Bootstrap Prediction Research Articles

Comb channel lightcone bootstrap: triple-twist anomalous dimensions

We advance the multipoint lightcone bootstrap and compute anomalous dimensions of triple-twist operators at large spin. In contrast to the well-studied double-twist operators, triple-twist primaries are highly degenerate so that their anomalous dimension is encoded in a matrix. At large spin, the degeneracy becomes infinite and the matrix becomes an integral operator. We compute this integral operator by studying a particular non-planar crossing equation for six-point functions of scalar operators in a lightcone limit. The bootstrap analysis is based on new formulas for six-point lightcone blocks in the comb-channel. For a consistency check of our results, we compare them to perturbative computations in the epsilon expansion of ϕ3 and ϕ4 theory. In both cases, we find perfect agreement between perturbative results and bootstrap predictions. As a byproduct of our studies, we complement previous results on triple-twist anomalous dimensions in scalar ϕ3 and ϕ4 theory at first and second order in epsilon, respectively.

Predictive Root Based Bootstrap Prediction Intervals in Neural Network Models for Time Series Forecasting

Predictive Root Based Bootstrap Prediction Intervals in Neural Network Models for Time Series Forecasting

Bootstrap prediction inference of nonlinear autoregressive models

The nonlinear 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 article, we first propose a simulation and/or bootstrap algorithm to construct optimal point predictors under an or 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. To correct the undercoverage of prediction intervals with finite samples, we further employ predictive – as opposed to fitted – residuals in the bootstrap process. Simulation and empirical studies are also given to substantiate the finite sample performance of our methods.

Strong consistency of parameter estimation for the CIR integrated diffusion process with long-span high-frequency data

In this article, we utilize the contrast function of the integrated diffusion process to derive parameter contrast estimators for the Cox-Ingersoll-Ross integrated diffusion process and discuss the asymptotic properties of the estimators using the mixing properties of the process. We first give the tail probability exponential inequality of the mixing long-span high-frequency data. Then, applying this inequality, we prove the strong consistency of the contrast estimators for the drift parameters and diffusion parameter of the CIR integrated diffusion process. In order to obtain these asymptotic properties, we require relatively low order r of the negative power moment E | X t − 1 | r of the diffusion process. In the existing literature, r > 9 is required in order to obtain weak consistency of the estimators. However, in our theorems, only r > 2 is required for the strong consistency of the diffusion parameter estimator, while r > 4 for the strong consistency of the drift parameter estimators. In the simulation analysis, we use the Euler discretization algorithm and the Milstein discretization algorithm, and the results show that the optimal sampling interval is around n − 1 / 3 . We use the daily log price data of the CSI 300 Index to estimate the CIR integrated diffusion model and construct a Bootstrap prediction model for the log price. The results show that the model has a good predictive performance.

Chaos and the reparametrization mode on the AdS2 string

We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS2 geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS2 black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS2 string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to SL(2, ℝ) invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.

Multi-Step-Ahead Prediction Intervals for Nonparametric Autoregressions via Bootstrap: Consistency, Debiasing, and Pertinence

To address the difficult problem of the multi-step-ahead prediction of nonparametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of nonparametric 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 nonparametric estimation by the bootstrap. As a result, we can build bootstrap prediction intervals that are pertinent, i.e., can capture the model estimation variability, thus improving the standard quantile prediction intervals. Simulation studies are presented to illustrate the performance of our point predictions and pertinent prediction intervals for finite samples.

Creation of a Risk Calculator for Predicting New-Onset Cardiac Arrhythmias in Patients Undergoing Lumbar Fusion.

