Conditional Expectation Approach Research Articles

On the optimal forecast with the fractional Brownian motion

This paper investigates the performance of different forecasting formulas with fractional Brownian motion based on discrete and finite samples. Existing literature presents two formulas for generating optimal forecasts when continuous records are available. One formula relies on a history over an infinite past, while the other is designed for a record limited to a finite past. In reality, only observations at discrete time points over a finite past are available. In this case, the forecasting formula, which has been widely used in the literature, is the one obtained by Gatheral et al. (Volatility is rough. Quant. Finance, 2018, 18(6), 933–949) that truncates and discretizes the formula based on continuous records over an infinite past. The present paper advocates an alternative forecasting formula, which is the conditional expectation based on finite past discrete-time observations. The findings suggest that the conditional expectation approach produces more accurate forecasts than the existing method, as demonstrated by both simulated data and actual daily realized volatility (RV) observations. Moreover, we also provide empirical evidence showing that the conditional expectation approach can lead to larger economic values than the existing method.

Understanding the operating landscape of the global airline industry: A DEA integrated alternating conditional expectation approach

Purpose: This study investigates the relationships between service efficiency in 5 major cost centres (namely, business orientation, network coverage, physical resources, maintenance, repair and overhaul (MRO), and human resources) and profitability in the global airline industry.Design/methodology/approach: The study integrates the Slack-based Model (SBM) of Data Envelopment Analysis (DEA) with the Alternating Conditional Expectation (ACE) regression to understand the relationships between an airline’s profitability and its efficiencies in 5 identified operations areas.Findings: Based on the observational data obtained from 75 international airlines, the relationships between operational performances and profitability are found to be curvilinear and contingent on an airline’s operating model.Research limitations/implications: The omission of non-IATA airlines and many low cost carriers may hinder a holistic view of the airline industry.Practical implications: Management can influence the profitability of an airline through its strategic operations decisions that affect an airline’s cost, service quality, and financial structure after the influences of location and size have set the stage. Airlines pursuing cost leadership should seek to increase productivity especially in MRO, human resources and physical resources; whereas airlines pursuing service differentiation may choose to provide quality service at lower efficiencies or pursue an approach to improve quality and efficiencies simultaneously.Originality/value: Identifying operations practices that are consistent with a firm’s competitive priorities is important in the multifaceted service environment today. An integrated SBM-ACE regression model, which permits different input-output mix, variable return to scale and non-linear relationship, is proposed and applied to analyze the profit impact of service efficiencies in the five key operations areas.

Obesity and Health-Care Costs in Switzerland: Dealing with Endogeneity in Non-Linear Regression Models

Summary We draw microdata from the Swiss Household Panel to estimate the causal effect of obesity on the number of physician visits, the amount of hospital days, and the respective costs incurred. We do so by simultaneously coping with three endogeneity issues, comprising reporting errors, omitted variables, and simultaneity. Using the conditional expectation approach, we first account for the reporting errors in weight and height. Second, we address endogeneity in the body mass index (BMI) by applying a control function approach. In contrast to the method of two-stage least squares, this technique is consistent in non-linear regression settings. Using the mean BMI of relatives as an instrument for the respondent’s BMI, we show that naïve regression methods considerably underestimate the impact of weight on the use of inpatient care, outpatient care, and costs. Accordingly, an additional unit of BMI raises annual health-care costs by CHF 253 or 11.5%, while the non-IV estimate amounts to only CHF 34 or 1.5%. Several robustness checks suggest the average marginal effect to be in the range of between CHF 220 and CHF 294. The model also predicts that if the overweight and obese people in the sample lost weight to the threshold of being of normal weight (BMI = 25), health-care costs could be reduced by about −4.7%. We conclude that the negative external effects caused by overweight and obesity are considerably larger than previously thought.

Probabilistic Approach to NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge Problem

A multifaceted exploration of the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge Problem aimed at examining the suitability of a probabilistic characterization of the epistemic uncertainties included with the problem statement is pursued. In the process, subproblems A through D are treated, and the opportunities and challenges associated with a probabilistic description are delineated as they pertain to each uncertainty characterization, uncertainty propagation, and uncertainty management, as well as to sensitivity analysis. All epistemic variables are replaced with random variables, and an equivalent effective uncertainty model with no epistemic component is identified. A Bayesian approach for parameter inference and an update that is applied directly on the probability densities of the various uncertainty variables are pursued, and sampling techniques for uncertainty propagation are used. A conditional expectation approach and a method based on the reduction of epistemic uncertainty are pursued for sensitivity analysis and uncertainty propagation.

A functional data approach to missing value imputation and outlier detection for traffic flow data

Missing values and outliers are frequently encountered in traffic monitoring data. We approach these problems by sampling the daily traffic flow rate trajectories from random functions and taking advantage of the data features using functional data analysis. We propose to impute missing values by using the conditional expectation approach to functional principal component analysis (FPCA). Our simulation study shows that the FPCA approach performs better than two commonly discussed methods in the literature, the probabilistic principal component analysis (PCA) and the Bayesian PCA, which have been shown to perform better than many conventional approaches. Based on the FPCA approach, the functional principal component scores can be applied to the functional bagplot and functional highest density region boxplot, which makes outlier detection possible for incomplete functional data. Our numerical results indicate that these two outlier detection approaches coupled with the proposed missing value imputation method can perform reasonably well. Although motivated by traffic flow data application, the proposed functional data methods for missing value imputation and outlier detection can be used in many applications with longitudinally recorded functional data.

