The series a, a(1-a), a(1-a)2, a(1-a) a(1-a)4: an exponential series(geometric series M=X+(1-)×t k7+(1 0 t2千0(1-0)×+3 M=ax+(1-0)[a×1+a(1)x2+a(1-)2x3 M=aX+(1-∞)M1 This is the basic exponential smoothing equation The estimate at time t= a proportion of the new information +one minus that proportion of the estimate at time t-1
– The series , (1-), (1- ) 2 , (1- ) 3 , (1- ) 4 : an exponential series (geometric series) – Mt = Xt + (1-) Xt-1 + (1-) 2Xt-2 + (1-) 3Xt-3 +… – Mt = Xt + (1-)[ Xt-1 + (1-)Xt-2 + (1-) 2Xt-3 +…] – Mt = Xt + (1-)Mt-1 – This is the basic exponential smoothing equation • The estimate at time t = a proportion of the new information +one minus that proportion of the estimate at time t-1
13.2.2 Forecasting with the Simple model ForX,t=1,2,…,n, M=X+(1∞)M1 Calculate M, using t=2 Calculate M3 using t=3 Calculate M, using t=4 Calculate M, using t=n The forecast of the value of Xn+1= Mn Two problems for the process How to start the calculation How to choose a value for a, the smoothing constant
13.2.2 Forecasting with the Simple model • For Xt , t=1,2,…,n, – Mt = Xt + (1-)Mt-1 – Calculate M2 using t=2 – Calculate M3 using t=3 – Calculate M4 using t=4 – Calculate Mn using t=n – The forecast of the value of Xn+1= Mn • Two problems for the process – How to start the calculation – How to choose a value for , the smoothing constant