As an increasing number of lumbar fusion procedures are being conducted at specialty hospitals and surgery centers, appropriate patient selection and risk stratification is critical to minimizing patient transfers. Postoperative cardiac arrhythmia has been linked to worse patient outcomes and is a common cause of patient transfer. Therefore, we created a risk calculator to predict a patient's likelihood of developing a new-onset postoperative cardiac arrhythmia after lumbar spinal fusion, which may improve preoperative facility selection. A retrospective review was conducted of patients who undergoing lumbar fusion from 2017 to 2021 at a single academic center. Patients were excluded if they had any medical history of a cardiac arrhythmia. Multivariable regression was conducted to determine independent predictors of inpatient arrhythmias. The final regression was applied to a bootstrap to validate an arrhythmia prediction model. A risk calculator was created to determine a patient's risk of new-onset cardiac arrhythmia. A total of 1,622 patients were included, with 45 patients developing a new-onset postoperative arrhythmia. Age (OR = 1.05; 95% CI, 1.02 to 1.09; P = 0.003), history of beta-blocker use (OR = 2.01; 95% CI, 1.08 to 3.72; P = 0.027), and levels fused (OR = 1.59; 95% CI, 1.20 to 2.00; P = 0.001) were all independent predictors of having a new-onset inpatient arrhythmia. This multivariable regression produced an area under the curve of 0.742. The final regression was applied to a bootstrap prediction modeling technique to create a risk calculator including the male sex, age, body mass index, beta-blocker use, and levels fused (OR = 1.04, [CI = 1.03 to 1.06]) that produced an area under the curve of 0.733. A patient's likelihood of developing postoperative cardiac arrhythmias may be predicted by comorbid conditions and demographic factors including age, sex, body mass index, and beta-blocker use. Knowledge of these risk factors may improve appropriate selection of an outpatient surgical center or orthopaedic specialty hospital versus an inpatient hospital for lumbar fusions.

On the consistency of sieve bootstrap prediction intervals for stationary time series

On the consistency of sieve bootstrap prediction intervals for stationary time series

Gravitational orbits, double-twist mirage, and many-body scars

We explore the implications of stable gravitational orbits around an AdS black hole for the boundary conformal field theory. The orbits are long-lived states that eventually decay due to gravitational radiation and tunneling. They appear as narrow resonances in the heavy-light OPE when the spectrum becomes effectively continuous due to the presence of the black hole horizon. Alternatively, they can be identified with quasi-normal modes with small imaginary part in the thermal two-point function. The two pictures are related via the eigenstate thermalisation hypothesis. When the decay effects can be neglected the orbits appear as a discrete family of double-twist operators. We investigate the connection between orbits, quasi-normal modes, and double-twist operators in detail. Using the corrected Bohr-Sommerfeld formula for quasi-normal modes, we compute the anomalous dimension of double-twist operators. We compare our results to the prediction of the light-cone bootstrap, finding perfect agreement where the results overlap. We also compute the orbit decay time due to scalar radiation and compare it to the tunneling rate. Perturbatively in spin, in the light-cone bootstrap framework double-twist operators appear as a small fraction of the Hilbert space which violate the eigenstate thermalization hypothesis, a phenomenon known as many-body scars. Nonperturbatively in spin, the double-twist operators become long-lived states that eventually thermalize. We briefly discuss the connection between perturbative scars in holographic theories and known examples of scars in the condensed matter literature.

Bootstrap prediction intervals with asymptotic conditional validity and unconditional guarantees

Abstract It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval’s performance one should employ conditional coverage probability, conditioning on all available observations. Focusing on a linear model, we derive the asymptotic distribution of the difference between the conditional coverage probability of a nominal prediction interval and the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap. Applying this result, we show that a prediction interval generated by the residual-based bootstrap has approximately $50\%$ probability to yield conditional under-coverage. We then develop a new bootstrap algorithm that generates a prediction interval that asymptotically controls both the conditional coverage probability as well as the possibility of conditional under-coverage. We complement the asymptotic results with several finite-sample simulations.

Model-free bootstrap for a general class of stationary time series

A model-free bootstrap procedure for a general class of stationary time series is introduced. The theoretical framework is established, showing asymptotic validity of bootstrap confidence intervals for many statistics of interest. In addition, asymptotic validity of one-step ahead bootstrap prediction intervals is also demonstrated. Finite-sample experiments are conducted to empirically confirm the performance of the new method, and to compare with popular methods such as the block bootstrap and the autoregressive (AR)-sieve bootstrap.

