p q .
1. ( 7.2) Transformations of Variables ( ) Autocorrs ().
2. Autocorrelations (), , p-level for highlighting. 7.6.
Partial autocorrelations, 7.7.
7.5 , ( )
7.6
7.7
7.1 ARMA . ( ) ARMA (1,0) ARMA (2,0). ( 7.7, ) . , x=f(x) Autocorr. (x=x-(a+b*x(lag))), ( ) x-0,000-1,00*x(t-1)
7.8 ( )
:
7.9
7.10
ARMA(1,0), - , - () 1. .
ARMA
:
1) ARMA Multiple regression
2) ARMA ARIMA & Autocorrelation function
7.7.1. ARMA Multiple regression
ARMA ( ). :
1. , Transformations of Variables Save variables , :
Y 0;
Y_1 ;
Y_2 .
2. : Y_1 D, Y_2 D.
Dt-1, Insert Add Variables. Add Variables Name NewVar Dt-1, Long name = v3.
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3. Date Shift (Lag) Dt-1 (Forward).
4. Statistics Multiple Regression. Select dependent and independent variable lists ( Variables) D - Dt-1.
5. Advanced options (stepwise or ridge regression) Model Definition Intercept Set to zero (.. ). :
7.2
Beta | Std.Err. of Betta | B | Std.Err. of B | t(24) | p-level | |
D''t-1 | -0,878 | 0,098 | -0,911 | 0,101 | -8,992 | 0,000 |
ARMA(1,0), a . , F - (F (1,24)=80,86 F (1,24)= 4,26).
6. (Multiple Regression Results) Residuals / assumptions / prediction, .
Residual Analysis Save Save residuals & predicted, Select variables to save with predicted/residual sc D . :
7.11 ARMA
7. . Graphs 2D Graphs Line Plots (Variables). Variables () D Predicted. Graph type ( 2D Line Plots Variables) Multiple ( , ).
7.12 - 0
ARMA (1,0) .
8. Residuals/assumptions/prediction Predict dependent variable .
9. Specify values for indep. vars Dt-1 -79, :
7.3 0 1 2006.
B-Weight | Value | B-Weight * Value | |
D''t-1 | -0,911 | -79,000 | 71,969 |
Predicted | 71,969 | ||
-95,0%CL | 55,451 | ||
+95,0%CL | 88,488 |
2-4 2006. :
7.4 - 0 2006.
/ | ARMA (1,0) | |||
I/2006 | -79,000 | 71,969 | 55,451 | 88,488 |
II/2006 | 71,969 | -65,564 | -80,612 | -50,516 |
III/2006 | -65,564 | 59,729 | 46,020 | 73,438 |
IV/2006 | 59,729 | -54,413 | -66,902 | -41,924 |
7.7.2. ARMA ARIMA & Autocorrelation function
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ARMA STATISTICA :
1. Statistics Advancer Linear/Nonlinear Models Time Series Analysis ARIMA & Autocorrelation function ( ARIMA & ).
2. Single Series ARIMA ( ) Quick (). , , x-0,000-1,00*x(t-1); x-0,000-1,00*x(t-1) ( ).
7.13 ARMA ( )
3. Single Series ARIMA Results ( ).
7.14
( 7.14) , : ARMA , , .
4. Advanced Summary: Parameter estimates 7.5.
7.5 ARMA(1,0)
Param. | Asympt. Std. Err. | Asympt. t(25) | p | Lower 95% Conf | Upper 95% Conf | |
p(1) | -0,911 | 0,102 | -8,895 | 0,000 | -1,122 | -0,700 |
:
.
t -.
p- 95% () .
t - .
5. Advanced Forecasting (). 4 , 4 Number of cases ( ). Forecast cases ( ), 7.6 7.15.
7.6 - 0 2006.
Forecast | Lower 95% | Upper 95% | Std.Err. | |
-162,614 | -291,707 | -33,522 | 62,680 | |
148,142 | -26,487 | 322,772 | 84,791 | |
-134,958 | -339,833 | 69,917 | 99,476 | |
122,947 | -103,989 | 349,884 | 110,188 |
7.15 ARMA (1,0)
1) () , () , :
) ARMA(0,2)
) ARMA(0,1)
) ARMA(1,0)
2) , , :
) ARMA(0,2)
) ARMA(0,1)
) ARMA(1,0)
3) , , :
) ARMA(2,0)
) ARMA(0,1)
) ARMA(1,0)
4) () 1 2, , :
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) ARMA(0,2)
) ARMA(0,1)
) ARMA(1,0)
5) yt = ayt-1 + et :
) AR(1)
) AR(2)
) MA(1)
) MA(2)
6) yt = a1yt-1 + a2yt-2 + et :
) AR(1)
) AR(2)
) MA(1)
) MA(2)
7) yt = et +qet-1 :
) AR(1)
) AR(2)
) MA(1)
) MA(2)
8) yt = et +q1et-1 + q2et-2 :
) AR(1)
) AR(2)
) MA(1)
) MA(2)
9) yt = a1yt- + et +qet-1 :
) ARIMA (1, 1, 1)
) ARMA (1, 1)
) ARMA (2, 2)
10) :
) yt = ayt-1 + et
) yt = a1yt-1 + a2yt-2 + et
) yt = a1yt- + et +qet-1