, , , . . () ().
, S1 1. 1. 1.
1. 1 =0. . .
2. 1 , ( ) . = 0 + 1 × tt. 1 .
Seasonal and Non-Seasonal Exponential smoothing User-def. initial value ( ) y1 =1259,1. Initial trend ( ) 1 =0.
Multiple Regression ( ).
1. t (. 5).
2. 8 (1999-2000.) Multiple Linear Regression ( ) Select cases ( ).
3. ( 6.7) Analysis/Graph Case Selection Conditions ( ), Enable Selection ConditionsSpecific, selected by: By Expression: ( 1-8 ).
6.7 ( )
:
6.2
Beta | Std.Err. of Beta | B | Std.Err. of B | t(6) | p-level | |
Intercept | 1148,007 | 134,123 | 8,559 | 0,000 | ||
t | 0,923 | 0,157 | 156,418 | 26,560 | 5,889 | 0,001 |
1 Exponential smoothing & forecasting , .. Initial trend a1 =156,418.
, . , Perform grid search ( ), .
|
|
Seasonal and Non-Seasonal Exponential smoothing Grid search ( ) ( 6.7). , 1 =0 1 =156,418. 6.3 6.4.
6.7 ( )
6.3 - 1 = 0 y1 =1259,1 ( )
Alpha | Gamma | Mean Error | Mean Abs Error | Sums of Squares | Mean Squares | Mean % Error | Mean Abs Error | |
0,1 | 0,9 | 161,153 | 378,617 | 232674,3 | 5,294 | 9,348 | ||
0,2 | 0,9 | 80,756 | 354,800 | 238328,4 | 2,368 | 8,133 |
6.4 - 1 = 156,418 y1 =1259,1 )
Alpha | Gamma | Mean Error | Mean Abs Error | Sums of Squares | Mean Squares | Mean % Error | Mean Abs Error | |
0,1 | 0,9 | 91,834 | 344,725 | 214004,0 | 1,188 | 7,711 | ||
0,1 | 0,8 | 100,869 | 344,618 | 215162,0 | 1,370 | 7,752 | ||
0,2 | 0,7 | 65,909 | 345,908 | 230436,2 | 0,584 | 7,556 | ||
0,2 | 0,8 | 58,892 | 348,233 | 232832,7 | 0,451 | 7,619 |
: Mean Error -
Mean Abs Error -
Sums of Squares -
Mean Squares -
Mean % Error -
Mean Abs Error -
:
(Mean error) .
(6.1) |
, , .
(Mean absolute error) .
(6.2) |
0 (), (). , .
(Sum of squared error (SSE), Mean squared error.), . ( ) .
.
(Percentage error (PE)). . . , , (, ) , , 10%. , . , . :
|
|
(6.3) |
: yt - t,
yt - ( ).
(Mean percentage error (MPE)).
(6.4) |
(Mean absolute percentage error (MAPE)). . ( ) .
(6.5) |
, , . :
< 10 10 20 20 50 > 50 |
6.3 9 18 ( Alpha =0,1 Gamma =0,9; Alpha =0,2 Gamma =0,9). 6.4, 9, 8, 16 17.
(6 ).
6.5
I/2006 | II/2006 | III/2006 | IV/2006 | % | |
7873,0 | 9575,8 | 9988,2 | - | - | |
Alpha =0,1 Gamma =0,9 (1 = 0 y1 =1259,1) | 8718,19 | 9179,22 | 9640,26 | 10101,29 | 5,85 |
Alpha =0,2 Gamma =0,9 (1 = 0 y1 =1259,1) | 9033,69 | 9604,47 | 10175,25 | 10746,03 | 2,91 |
Alpha =0,1 Gamma =0,9 (1 = 156,418 y1 =1259,1) | 8784,57 | 9223,70 | 9662,84 | 10101,97 | 1,49 |
Alpha =0,1 Gamma =0,8 (1 = 156,418 y1 =1259,1) | 8808,39 | 9241,52 | 9674,64 | 10107,77 | 1,70 |
Alpha =0,2 Gamma =0,7 (1 = 156,418 y1 =1259,1) | 8964,61 | 9486,17 | 10007,72 | 10529,27 | 0,85 |
Alpha =0,2 Gamma =0,8 (1 = 156,418 y1 =1259,1) | 9000,21 | 9550,73 | 10101,24 | 10651,75 | 0,83 |
6.5 , Alpha =0,1 Gamma =0,9, .
, Alpha =0,1 Gamma =0,9 (1 = 0 y1 =1259,1), . ( 6.5) . , - Alpha =0,2 Gamma =0,8 (1 = 156,418 y1 =1259,1).