Combining exponential smoothing forecasts using Akaike weights

Simple forecast combinations such as medians and trimmed or winsorized means are known to improve the accuracy of point forecasts, and Akaike’s Information Criterion (AIC) has given rise to so-called Akaike weights, which have been used successfully to combine statistical models for inference and prediction in specialist fields, e.g., ecology and medicine. We examine combining exponential smoothing point and interval forecasts using weights derived from AIC, small-sample-corrected AIC and BIC on the M1 and M3 Competition datasets. Weighted forecast combinations perform better than forecasts selected using information criteria, in terms of both point forecast accuracy and prediction interval coverage. Simple combinations and weighted combinations do not consistently outperform one another, while simple combinations sometimes perform worse than single forecasts selected by information criteria. We find a tendency for a longer history to be associated with a better prediction interval coverage.     

指数平滑预测法在汽车涡轮增压器市场的应用

汽车涡轮增压器市场目前进入高速增长期,业内竞争愈发激烈,对未来市场需求做出准确预测对各企业制定相关决策也愈发重要。文章通过分析汽车涡轮增压器市场需求的影响因素和变化规律,结合指数平滑预测法的适用原则,建立数学预测模型,对中短期未来需求进行预测,为相关企业提供决策依据。     

Data transforms with exponential smoothing methods of forecasting

In this paper, transforms are used with exponential smoothing, in the quest for better forecasts. Two types of transforms are explored: those which are applied to a time series directly, and those which are applied indirectly to the prediction errors. The various transforms are tested on a large number of time series from the M3 competition, and ANOVA is applied to the results. We find that the non-transformed time series is significantly worse than some transforms on the monthly data, and on a distribution-based performance measure for both annual and quarterly data.     

Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

The correlation theory for stationary stochastic processes applied to exponential smoothing

Er wordt aangetoond dat tijdreeksen x (t), die stationaire eerste incrementen y (t) met een zeer speciale correlatiefunctie (φ_yy() hebben, d.m.v. exponential smoothing optimaal in de zin van Wiener geëxtrapoleerd worden.
De smoothing parameter a. is gemakkelijk met behulp van (φ_yy() te berekenen. Het blijkt bovendien dat deze parameter soms ook groter dan één kan zijn. Een aantal generalisatus worden gediscussieerd en voor een daarvan wordt de extra-polatie formule berekend.     

Seasonal exponential smoothing with damped trends : An application for production planning

This paper reviews a spreadsheet-based forecasting approach which a process industry manufacturer developed and implemented to link annual corporate forecasts with its manufacturing/distribution operations. First, we consider how this forecasting system supports overall production planning and why it must be compatible with corporate forecasts. We then review the results of substantial testing of variations on the Winters three-parameter exponential smoothing model on 28 actual product family time series. In particular, we evaluate whether the use of damping parameters improves forecast accuracy. The paper concludes that a Winters four-parameter model (i.e. the standard Winters three-parameter model augmented by a fourth parameter to damp the trend) provides the most accurate forecasts of the models evaluated. Our application confirms the fact that there are situations where the use of damped trend parameters in short-run exponential smoothing based forecasting models is beneficial.     

Modeling the number of unemployed in South Sumatra Province using the exponential smoothing methods

The number of open unemployment in South Sumatra Province from year to year is found to be unstable. It can cause serious developmental problems. One solution to this problem is to build an early warning system by predicting the number of open unemployment in the future so that the Regional Government can establish relative policies to anticipate the negative impacts it will have on the environment, economy, social and politics. Therefore, this study discusses the best model to predict the number of unemployed in South Sumatra Province. The methods used to identify the best model are Single Exponential Smoothing (SES), Brown’s Exponential Smoothing (BES), and Holt’s Exponential Smoothing (HES). The Exponential Smoothing methods are compared to obtain forecasting results with a minimal error rate. Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) metrics are used to measure the performance of the forecasting model. Empirical results show that the SES model with the smoothing parameter value?=?0.7 is the best significant model in predicting the number of open unemployment in South Sumatra Province with a MAPE value of 6.24% and an RMSE value of 23.058. Thus, this SES model can be a reference for the Government to predict the number of open unemployment in South Sumatra Province so that the Regional Government can anticipate the negative impacts it can cause.

     

Holt’s exponential smoothing and neural network models for forecasting interval-valued time series

Interval-valued time series are interval-valued data that are collected in a chronological sequence over time. This paper introduces three approaches to forecasting interval-valued time series. The first two approaches are based on multilayer perceptron (MLP) neural networks and Holt’s exponential smoothing methods, respectively. In Holt’s method for interval-valued time series, the smoothing parameters are estimated by using techniques for non-linear optimization problems with bound constraints. The third approach is based on a hybrid methodology that combines the MLP and Holt models. The practicality of the methods is demonstrated through simulation studies and applications using real interval-valued stock market time series.     

