Lag weighted lasso for time series model

The adaptive lasso can consistently identify the true model in regression model. However, the adaptive lasso cannot account for lag effects, which are essential for a time series model. Consequently, the adaptive lasso can not reflect certain properties of a time series model. To improve the forecast accuracy of a time series model, we propose a lag weighted lasso. The lag weighted lasso imposes different penalties on each coefficient based on weights that reflect not only the coefficients size but also the lag effects. Simulation studies and a real example show that the proposed method is superior to both the lasso and the adaptive lasso in forecast accuracy.     

Optimal choice of the moments of observation in a problem of distinguishing stochastic processes

The problem is considered of distinguishing two Wiener processes with known diffusion coefficients on the basis of a finite number of inexact observations on a given time interval. In connection with the optimal choice of the moments of observation, the asymptotics of the maximum of the entropy distance of the arising pairs of finite-dimensional Gaussian distributions are found; the question of the optimal choice of the moments of observations is discussed, and the behavior of the entropy distance is studied for a fixed number of observations when the accuracy is increased.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 129–136, 1979.     

Temporal hierarchies with autocorrelation for load forecasting

We propose four different estimators that take into account the autocorrelation structure when reconciling forecasts in a temporal hierarchy. Combining forecasts from multiple temporal aggregation levels exploits information differences and mitigates model uncertainty, while reconciliation ensures a unified prediction that supports aligned decisions at different horizons. In previous studies, weights assigned to the forecasts were given by the structure of the hierarchy or the forecast error variances without considering potential autocorrelation in the forecast errors. Our first estimator considers the autocovariance matrix within each aggregation level. Since this can be difficult to estimate, we propose a second estimator that blends autocorrelation and variance information, but only requires estimation of the first-order autocorrelation coefficient at each aggregation level. Our third and fourth estimators facilitate information sharing between aggregation levels using robust estimates of the cross-correlation matrix and its inverse. We compare the proposed estimators in a simulation study and demonstrate their usefulness through an application to short-term electricity load forecasting in four price areas in Sweden. We find that by taking account of auto- and cross-covariances when reconciling forecasts, accuracy can be significantly improved uniformly across all frequencies and areas.     

基于理想点-矢量投影法的创新需求权重确定方法

现有的创新需求权重计算方法大多只考虑顾客、技术人员和决策者三者中的一方或者两方对创新需求权重的影响,鲜有方法将三方同时纳入需求权重计算过程,这很容易造成因信息考虑不全面,造成需求权重的精确度不高或失准等问题。鉴于此,本文提出一种基于理想点-矢量投影法的创新需求权重确定方法,它将顾客、技术人员和决策者三方的诉求在三维矢量空间中进行集成。分别计算创新需求的需求类别因子、需求技术成熟度和需求偏好度,采用理想点-矢量投影法得到理想需求矢量,并在此基础上计算每项创新需求权重值。文章最后通过汽车方向盘的研发的案例,验证了所提方法的有效性和可行性。     

Forecasting tender price index under incomplete information

Tender price index (TPI) is essential for estimating the likely tender price of a given project. Due to incomplete information on future market conditions, it is difficult to accurately forecast the TPI. Most traditional statistical forecasting models require a certain number of historical data, which may not be completely available in many practical situations. In order to overcome this problem, the grey model is proposed for forecasting TPIs because it only requires a small number of input data. For this study, the data source was based on the TPIs produced by the Government's Architectural Services Department. On the basis of four input data, the grey model forecasted TPIs from 1981Q1 to 2011Q4. The mean absolute percentage errors of forecast TPIs in one quarter and two quarters ahead were 3.62 and 7.04%, respectively. In order to assess the accuracy and reliability of the grey model further, the same research method was used to forecast other three TPIs in Hong Kong. The forecasting results of all four TPIs were found to be very good. It was thus concluded that the grey model could be able to produce accurate TPI forecasts for a one-quarter to two-quarter forecast horizon.     

The Order of the Error Term for Moments of the Log Likelihood Ratio Unit Root Test in an Autoregressive Process

This paper investigates the asymptotics of the log likelihood ratio test for a unit root in an autoregressive (AR) process of general order. The main result is that the expectation and variance (in fact, all moments) of the test statistic may, to the order of T-1, where T is the number of observations, be approximated by the expectation and variance of the corresponding test in an AR(1) process. This result has obvious implications for the asymptotics of unit root tests for panels. An explicit formula for the approximation error of a test in an AR(2) process is also given.     

