Tham khảo tài liệu 'engineering statistics handbook episode 8 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Single Exponential Smoothing Example Let us illustrate this principle with an example. Consider the following data set consisting of 12 observations taken over time Time yt S o .1 Error Error squared 1 71 2 70 71 3 69 4 68 5 64 6 65 7 72 8 78 9 75 10 75 11 75 12 70 The sum of the squared errors SSE . The mean of the squared errors MSE is the SSE 11 . Calculate The MSE was again calculated for Ct .5 and turned out to be so for different in this case we would prefer an Ct of .5. Can we do better We could values of Ct apply the proven trial-and-error method. This is an iterative procedure beginning with a range of Ct between .1 and .9. We determine the best initial choice for Ct and then search between Ct - A and Ct A. We could repeat this perhaps one more time to find the best Ct to 3 decimal places. Nonlinear optimizers can be used But there are better search methods such as the Marquardt procedure. This is a nonlinear optimizer that minimizes the sum of squares of residuals. In general most well designed statistical software programs should be able to find the value of Ct that minimizes the MSE. http div898 handbook pmc section4 4 of 5 5 1 2006 10 35 10 AM . Single Exponential Smoothing Sample plot showing smoothed data for 2 values of Ct Exponential Smoothing Original and Smoothed Values Y Original Y n afpfta Ji alpha .5 NIST SEMATECH HOME tools RAIDS search SACK NEXT http div898 handbook pmc section4 5 of 5 5 1 2006 10 35 10 AM Example of Bootstrapping Example The last data point in the previous example was 70 and its forecast smoothed value S was . Since we do have the data point and the forecast available we can calculate the next forecast using the regular .
