2.6.Methods of Forecasting Stationary Series Exponential Smoothing-the current forecast is weighted average of the last forecast and the last value of demand. new forecast a(current observation of demand)+(1-a)(Last forecast) E,=aD,-1+(1-a)E,-1 where 0<a1 is the smoothing constant,which determines the relative weight placed on the last observation of demand, while 1-a is weight placed on the last forecast. F=aD,-1+(1-a)F,-=F-1-a(F-1-D-i)=F-1-Ce-l
Exponential Smoothing -the current forecast is weighted average of the last forecast and the last value of demand. 1 1 ( ) (1 )(Last forecast) (1 ) tt t new forecast current observation of demand FD F where 0<1 is the smoothing constant, which determines the relative weight placed on the last observation of demand, while 1- is weight placed on the last forecast. 1 1 FD F tt t (1 ) 2.6. Methods of Forecasting Stationary Series 1 11 ( ) F FD t tt F e t t 1 1
2.6.Methods of Forecasting Stationary Series a) 0.1 The older of a past data,the =018 0.09 smaller of its contribution to 0.08 the forecast for a future 0.07 period. 0.06 0.05 0.04 0.03 0.02 0.01 0 0 12345678910111213141516171819 Fig.2-5 Weights in Exponential Smoothing
Fig.2-5 Weights in Exponential Smoothing The older of a past data, the smaller of its contribution to the forecast for a future period. (1 ) 0.1 i 2.6. Methods of Forecasting Stationary Series
2.6.Methods of Forecasting Stationary Series 100 Smaller a turns out a 90 stable forecast,while 80 larger a results in better 70 track of series 60 8 0 10 12345678910111213141516171819202122232425 Time -Demand ES(.4) ES(.1) Fig.2-6 Exponential Smoothing for Different Values of Alpha
Fig.2-6 Exponential Smoothing for Different Values of Alpha Smaller turns out a stable forecast, while larger results in better track of series 2.6. Methods of Forecasting Stationary Series
图 2.7.Trend-Based Methods Regression analysis .A method that fits a straight line to a set of Holt's Method data .Double exponential smoothing
2.7. Trend-Based Methods Holt’s Method Regression analysis •A method that fits a straight line to a set of data •Double exponential smoothing
2.7.Trend-Based Methods 。 Regression Analysis >Let (x1,y),(x2,y2),...,(xn y)are n paired data points for the two variables X and Y;and >Assume that y;is the observed value of Y when xi is the observed value of X. >It is believed that there is a relationship between X and Y as follows Represents the predicated value of Y; y=a+bx a and b are chosen to minimize the sum of squared distance between regression line and the data point
• Regression Analysis Let (x1, y1), (x2, y2), …, (xn, yn) are n paired data points for the two variables X and Y; and Assume that yi is the observed value of Y when xi is the observed value of X. It is believed that there is a relationship between X and Y as follows Y a bX ˆ • Represents the predicated value of Y; • a and b are chosen to minimize the sum of squared distance between regression line and the data point 2.7. Trend-Based Methods