An optimization technique based on a vector autoregression model with state space representation: application to Ukrainian cargo transport data

This paper proposes to forecast indicators of the Ukrainian cargo transport system, taking into account their relations with macroeconomic indicators. Increased forecast accuracy at a priori information uncertainty is attained through an optimization technique, starting with a Vector Autoregression (VAR) model of observed multiple time series, its state space representation and subsequent adaptive filtering. The adaptive filter, earlier proposed by the authors, minimizes forecasting errors. Under an optimization criterion, the information divergence of Kullback–Leibler between probability distributions of real values and their estimations is established. The main advantage of the proposed technique is connected with the opportunity to estimate future values of multiple time series even in presence of structural breaks (describing the changes of the status ‘before crisis’ / ‘after crisis’). The observations are available from 2003:1–2011:12, the analysis is performed for the period 2003:1–2011:9. In-sample forecasting of multiple time series of cargo volumes transferred by different transport modes and two macro indicators is compared with the forecast based on a VAR model. In-sample forecast is realized for the last three months 2011:10–2011:12.     

The time of deducting fees for variable annuities under the state-dependent fee structure

We investigate the total time of deducting fees for variable annuities with state-dependent fee. This fee charging method is studied recently by Bernard et al. (2014) and Delong (2014) in which the fees deducted from the policyholder’s account depend on the account value. However, both of them have not considered the problem of analyzing probabilistic properties of the total time of deducting fees. We approximate the maturity of a general variable annuity contract by combinations of exponential distributions which are (weakly) dense in the space that is composed of all probability distributions on the positive axis. Working under general jump diffusion process, we derive analytic formulas for the expectation of the time of deducting fees as well as its Laplace transform.     

A Simplification of the Matrix Beta Distribution for Combining Estimators

The problem of estimating a simplex of weights with a direct probabilistic interpretation for combining a set of estimators, either forecasts or expert opinions on an uncertain quantity, is approached via the outperformance construct. Thus, each weight represents the probability that its estimator will perform best. These outperformance probability weights are derived from a generalization of the beta distribution, i.e. the Matrix Beta. A simplified procedure for estimating the outperformance probability weights from this distribution is presented.     

The value of combining forecasts in inventory management – a case study in banking

Managing inventories in the face of uncertain stochastic demand requires an investment in safety stocks. These are related to the accuracy in forecasting future demands and the noise in the demand generation process. Reducing the demand forecasting error can free up capital and space, and reduce the operating costs of managing the inventories. A leading bank in Hong Kong consumes more than three hundred kinds of printed forms for its daily operations. A major problem of its inventory control system for the forms management is to forecast the monthly demand of these forms. In this study the idea of combining forecasts is introduced and its practical application is addressed. The individual forecasts come from well established time series models and the weights for combination are estimated with Quadratic Programming. The combined forecast is found to perform better than any of the individual forecasts.     

On sequential estimation of the shift parameter

The problem is considered of estimating the minimal sample size that guarantees the required accuracy, with confidence level fixed, of the estimate of the expectation. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 32–36, Perm, 1991.     

The tolerance approach in multiobjective linear fractional programming

When solving a multiobjective programming problem by the weighted sum approach, weights represent the relative importance associated to the objectives. As these values are usually imprecise, it is important to analyze the sensitivity of the solution under possible deviations on the estimated values. In this sense, the tolerance approach provides a direct measure of how weights may vary simultaneously and independently from their estimated values while still retaining the same efficient solution. This paper provides an explicit expression to the maximum tolerance on weights in a multiobjective linear fractional programming problem when all the denominators are equal. An application is also presented to illustrate how the results may help the decision maker to choose a most satisfactory solution in a production problem.     

Optimal portfolio for nonstationary security market

A new interpretation of the classical portfolio problem is suggested. It is based on the optimization on the conditional expectation of a utility function where the conditional expectation is calculated taking into account all information available at the moment of decision making. This approach allows to show that the risk is a sequence of forecasting errors. Main classes of forecasting algorithms are described and compared. A similarity between some variants of solutions to the modified portfolio problem and the traditional technical analysis recommendations is shown. The scheme is essentially important for nonstationary nonequilibrium security market. Some results of its practical application to the Russian bond market are presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Financial scenario generation for stochastic multi-stage decision processes as facility location problems

The quality of multi-stage stochastic optimization models as they appear in asset liability management, energy planning, transportation, supply chain management, and other applications depends heavily on the quality of the underlying scenario model, describing the uncertain processes influencing the profit/cost function, such as asset prices and liabilities, the energy demand process, demand for transportation, and the like. A common approach to generate scenarios is based on estimating an unknown distribution and matching its moments with moments of a discrete scenario model. This paper demonstrates that the problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function. We show that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance. The resulting optimization problem can be viewed as a multi-dimensional facility location problem, for which at least good heuristic algorithms exist. For multi-stage problems, a scenario tree is constructed as a nested facility location problem. Numerical convergence results for financial mean-risk portfolio selection conclude the paper.     