Simultaneous estimation after selection and ranking and other procedures: The negative exponential case

We considerk (≥2) independent negative exponential populations with unknown location parameters and unknown but equal scale parameter. We incorporate the existing purely sequential and three-stage sampling procedures for selecting the “best” population and study the asymptotic second-order characteristics of the proposed fixed-size simultaneous confidence regions for the location parameters constructed after selection and ranking. Some direct estimation procedures have also been discussed.     

Designs for smoothing spline ANOVA models

Smoothing spline estimation of a function of several variables based on an analysis of variance decomposition (SS-ANOVA) is one modern nonparametric technique. This paper considers the design problem for specific types of SS-ANOVA models. As criteria for choosing the design points, the integrated mean squared error (IMSE) for the SS-ANOVA estimate and its asymptotic approximation are derived based on the correspondence between the SS-ANOVA model and the random effects model with a partially improper prior. Three examples for additive and interaction spline models are provided for illustration. A comparison of the asymptotic designs, the 2^d factorial designs, and the glp designs is given by numerical computation. Received May 2000     

Note on the optimality of unemployment equilibria

An equilibrium concept for an economy with rigid prices has been given by Drèze (1975). He formulated a model where for some commodity, either the supplies or the demands are rationed. In this note we discuss ‘unemployment equilibria’, i.e., fixed price equilibria for which the quantity rationing affects the supplies only. It can be proved that there exists a set of unemployment equilibria. Therefore we consider the question whether it is possible to characterize the set of undominated unemployment equilibria.     

Using forecast evaluation to improve the accuracy of the Greenbook forecast

Recently, Patton and Timmermann (2012) proposed a more powerful kind of forecast efficiency regression at multiple horizons, and showed that it provides evidence against the efficiency of the Fed’s Greenbook forecasts. I use their forecast efficiency evaluation to propose a method for adjusting the Greenbook forecasts. Using this method in a real-time out-of-sample forecasting exercise, I find that it provides modest improvements in the accuracies of the forecasts for the GDP deflator and CPI, but not for other variables. The improvements are statistically significant in some cases, with magnitudes of up to 18% in root mean square prediction error.     

On the exponential law

A characterization of the exponential law is given using its property thatE[(X–a)^r|X>a] is constant for alla0,r being a positive integer. Then this result is applied to the order statistics and some further characterizations are found.     

Burn-in for a time-transformed exponential model

The problem of the optimal duration of a burn-in experiment is considered in the case of simultaneous testing n components with the conditionally independent time-transformed exponential life-times, given an unknown parameter. The explicit solution is derived by reformulation of the problem considered to an optimal stopping problem for a suitable defined three-dimensional Markov process and reduction to a free-boundary problem.     

A note on the optimality ofk-stage tests

Summary This note deals with sequential tests requiring at mostk observations. First a lemma is proved concerning the form of Bayes solutions. Then it is demonstrated by giving a counter-example that the theorem ofWald andWolfowitz has no correspondence fork-stage tests.

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Zusammenfassung Es wird gezeigt, daß man beik-stufigen Tests zwar für die Gestalt vonBayes-Lösungen ein Analogon zu den unbeschränkten Sequenztests hat, daß aber der Satz vonWald undWolfowitz über die gleichmäßige Optimalität bzgl. des Stichprobenumfangs keine Entsprechung besitzt.

     

Statistical tests for multiple forecast comparison

We consider a multivariate version of the Diebold–Mariano test for equal predictive ability of three or more forecasting models. The Wald-type test, $S$, which has a null distribution that is asymptotically chi-squared, is shown to be generally invariant with respect to the ordering of the models being compared. Finite-sample corrections for the test are also developed. Monte Carlo simulations indicate that $S$ has reasonable size properties in large samples but tends to be oversized in moderate samples. The finite-sample correction succeeds in correcting for size, but only partially. For the size-adjusted tests, power increases with sample size, as expected. It is speculated that further finite-sample improvements can be achieved using Hotelling’s $T^2$ or bootstrap critical values.     

An extremal quotient test for exponential distributions

Summary A procedure based on the extremal quotient is proposed for testing the null hypothesis H ₀: the population of the sample has an exponential distribution against H _a : it does not have an exponential distribution.The proposed procedure is a nonparametric test which could lead to an early decision for the rejection ofH ₀