Winters Method

For many years fluorine has been deterrnined by the Willard-Winters method in which finely ground ore, after removal of organic matter, is distilled with 72% perchloric acid in glass apparatus. The distillate, a dilute solution of fluorosiUcic acid, is made alkaline to release fluoride ion, adjusted with monochloroacetic acid at pH 3.4, and titrated with thorium nitrate, using sodium a1i2arine sulfonate as indicator. 

The di-O-tosylates (prepared by action of tosyl chloride in pyridine) are reduced with zinc (Nal/Zn route e Tipson-Cohen reaction) [13]. Cyclic ortho-esters (prepared by reaction of the diol with ethyl orthoformate) are transformed into olefins by simple heating in the presence of acids (Eastwood reaction, route b) [14]. Cyclic thiocarbonates (obtained by reaction of a diol with thiophosgene or (V,(V -thiocarbonyl-di-imidazole) are reduced to olefin with trimethyl phosphite (Corey-Winter method, route c) [15]. Finally, reduction of vicinal di-xanthates with tri- -butyltin hydride according to the Barton procedure [16] affords olefins via a reductive elimination process route a). The Corey-Winter, Garegg, and Tipson-Cohen methods are most commonly applied for deoxygenation of sugar diols. 

Univariate Forecasts of a given variable demand are based on a model fitted only to present and past observations of a given time series. There are several different univariate models, like Extrapolation of Trend Curves, Simple Exponential Smoothing, Holt Method, Holt-Winters Method, Box-Jenkins Procedure, and Stepwise Auto-regression, which can be regarded as a subset of the Box-Jenkins Procedure. 

Consider the quarterly laptop computer sales data for 3 years (2008-2010) given in Table 2.2. The problem is to determine the forecast for quarter 1 of year 2011 using Winters method with a = P = 0.2 andy= 0.3. 

The remaining calculations are shown in Table 2.8 using a spreadsheet. Comparing the forecast of Example 2.6 (Holt s method) and Example 2.7 (Winters method), we note that the forecasts are the same for the first four quarters (2008). However, they are different from 2009 onward due to the updating of the seasonality indices. The forecast for the first quarter of 2011 is given by... 

Using Winters method to incorporate seasonality and trend (Section 2.7.2), forecasts for multiple periods are given by... 

Consider Example 2.7 where Winters method was used to forecast the demand for the first quarter of 2011. Determine the demand forecasts all four quarters of 2011. 

Automatic software These are designated stand alone programs and may cost thousands of dollars. The user does not have to be proficient in forecasting. The soffware asks fhe user to enter the time series data. It selects the appropriate method based on the analysis of the data and recommends a forecasting method. It also computes the optimal values of fhe parameters (e.g., smoothing constants a, P, and y for Winters method) using forecast errors. It then... 

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