Bootstrap Prediction Intervals of Temporal Disaggregation

In this article, we propose an interval estimation method to trace an unknown disaggregate series within certain bandwidths. First, we consider two model-based disaggregation methods called the GLS disaggregation and the ARIMA disaggregation. Then, we develop iterative steps to construct AR-sieve bootstrap prediction intervals for model-based temporal disaggregation. As an illustration, we analyze the quarterly total balances of U.S. international trade in goods and services between the first quarter of 1992 and the fourth quarter of 2020.

Robust factor models for high-dimensional time series and their forecasting

This paper deals with the factor modeling and forecasting for high-dimensional time series with additive outliers. Under the assumption that the sample size n and the dimension of time series p tend to infinity together, the asymptotic properties of several robust estimators are established, including estimation errors and forecast errors. We also propose a detailed algorithm of constructing bootstrap prediction intervals for the high-dimensional time series. We show the superiority of the approach by both simulation studies and an application to the daily air quality index for the main cities in the Yangtze River Delta region of China.

The prediction intervals of remaining useful life based on constant stress accelerated life test data

In practice, the prediction of the remaining useful life (RUL) of the product is a very important issue. This paper considers the prediction intervals of the RUL of the product at the normal operating stress level based on the exponential or Weibull constant stress accelerated life test (CSALT) data. For the exponential CSALT with type II censoring, we derive the exact and approximate prediction intervals for the RUL of the product. Using the asymptotic normality of the maximum likelihood estimation and the bootstrap method, we provide the two prediction intervals for the RUL of the product based on the exponential CSALT type I censored data. Under the Weibull CSALT with type II censoring, we use the generalized inferential procedure to obtain the generalized prediction interval of the RUL of the product. We also get the bootstrap prediction interval of the RUL of the product based on the Weibull CSALT type I censored data. The performance of the proposed prediction intervals is assessed by Monte Carlo simulation. The simulation results show that the coverage probabilities of the proposed prediction intervals are very close to the nominal confidence level. Finally, two examples are used to illustrate the proposed methods.

Bootstrap Prediction Bands for Functional Time Series

A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing in the Karhunen–Loève representation of the functional process. It generates backward-in-time functional replicates that adequately mimic the dependence structure of the underlying process in a model-free way and have the same conditionally fixed curves at the end of each functional pseudo-time series. The bootstrap prediction error distribution is then calculated as the difference between the model-free, bootstrap-generated future functional observations and the functional forecasts obtained from the model used for prediction. This allows the estimated prediction error distribution to account for the innovation and estimation errors associated with prediction and the possible errors due to model misspecification. We establish the asymptotic validity of the bootstrap procedure in estimating the conditional prediction error distribution of interest, and we also show that the procedure enables the construction of prediction bands that achieve (asymptotically) the desired coverage. Prediction bands based on a consistent estimation of the conditional distribution of the studentized prediction error process also are introduced. Such bands allow for taking more appropriately into account the local uncertainty of the prediction. Through a simulation study and the analysis of two datasets, we demonstrate the capabilities and the good finite-sample performance of the proposed method.

Prediction intervals in the ARFIMA model using bootstrap G

This paper presents a bootstrap resampling scheme to build prediction intervals for future values in fractionally autoregressive moving average (ARFIMA) models. Standard techniques to calculate forecast intervals rely on the assumption of normality of the data and do not take into account the uncertainty associated with parameter estimation. Bootstrap procedures, as nonparametric methods, can overcome these diculties. In this paper, we test two bootstrap prediction intervals based on the nonparametric bootstrap in the residuals of the ARFIMA model. In this paper, two bootstrap prediction intervals are proposed based on the nonparametric bootstrap in the residuals of the ARFIMA model. The rst one is the well known percentile bootstrap, (Thombs and Schucany, 1990; Pascual et al., 2004), never used for ARFIMA models to the knowledge of the authors. For the second approach, the intervals are calculated using the quantiles of the empirical distribution of the bootstrap prediction errors (Masarotto, 1990; Bisaglia e Grigoletto, 2001). The intervals are compared, through a Monte Carlo experiment, to the asymptotic interval, under Gaussian and non-Gaussian error distributions. The results show that the bootstrap intervals present coverage rates closer to the nominal level assumed, when compared to the asymptotic standard method. An application to real data of temperature in New York city is also presented to illustrate the procedures.

