From: Dave Rusin Subject: Re: Holt-Winters Method Date: Tue, 27 Jun 2000 09:15:55 -0500 (CDT) To: alan.sausse@saga.co.uk Summary: [missing] I don't think this is a _research_ _math_ question; you might get more interesting responses on one of the statistics newsgroups. I did look for matches to "Holt and Winters" for you in the MathSciNet database; the matched entries, and a few of the reviews, are attached. dave (sci.math.research moderator) Matches for: Anywhere=Holt and Winters [_] [1] [PDF] 99b:62130 Chen, Chunhang Some statistical properties of the Holt-Winters seasonal forecasting method. J. Japan Statist. Soc. 26 (1996), no. 2, 173--187. 62M10 [_] [2] [PDF] 97e:62116 Brockwell, Peter J.; Davis, Richard A. Introduction to time series and forecasting. With 1 IBM-PC floppy disk (3.5 inch; HD). Springer Texts in Statistics. Springer-Verlag, New York, 1996. xiv+420 pp. ISBN: 0-387-94719-1 62M10 [_] [3] [PDF] 97c:62221 Ratinger, Tom�\v s Seasonal time series with missing observations. Appl. Math. 41 (1996), no. 1, 41--55. 62M10 (90A20) [_] [4] [PDF] 96j:05009 Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Held at Florida Atlantic University, Boca Raton, Florida, March 7--11, 1994. Congr. Numer. {105} (1994). Utilitas Mathematica Publishing, Inc., Winnipeg, MB, 1994. pp. 1--224. 05-06 [_] [5] [PDF] 96c:62146 Chen, Chunhang On asymptotic normality of estimates for smoothing parameters in the Holt-Winters seasonal forecasting method. Ryukyu Math. J. 7 (1994), 1--11. (Reviewer: N. Leonenko) 62M10 (62M20) [_] [6] [PDF] 88k:62120 Quesenberry, Charles P., Jr.; Jewell, Nicholas P. Regression analysis based on stratified samples. Biometrika 73 (1986), no. 3, 605--614. (Reviewer: I. S. Alalouf) 62J05 (62D05) [_] [7] [PDF] 85c:62248 Durbin, J. Extensions of the Brown and Holt\mhy Winters forecasting systems and their relation to Box\mhy Jenkins models. Time series analysis: theory and practice, 3 (Valencia, 1982), 7--18, North-Holland, Amsterdam-New York, 1983. 62M20 [_] [8] [PDF] 85a:62007 Time series analysis: theory and practice. 3. Proceedings of the second international forecasting conference (IFC) held in Valencia, May 24--28, 1982. Edited by Oliver Duncan Anderson. North-Holland Publishing Co., Amsterdam-New York, 1983. viii+301 pp. ISBN: 0-444-86625-6 62-06 [_] [9] [PDF] 83j:62135 Roberts, S. A. A general class of Holt\mhy Winters type forecasting models. Management Sci. 28 (1982), no. 7, 808--820. 62M10 (62P20) [_] [10] [PDF] 82a:62025 Holt, D.; Smith, T. M. F.; Winter, P. D. Regression analysis of data from complex surveys. J. Roy. Statist. Soc. Ser. A 143 (1980), no. 4, 474--487. 62D05 [_] [11] [PDF] 56 #9865 Newbold, P.; Granger, C. W. J. Experience with forecasting univariate time series and the combination of forecasts. With discussion by D. J. Reid, G. M. Jenkins, G. J. A. Stern, M. B. Priestley, C. Chatfield, H. Herne, E. J. Godolphin, K. F. Wallis, J. M. Craddock, M. J. Bramson, D. H. Ward, S. M. Stigler, D. W. Bunn and H. S. Konijn. J. Roy. Statist. Soc. Ser. A 137 (1974), 131--164. 62M10 (90A20) [_] [12] [PDF] 55 #9888 Adaptive economic models. Proceedings of a Symposium conducted by the Mathematics Research Center, University of Wisconsin, Madison, Wis., October 21--23, 1974. Edited by Richard H. Day and Theodore Groves. Mathematics Research Center, University of Wisconsin, Madison, Wis., Publ. No. 34. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. ix+581 pp. 90A15 [_] [13] [PDF] 22 #3591 Winters, Peter R. Forecasting sales by exponentially weighted moving averages. Management. Sci. 6 1960 324--342. (Reviewer: G. Morton) 90.00 _________________________________________________________________ 99b:62130 62M10 Chen, Chunhang(J-RYKS) Some statistical properties of the Holt-Winters seasonal forecasting method. (English. English summary) J. Japan Statist. Soc. 26 (1996), no. 2, 173--187. Summary: "The Holt-Winters method has been widely used to forecast a seasonal time series in application fields as a nonparametric forecasting technique. In this paper, we investigate the asymptotic forecast errors of the Holt-Winters method. For that purpose