Determination of an Optimal Forecast Model for Ambulance Demand Using Goal Programming

A multistep approach to determining the optimal parameters of an exponential smoothing model was used to forecast emergency medical service (E.M.S.) demand for four counties of South Carolina. Daily emergency and routine (non-emergency) demand data were obtained and forecast statistics generated for each county sampled, using Winters' exponential smoothing model. A goal programme was formulated to combine forecast results for emergency calls with routine call forecasts. The goal programme gave a higher priority to accurate forecasting of emergency demand. The forecast model generated implicitly weights demand by severity and provides a reliable estimate of demand overall. The optimal parameter values for the smoothing model were obtained by minimizing the objective function value of the goal programming problem. The parameter values obtained were used to forecast demand for E.M.S. in the selected counties. The results of the model were compared to those using a multiple linear regression model and a single-objective-based exponential smoothing model for 2 months of data. When compared with two single-objective forecast models, the multiple-objective approach yielded more accurate forecasts and, therefore, was more cost-effective for the planner. The model presents and demonstrates a theoretical approach to improving the accuracy of ambulance demand forecasts. The possible impact of this approach on planning efficiency is discussed.     

Valuating residential real estate using parametric programming

When the estimation of the single equation multiple linear regression model is looked upon as an optimization problem, we show how the principles and methods of optimization can assist the analyst in finding an attractive prediction model. We illustrate this with the estimation of a linear prediction model for valuating residential property using regression quantiles. We make use of the linear parametric programming formulation to obtain the family of regression quantile models associated with a data set. We use the principle of dominance to reduce the number of models for consideration in the search for the most preferred property valuation model (s). We also provide useful displays that assist the analyst and the decision maker in selecting the final model (s). The approach is an interface between data analysis and operations research.     

Bayesian forecasting with the Holt–Winters model

Exponential smoothing methods are widely used as forecasting techniques in inventory systems and business planning, where reliable prediction intervals are also required for a large number of series. This paper describes a Bayesian forecasting approach based on the Holt–Winters model, which allows obtaining accurate prediction intervals. We show how to build them incorporating the uncertainty due to the smoothing unknowns using a linear heteroscedastic model. That linear formulation simplifies obtaining the posterior distribution on the unknowns; a random sample from such posterior, which is not analytical, is provided using an acceptance sampling procedure and a Monte Carlo approach gives the predictive distributions. On the basis of this scheme, point-wise forecasts and prediction intervals are obtained. The accuracy of the proposed Bayesian forecasting approach for building prediction intervals is tested using the 3003 time series from the M3-competition.     

Computational aspects of robust Holt-Winters smoothing based on M-estimation

To obtain a robust version of exponential and Holt-Winters smoothing the idea of M-estimation can be used. The difficulty is the formulation of an easy-to-use recursive formula for its computation. A first attempt was made by Cipra (Robust exponential smoothing, J. Forecast. 11 (1992), 57–69). The recursive formulation presented there, however, is unstable. In this paper, a new recursive computing scheme is proposed. A simulation study illustrates that the new recursions result in smaller forecast errors on average. The forecast performance is further improved upon by using auxiliary robust starting values and robust scale estimates. This research has been supported by the Research Fund K.U. Leuven and the Fonds voor Wetenschappelijk Onderzoek (Contract number G.0594.05).     

SIOPRED: a prediction and optimisation integrated system for demand

This paper presents a forecasting support system based on the generalised Holt-Winters exponential smoothing scheme to forecast time series of levels of demand. It is conceived as an integrated tool which has been implemented in Visual Basic. For improving the accuracy of automatic forecasting it uses an optimisation-based scheme which unifies the stages of estimation of the parameters and model selection. Based on this scheme, suitable forecasts and prediction intervals are obtained. The performance of the proposed system is compared with a number of well-established automatic forecasting procedures with respect to the 3003 time series included in the M3-competition.      

Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on the notion of autoregressive Hilbert processes that represent a generalization of the classical autoregressive processes to random variables with values in a Hilbert space. A careful analysis reveals, in particular, that this approach is related to the theory of function estimation in linear ill-posed inverse problems. In the deterministic literature, such problems are usually solved by suitable regularization techniques. We describe some recent approaches from the deterministic literature that can be adapted to obtain fast and feasible predictions. For large sample sizes, however, these approaches are not computationally efficient.With this in mind, we propose three linear wavelet methods to efficiently address the aforementioned prediction problem. We present regularization techniques for the sample paths of the stochastic process and obtain consistency results of the resulting prediction estimators. We illustrate the performance of the proposed methods in finite sample situations by means of a real-life data example which concerns with the prediction of the entire annual cycle of climatological El Niño-Southern Oscillation time series 1 year ahead. We also compare the resulting predictions with those obtained by other methods available in the literature, in particular with a smoothing spline interpolation method and with a SARIMA model.     

Forecasting time series with multiple seasonal patterns

A new approach is proposed for forecasting a time series with multiple seasonal patterns. A state space model is developed for the series using the innovations approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be obtained using methods from exponential smoothing. The proposed model is used to examine hourly and daily patterns in hourly data for both utility loads and traffic flows. Our formulation provides a model for several existing seasonal methods and also provides new options, which result in superior forecasting performance over a range of prediction horizons. In particular, seasonal components can be updated more frequently than once during a seasonal cycle. The approach is likely to be useful in a wide range of applications involving both high and low frequency data, and it handles missing values in a straightforward manner.     

Estimation of nonbinary random response

The paper treats a new approach to reducing the dimension of factors which affect the non-binary response variable Y. This is relevant in analysis of a number of stochastic models, for instance, in biological and medical studies. The quality of Y estimation by means of a function in those factors is described by a specified error functional. It involves a penalty function to take into account the importance of the forecast for different response values. The joint distribution of factors and response variable is unknown. Thus it is quite natural to employ for statistical inference the estimates of the error functional constructed by prediction algorithm and cross-validation procedure. One of our main results provides the criterion of strong consistency of such estimates as the number of observations tends to infinity. Due to this result one can identify the significant factors. We introduce also the regularized versions of estimates and establish for them the central limit theorem (CLT). The statistical variant of our CLT permits to construct the approximate confidence intervals for unknown error functional.     

Efficient parameter estimation via modified Cholesky decomposition for quantile regression with longitudinal data

It is well known that specifying a covariance matrix is difficult in the quantile regression with longitudinal data. This paper develops a two step estimation procedure to improve estimation efficiency based on the modified Cholesky decomposition. Specifically, in the first step, we obtain the initial estimators of regression coefficients by ignoring the possible correlations between repeated measures. Then, we apply the modified Cholesky decomposition to construct the covariance models and obtain the estimator of within-subject covariance matrix. In the second step, we construct unbiased estimating functions to obtain more efficient estimators of regression coefficients. However, the proposed estimating functions are discrete and non-convex. We utilize the induced smoothing method to achieve the fast and accurate estimates of parameters and their asymptotic covariance. Under some regularity conditions, we establish the asymptotically normal distributions for the resulting estimators. Simulation studies and the longitudinal progesterone data analysis show that the proposed approach yields highly efficient estimators.     

Improving demand forecasting accuracy using nonlinear programming software

We address the problem of forecasting real time series with a proportion of zero values and a great variability among the nonzero values. In order to calculate forecasts for a time series, the model coefficients must be estimated. The appropriate choice of values for the smoothing parameters in exponential smoothing methods relies on the minimization of the fitting errors of historical data. We adapt the generalized Holt–Winters formulation so that it can consider the starting values of the local components of level, trend and seasonality as decision variables of the nonlinear programming problem associated with this forecasting procedure. A spreadsheet model is used to solve the problems of optimization efficiently. We show that our approach produces accurate forecasts with little data per product.     

Multi-item sales forecasting with total and split exponential smoothing

Efficient supply chain management relies on accurate demand forecasting. Typically, forecasts are required at frequent intervals for many items. Forecasting methods suitable for this application are those that can be relied upon to produce robust and accurate predictions when implemented within an automated procedure. Exponential smoothing methods are a common choice. In this empirical case study paper, we evaluate a recently proposed seasonal exponential smoothing method that has previously been considered only for forecasting daily supermarket sales. We term this method ‘total and split’ exponential smoothing, and apply it to monthly sales data from a publishing company. The resulting forecasts are compared against a variety of methods, including several available in the software currently used by the company. Our results show total and split exponential smoothing outperforming the other methods considered. The results were also impressive for a method that trims outliers and then applies simple exponential smoothing.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Potential inventory cost reductions using advanced time series forecasting techniques