Prediction intervals in the beta autoregressive moving average model

In this article, we propose five prediction intervals for the beta autoregressive moving average model. This model is suitable for modeling and forecasting variables that assume values in the interval (0, 1). Two of the proposed prediction intervals are based on approximations considering the normal distribution and the quantile function of the beta distribution. We also consider bootstrap-based prediction intervals, namely: (i) bootstrap prediction errors (BPE) interval; (ii) bias-corrected and acceleration (BCa) prediction interval; and (iii) percentile prediction interval based on the quantiles of the bootstrap-predicted values for two different bootstrapping schemes. The proposed prediction intervals were evaluated according to Monte Carlo simulations. The BCa prediction interval offered the best performance among the evaluated intervals, showing lower coverage rate distortion and small average length. We applied our methodology for predicting the water level of the Cantareira water supply system in São Paulo, Brazil.

Modelling International Tourist Arrivals Volatility in Zimbabwe Using a GARCH Process

The aim of the paper was to develop bootstrap prediction intervals for international tourism demand and volatility in Zimbabwe after modelling with an ARMA-GARCH process. ARMA-GARCH models have better forecasting power and are capable of capturing and quantifying volatility. Bootstrap prediction intervals can account for future uncertainty that arises through parameter estimation. The monthly international tourism data obtained from the Zimbabwe Tourism Authority (ZTA) (January 2000 to June 2017) is neither seasonal nor stationary and is made stationery by taking a logarithm transformation. An ARMA(1,1) model fits well to the data; with forecasts indicating a slow increase in international tourist arrivals (outside of the Covid-19 period). The GARCH(1,1) process indicated that unexpected tourism shocks will significantly impact the Zimbabwe international tourist arrivals for longer durations. Volatility bootstrap prediction intervals indicated minimal future uncertainty in international tourist arrivals. For the Zimbabwe tourism industry to remain relevant, new tourism products and attraction centres need to be developed, as well as embarking on effective marketing strategies to lure even more tourists from abroad. This will go a long way in increasing the much-needed foreign currency earnings needed to revive the Zimbabwean economy.

U-survival for prognostic prediction of disease progression and mortality of patients with COVID-19

The rapid increase of patients with coronavirus disease 2019 (COVID-19) has introduced major challenges to healthcare services worldwide. Therefore, fast and accurate clinical assessment of COVID-19 progression and mortality is vital for the management of COVID-19 patients. We developed an automated image-based survival prediction model, called U-survival, which combines deep learning of chest CT images with the established survival analysis methodology of an elastic-net Cox survival model. In an evaluation of 383 COVID-19 positive patients from two hospitals, the prognostic bootstrap prediction performance of U-survival was significantly higher (P < 0.0001) than those of existing laboratory and image-based reference predictors both for COVID-19 progression (maximum concordance index: 91.6% [95% confidence interval 91.5, 91.7]) and for mortality (88.7% [88.6, 88.9]), and the separation between the Kaplan–Meier survival curves of patients stratified into low- and high-risk groups was largest for U-survival (P < 3 × 10–14). The results indicate that U-survival can be used to provide automated and objective prognostic predictions for the management of COVID-19 patients.

Bootstrap joint prediction regions for sequences of missing values in spatio-temporal datasets

Missing data reconstruction is a critical step in the analysis and mining of spatio-temporal data. However, few studies comprehensively consider missing data patterns, sample selection and spatio-temporal relationships. To take into account the uncertainty in the point forecast, some prediction intervals may be of interest. In particular, for (possibly long) missing sequences of consecutive time points, joint prediction regions are desirable. In this paper we propose a bootstrap resampling scheme to construct joint prediction regions that approximately contain missing paths of a time components in a spatio-temporal framework, with global probability 1-alpha . In many applications, considering the coverage of the whole missing sample-path might appear too restrictive. To perceive more informative inference, we also derive smaller joint prediction regions that only contain all elements of missing paths up to a small number k of them with probability 1-alpha . A simulation experiment is performed to validate the empirical performance of the proposed joint bootstrap prediction and to compare it with some alternative procedures based on a simple nominal coverage correction, loosely inspired by the Bonferroni approach, which are expected to work well standard scenarios.