models including exogenous variables are typically termed GARCHX-type models. Being a Model-free prediction method, NoVaS has generally shown more accurate, stable and robust (to misspecifications) performance than that compared to classical GARCH-type methods. This motivates us to extend this framework to the GARCHX forecasting as well. We derive the NoVaS transformation needed to include exogenous covariates and then construct the corresponding prediction procedure. We show through extensive simulation studies that bolster our claim that the NoVaS method outperforms traditional ones, especially for long-term time aggregated predictions. We also provide an interesting data analysis to exhibit how our method could possibly shed light on the role of geopolitical risks in forecasting volatility in national stock market indices for three different countries in Europe.

econ.EM↗

arXiv2024

Deep Limit Model-free Prediction in Regression

In this paper, we provide a novel Model-free approach based on Deep Neural Network (DNN) to accomplish point prediction and prediction interval under a general regression setting. Usually, people rely on parametric or non-parametric models to bridge dependent and independent variables (Y and X). However, this classical method relies heavily on the correct model specification. Even for the non-parametric approach, some additive form is often assumed. A newly proposed Model-free prediction principle sheds light on a prediction procedure without any model assumption. Previous work regarding this principle has shown better performance than other standard alternatives. Recently, DNN, one of the machine learning methods, has received increasing attention due to its great performance in practice. Guided by the Model-free prediction idea, we attempt to apply a fully connected forward DNN to map X and some appropriate reference random variable Z to Y. The targeted DNN is trained by minimizing a specially designed loss function so that the randomness of Y conditional on X is outsourced to Z through the trained DNN. Our method is more stable and accurate compared to other DNN-based counterparts, especially for optimal point predictions. With a specific prediction procedure, our prediction interval can capture the estimation variability so that it can render a better coverage rate for finite sample cases. The superior performance of our method is verified by simulation and empirical studies.

stat.ML↗

arXiv2024

Scalable Subsampling Inference for Deep Neural Networks

Deep neural networks (DNN) has received increasing attention in machine learning applications in the last several years. Recently, a non-asymptotic error bound has been developed to measure the performance of the fully connected DNN estimator with ReLU activation functions for estimating regression models. The paper at hand gives a small improvement on the current error bound based on the latest results on the approximation ability of DNN. More importantly, however, a non-random subsampling technique--scalable subsampling--is applied to construct a `subagged' DNN estimator. Under regularity conditions, it is shown that the subagged DNN estimator is computationally efficient without sacrificing accuracy for either estimation or prediction tasks. Beyond point estimation/prediction, we propose different approaches to build confidence and prediction intervals based on the subagged DNN estimator. In addition to being asymptotically valid, the proposed confidence/prediction intervals appear to work well in finite samples. All in all, the scalable subsampling DNN estimator offers the complete package in terms of statistical inference, i.e., (a) computational efficiency; (b) point estimation/prediction accuracy; and (c) allowing for the construction of practically useful confidence and prediction intervals.

stat.ML↗

arXiv2023

Multi-step ahead prediction intervals for non-parametric autoregressions via bootstrap: consistency, debiasing and pertinence

To address the difficult problem of multi-step ahead prediction of non-parametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of non-parametric time series model, and show that the proposed point predictions are consistent with the true optimal predictor. We construct a quantile prediction interval that is asymptotically valid. Moreover, using a debiasing technique, we can asymptotically approximate the distribution of multi-step ahead non-parametric estimation by bootstrap. As a result, we can build bootstrap prediction intervals that are pertinent, i.e., can capture the model estimation variability, thus improving upon the standard quantile prediction intervals. Simulation studies are given to illustrate the performance of our point predictions and pertinent prediction intervals for finite samples.

stat.ME↗

arXiv2023

Bootstrap Prediction Inference of Non-linear Autoregressive Models

The non-linear autoregressive (NLAR) model plays an important role in modeling and predicting time series. One-step ahead prediction is straightforward using the NLAR model, but the multi-step ahead prediction is cumbersome. For instance, iterating the one-step ahead predictor is a convenient strategy for linear autoregressive (LAR) models, but it is suboptimal under NLAR. In this paper, we first propose a simulation and/or bootstrap algorithm to construct optimal point predictors under an $L_1$ or $L_2$ loss criterion. In addition, we construct bootstrap prediction intervals in the multi-step ahead prediction problem; in particular, we develop an asymptotically valid quantile prediction interval as well as a pertinent prediction interval for future values. In order to correct the undercoverage of prediction intervals with finite samples, we further employ predictive -- as opposed to fitted -- residuals in the bootstrap process. Simulation studies are also given to substantiate the finite sample performance of our methods.

stat.ME↗

arXiv2021

A New Model-free Prediction Method: GA-NoVaS

Volatility forecasting plays an important role in the financial econometrics. Previous works in this regime are mainly based on applying various GARCH-type models. However, it is hard for people to choose a specific GARCH model which works for general cases and such traditional methods are unstable for dealing with high-volatile period or using small sample size. The newly proposed normalizing and variance stabilizing (NoVaS) method is a more robust and accurate prediction technique. This Model-free method is built by taking advantage of an inverse transformation which is based on the ARCH model. Inspired by the historic development of the ARCH to GARCH model, we propose a novel NoVaS-type method which exploits the GARCH model structure. By performing extensive data analysis, we find our model has better time-aggregated prediction performance than the current state-of-the-art NoVaS method on forecasting short and volatile data. The victory of our new method corroborates that and also opens up avenues where one can explore other NoVaS structures to improve on the existing ones or solve specific prediction problems.

stat.AP↗

arXiv2021

Model-free time-aggregated predictions for econometric datasets

This article explores the existing normalizing and variance-stabilizing (NoVaS) method on predicting squared log-returns of financial data. First, we explore the robustness of the existing NoVaS method for long-term time-aggregated predictions. Then we develop a more parsimonious variant of the existing method. With systematic justification and extensive data analysis, our new method shows better performance than current NoVaS and standard GARCH(1,1) methods on both short- and long-term time-aggregated predictions.

stat.ME↗