This paper compares demand forecasts computed using the time series forecasting techniques of vector autoregression (VAR) and Bayesian VAR (BVAR) with forecasts computed using exponential smoothing and seasonal decomposition. These forecasts for three demand data series were used to determine three inventory management policies for each time series. The inventory costs associated with each of these policies were used as a further basis for comparison of the forecasting techniques. The results show that the BVAR technique, which uses mixed estimation, is particularly useful in reducing inventory costs in cases where the limited historical data offer little useful information for forecasting. The BVAR technique was effective in improving forecast accuracy and reducing inventory costs in two of the three cases tested. In the third case, unrestricted VAR and exponential smoothing produced the lowest experimental forecast errors and computed inventory costs. Furthermore, this research illustrates that improvements in demand forecasting can provide better cost reductions than relying on stochastic inventory models to provide cost reductions.     

Nonuniform exponential dichotomy for linear skew-product semiflows over semiflows

The aim of this paper is to obtain necessary and sufficient conditions for the existence of a nonuniform exponential dichotomy over a general class of linear skew-product semiflows (over semiflows) on a Banach space. We extend Datko’s classical result to the case of the exponential nonuniform dichotomy of linear skew-product semiflows over semiflows on a Banach space, by using Lyapunov norms.     

Exponential smoothing for irregular data

Various types of exponential smoothing for data observed at irregular time intervals are surveyed. Double exponential smoothing and some modifications of Holt’s method for this type of data are suggested. A real data example compares double exponential smoothing and Wright’s modification of Holt’s method for data observed at irregular time intervals. This research has been supported by the Ministry of Education, Youth and Sports of the Czech Republic, Research Project MSM 0021620839, and by the Grant Agency of Charles University, Grant No. 342/2005.     

Forecasting sales of slow and fast moving inventories

Traditional computerised inventory control systems usually rely on exponential smoothing to forecast the demand for fast moving inventories. Practices in relation to slow moving inventories are more varied, but the Croston method is often used. It is an adaptation of exponential smoothing that (1) incorporates a Bernoulli process to capture the sporadic nature of demand and (2) allows the average variability to change over time. The Croston approach is critically appraised in this paper. Corrections are made to underlying theory and modifications are proposed to overcome certain implementation difficulties. A parametric bootstrap approach is outlined that integrates demand forecasting with inventory control. The approach is illustrated on real demand data for car parts.     

基于自回归XGBoost时序模型的GDP预测实证

GDP是反映一个国家国民收入、居民消费能力和经济发展的重要宏观经济指标,也是制定相关经济政策的重要依据.选择合适的统计方法研究GDP的发展变化规律,进行短期的高精度预测,对我国的宏观经济决策具有重要意义.研究选用基于自回归的XGBoost时序模型对我国1978-2018年GDP进行拟合预测,Rstudio软件运行结果显...     

A wavelet smoothing method to improve conditional sales forecasting

This article proposes a wavelet smoothing method to improve conditional forecasts generated from linear regression sales response models. The method is applied to the forecasted values of the predictors to remove forecast errors and thereby improve the overall forecasting performance of the models. Eight empirical studies are presented in which the purpose was to forecast detergent sales in the Netherlands, and wavelet smoothing was compared with a moving average and a band-pass filter. All methods were found to improve forecasts. Wavelet smoothing provided the best results when applied on highly volatile marketing time series. In contrast, it was less effective when applied on highly aggregated and smooth time series. An advantage of wavelets is that they are flexible enough to allow for data characteristics like abrupt changes, spikes and cyclical changes that are usually associated with price changes and promotions.     

基于加权损失函数下广义指数预报因子模型的汇率预测

本文提出在加权损失函数下构建汇率预测的广义指数预报因子模型。该方法首先选取有限个不同滑动参数构造指数预报因子,同时基于绝对值损失和平方损失的提出加权损失函数作为变量筛选的准则,然后在该准则下将指数预报因子进行线性组合,建立汇率预报的广义指数预报因子模型。本文最后用英镑/美元单周汇率数据与文献中的一些已有方法做比较,实证分析表明本文提出的方法在汇率预测效果上有较大改进。     

Heteroscedasticity checks for regression models

For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach may readily be extended to handle partial linear, and linear autoregressive models.