A two-step PLS inspired method for linear prediction with group effect

In this article, we consider prediction of a univariate response from background data. The data may have a near-collinear structure and additionally group effects are assumed to exist. A two-step method is proposed. The first step summarizes the information in the predictors via a bilinear model. The bilinear model has a Krylov structured within individual design matrix, which is the link to classical partial least squares (PLS) analysis and a between-individual design matrix which handles group effects. The second step is the prediction step where a conditional expectation approach is used. The two-step method gives new insight into PLS. Explicit maximum likelihood estimators of the dispersion matrix and mean for the predictors are derived under the assumption that the covariance between the response and explanatory variables is known. It is shown that for within-sample prediction the mean squared error of the two-step method is always smaller than PLS.

The Consequences of Measurement Error When Estimating the Impact of BMI on Labour Market Outcomes

This paper uses data on both self-reported and true measures of individual Body Mass Index (BMI) to examine the nature of measurement error in self-reported BMI and to look at the consequences of using self-reported measures when estimating the effect of BMI on economic outcomes. In keeping with previous studies we find that self-reported BMI is subject to significant measurement error and this error is negatively correlated with the true measure of BMI. In our analysis this non-classical measurement error causes the traditional approach to overestimate the relationship between BMI and both income and education. Furthermore we show that popular alternatives estimators that have been adopted to address problems of measurement error in BMI, such as the conditional expectation approach and the instrumental variables approach, also exhibit significant biases.

A conditional expectation approach for associating ambient air pollutant exposures with health outcomes

Our research focuses on the association between exposure to an airborne pollutant and counts of emergency department visits attributed to a specific chronic illness. The motivating example for this analysis of measurement error in time series studies of air pollution and acute health outcomes was a study of emergency department visits from a 20-county Atlanta metropolitan statistical area from 1993-1999. The research presented illustrates the impact of using various surrogates for unobserved measurements of ambient concentrations at the zip code level. Simulation results indicate that the impact of measurement error on the association between pollutant exposure and a health outcome can be substantial. The proposed conditional expectation approach provided reliable estimates of the association and exhibited good confidence interval coverage for a variety of magnitudes of association. Use of a single-centrally located monitor, the arithmetic average, the nearest-neighbor monitor, and the inverse-distance weighted average surrogates resulted in biased estimates and poor coverage rates, especially for larger magnitudes of the association. A focus on obtaining reasonable exposure measurements within clearly defined subregions is important when the pollutant exposure of interest exhibits strong spatial variability.

The Characteristic Function of Elliptical T-distribution Using a Conditional Expectation Approach

Abstract The characteristic function of eliptical t-distribution has been derived by exploiting the conditional expectation technique. Some moments of the t-distribution have also been derived.

FORECASTING OF MULTIVARIATE PERIODIC AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES

Abstract. Minimum mean square error forecasting of multivariate autoregressive moving‐average processes with periodically varying parameters and orders is considered. General expressions are obtained for the forecasts, their errors and the covariance matrices of the forecast errors. Recursive evaluations of these quantities are shown to follow from the conditional expectation approach. Prediction ellipsoids and intervals for future values of the process are given. Update equations for the forecasts are obtained. The general results are illustrated and verified for a particular case of the process. A simulated example is given.

Adaptive hybrid conditional expectation approaches for reliability estimation

Conditional expectation is a simulation procedure that can be used to estimate the reliability of structures. It involves selecting an important random variable, using Monte Carlo simulation to generate sets of sample outcomes of the remaining “unimportant” random variables, estimating the conditional failure probability for each set of sample outcomes and using the average conditional failure probability as the estimate of the failure probability. This direct conditional expectation approach can be extremely effective, but only if the selected important random variable is much more important than the combined effect of the remaining random variables. In this paper, the concept of using importance sampling to generate the unimportant random variables is introduced. With a good sampling density, this greatly improves the efficiency for cases in which the selected important random variable does not dominate. To select such a density, however, one needs informations about the important regions of the failure domain. Typically, such information is not available a priori, and the direct application of this concept is limited. This concept can, however, be used in an adaptive format and two such adaptive hybrid conditional expectation approaches are developed in this paper. They are based on the idea that, as one generates sample outcomes and calculates the conditional failure probabilities at these outcomes, the knowledge of the failure domain increases. If one keeps modifying the importance sampling density to reflect this increasing state of knowledge, one can develop a good sampling density and simultaneously estimate the failure probability efficiently. Examples are used to demonstrate the efficacy of these approches and study the influence of factors like failure probability level and relative importance of random variables. Also discussed are issues such as the efficiency of the new methods (compared to FORM) and the applications to problems involving unions and intersections.