we show that the nonlinear least squares estimates of the smoothing parameters included in the smoothing algorithm hold strong convergence properties under suitable conditions. Then we show the mean squared errors and the limiting distributions of the forecast errors for some stochastic processes. Finally, numerical studies are performed to evaluate the forecasting performance of the Holt-Winters method." _________________________________________________________________ 96c:62146 62M10 (62M20) Chen, Chunhang(J-RYKED) On asymptotic normality of estimates for smoothing parameters in the Holt-Winters seasonal forecasting method. (English. English summary) Ryukyu Math. J. 7 (1994), 1--11. Let $Y\sb 1,\cdots,Y\sb n$ be an observation of seasonal time series $Y\sb t=T\sb t+S\sb t+W\sb t$, where $t\in\bold Z$ and $T\sb t$, $S\sb t$, $W\sb t$ represent the trend, seasonal and irregular components respectively. The smoothing parameters in the Holt-Winters seasonal forecasting method are often estimated by minimizing the mean square error of one-step forecasts using the sample. Let $\hat\theta$ be the estimator of $\theta$ by minimizing the functional $Q\sb n(\theta)=n\sp {-1}\sum\sp n\sb {i=1} [Y\sb t-\hat Y\sb {t-1}(1)]\sp 2$, $\theta\in\Theta\sp *\subset\bold R\sp 3$. For some class of processes $Y\sb t$ the asymptotic normality of $\sqrt n(\hat\theta\sb n-\theta)$ is proved. Reviewed by N. Leonenko _________________________________________________________________ 85c:62248 62M20 Durbin, J.(4-LSE) Extensions of the Brown and Holt\mhy Winters forecasting systems and their relation to Box\mhy Jenkins models. Time series analysis: theory and practice, 3 (Valencia, 1982), 7--18, North-Holland, Amsterdam-New York, 1983. Author's summary: "Brown's forecasting system based on discounted least squares [R. G. Brown , Smoothing, forecasting and prediction of discrete time series, Prentice-Hall, Englewood Cliffs, N.J., 1963] is generalised by replacing the discount function $\lambda\sp j$ by the function $\sum\sb {r=1}\sp n\,A\sb r\lambda\sp j\sb r$. A recursion for constructing the forecasts is derived and the stochastic models for which the one step ahead forecasts are optimal are obtained. These models are found to be special cases of Box-Jenkins models. The results are applied to obtain a general form of the Holt-Winters forecasting system." _________________________________________________________________ 83j:62135 62M10 (62P20) Roberts, S. A. A general class of Holt\mhy Winters type forecasting models. Management Sci. 28 (1982), no. 7, 808--820. Author's summary: "This paper is concerned with the formulation of short-term forecasting models, and introduces a range of models of considerable importance. These are defined in terms of predictions and sensible updating mechanisms for estimates of quantities such as level, growth, and seasonality, and constitute generalizations of familiar (linear) exponential smoothing predictors. They are shown to be equivalent to particular ARIMA models, and generally these do not lie within that subset of the ARIMA class which forms the basis of the Box-Jenkins modelling approach. It is argued that the models of this paper have a reasoned structure, and are to be preferred to the Box-Jenkins models for most socio-economic applications." _________________________________________________________________ 22 #3591 90.00 Winters, Peter R. Forecasting sales by exponentially weighted moving averages. Management. Sci. 6 1960 324--342. This paper develops an earlier method of C. C. Holt's for estimating future sales through a weighting of forecasts and actual data. In a similar way the seasonal and trend factors can be used and adjusted. The method has the advantage of simplicity and of requiring no external data (and with it the disadvantage of ignoring other relevant economic information), and that forecasts can be computed quickly.---Three real life examples are given in which the forecasting of errors compares favourably with those found in more detailed economic studies. Reviewed by G. Morton � Copyright American Mathematical Society 2000