太湖水华危机应急预案在线风险补偿启动策略

应急预案启动时机的选择是应急管理领域中应对危机时需要解决的关键问题.太湖水华危机代表一类具有生长速度或传播速度不确定性的突发公共卫生事件,以此为背景基于在线方法,设计了应急预案启动策略,并证明是最优竞争比策略.同时,考虑到对未知信息的预期,设计了在线风险补偿启动策略.最后对危机进行实际数值计算,并指出策略的竞争性与预案应对强度之间的关系,还有在线风险补偿策略的补偿收益与决策者风险容忍度之间的关系,研究结果具有一定的实际指导意义和参考价值.     

Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density

In the context of semi-functional partial linear regression model, we study the problem of error density estimation. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance a constant parameter. This mixture error density has a form of a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, is estimated by the ordinary least squares and functional Nadaraya–Watson estimators. The estimation accuracy of the ordinary least squares and functional Nadaraya–Watson estimators jointly depends on the same bandwidth parameter. A Bayesian approach is proposed to simultaneously estimate the bandwidths in the kernel-form error density and in the regression function. Under the kernel-form error density, we derive a kernel likelihood and posterior for the bandwidth parameters. For estimating the regression function and error density, a series of simulation studies show that the Bayesian approach yields better accuracy than the benchmark functional cross validation. Illustrated by a spectroscopy data set, we found that the Bayesian approach gives better point forecast accuracy of the regression function than the functional cross validation, and it is capable of producing prediction intervals nonparametrically.     

Outlier detection and robust covariance estimation using mathematical programming

The outlier detection problem and the robust covariance estimation problem are often interchangeable. Without outliers, the classical method of maximum likelihood estimation (MLE) can be used to estimate parameters of a known distribution from observational data. When outliers are present, they dominate the log likelihood function causing the MLE estimators to be pulled toward them. Many robust statistical methods have been developed to detect outliers and to produce estimators that are robust against deviation from model assumptions. However, the existing methods suffer either from computational complexity when problem size increases or from giving up desirable properties, such as affine equivariance. An alternative approach is to design a special mathematical programming model to find the optimal weights for all the observations, such that at the optimal solution, outliers are given smaller weights and can be detected. This method produces a covariance estimator that has the following properties: First, it is affine equivariant. Second, it is computationally efficient even for large problem sizes. Third, it easy to incorporate prior beliefs into the estimator by using semi-definite programming. The accuracy of this method is tested for different contamination models, including recently proposed ones. The method is not only faster than the Fast-MCD method for high dimensional data but also has reasonable accuracy for the tested cases.     

An interpolation approximation for the GI/G/1 queue based on multipoint Padé approximation

The performance evaluation of many complex manufacturing, communication and computer systems has been made possible by modeling them as queueing systems. Many approximations used in queueing theory have been drawn from the behavior of queues in light and heavy traffic conditions. In this paper, we propose a new approximation technique, which combines the light and heavy traffic characteristics. This interpolation approximation is based on the theory of multipoint Padé approximation which is applied at two points: light and heavy traffic. We show how this can be applied for estimating the waiting time moments of the ^GI/G/1 queue. The light traffic derivatives of any order can be evaluated using the MacLaurin series analysis procedure. The heavy traffic limits of the ^GI/G/1 queue are well known in the literature. Our technique generalizes the previously developed interpolation approximations and can be used to approximate any order of the waiting time moments. Through numerical examples, we show that the moments of the steady state waiting time can be estimated with extremely high accuracy under all ranges of traffic intensities using low orders of the approximant. We also present a framework for the development of simple analytical approximation formulas. This revised version was published online in June 2006 with corrections to the Cover Date.     

A portfolio-based evaluation of affine term structure models

We focus on affine term structure models as tools for active bond portfolio management. Our financial exercise comprises the following steps: 1) forecast the future values of the state variables implied by several multi-factor models; 2) approximate the conditional moments of the state vector to come up with discrete scenarios for the future state variables 3) compute bond returns for various maturities at future dates from the theoretical asset pricing relations 4) solve the portfolio problem faced by an investor with a six month horizon who takes into account the possibility to rebalance after one quarter. The sequence of optimal portfolios is evaluated in terms of financial properties. We show that a financial based evaluation of term structure models may yield results conflicting with those obtained from a statistical evaluation.     

Large Deviations of the Threshold Estimator of Integrated (Co-)Volatility Vector in the Presence of Jumps

Recently considerable interest has been paid to the estimation problem of the realized volatility and covolatility by using high-frequency data of financial price processes in financial econometrics. Threshold estimation is one of the useful techniques in the inference for jump-type stochastic processes from discrete observations. In this paper, we adopt the threshold estimator introduced by Mancini (Scand Actuar J 1:42–52, 2004) where only the variations under a given threshold function are taken into account. The purpose of this work is to investigate large and moderate deviations for the threshold estimator of the integrated variance–covariance vector. This paper is an extension of the previous work in Djellout et al. (Stoch Process Appl 1–35, 2017), where the problem has been studied in the absence of a jump component. We will use the approximation lemma to prove large and moderate deviations results. As the reader can expect, we obtain the same results as in the case without jump.