1.1 , . :
, . , - . Gretl , . :
- A
99
: a = 1
: (1-L)y = b0 + (a-1)*y(-1) + e
. 1- e: 0,068
(a - 1): 0,0202285
: tau_c(1) = 30,1664
P- 1
: (1-L)y = b0 + b1*t + (a-1)*y(-1) +... + e
. 1- e: -0,009
: F(9, 78) = 0,685 [0,7202]
(a - 1): 0,0225823
: tau_ct(1) = 3,38825
. - 1
P-value = 1 , , - ( ) , .
d_A. :
, d_A . , - :
- d_A
6 (-) (1-L)d_A ( 12)
92
: a = 1
: (1-L)y = b0 + (a-1)*y(-1) +... + e
. 1- e: 0,005
: F(6, 84) = 9,077 [0,0000]
(a - 1): 0,0618306
: tau_c(1) = 1,49658
. - 0,9993
: (1-L)y = b0 + b1*t + (a-1)*y(-1) +... + e
. 1- e: -0,056
: F(5, 85) = 1,698 [0,1440]
(a - 1): -0,319884
: tau_ct(1) = -1,76781
. - 0,7205
P-value , - : d_A . , , d_d_A. d_d_A:
, . - d_d_A:
- d_d_A
4 (-) (1-L)d_d_A ( 12)
93
: a = 1
|
|
: (1-L)y = b0 + (a-1)*y(-1) +... + e
. 1- e: -0,049
: F(4, 87) = 7,583 [0,0000]
(a - 1): -3,40646
: tau_c(1) = -7,17745
. - 1,088e-010
: (1-L)y = b0 + b1*t + (a-1)*y(-1) +... + e
. 1- e: 0,005
: F(5, 84) = 7,100 [0,0000]
(a - 1): -4,19552
: tau_ct(1) = -6,92063
. - 4,208e-009
P-value = 1,088e-10 < 0,01 ( ), , - , d_d_A .
d_d_A, .
1.2. . d_d_A ( 20) :
ACF , d_d_A ( , , ACF, ).
1.3. . , ARIMA (0,2,1), d_d_A ARIMA (0,0,1) = MA (1):
1: ARMA, 1980:3-2004:4 (T = 98)
: d_d_A
. | z | P- | |||
const | 0,118343 | 0,0217786 | 5,4339 | <0,00001 | *** |
theta_1 | -0,825297 | 0,0582614 | -14,1654 | <0,00001 | *** |
. | 0,124087 | . . . | 1,484416 | |
-0,014903 | . . | 1,170854 | ||
. | -155,0853 | . | 316,1706 | |
. | 323,9255 | . - | 319,3073 |
MA | 1 | 1,2117 | 0,0000 | 1,2117 | 0,0000 |
, , - .
d_d_A. , , , AR- MA- . , d_d_A ARMA (2,0,2):
2: ARMA, 1980:3-2004:4 (T = 98)
: d_d_A
. | z | P- | |||
const | 0,118738 | 0,0232806 | 5,1003 | <0,00001 | *** |
phi_1 | 0,356885 | 0,64692 | 0,5517 | 0,58118 | |
phi_2 | -0,177353 | 0,123524 | -1,4358 | 0,15107 | |
theta_1 | -1,12246 | 0,652809 | -1,7194 | 0,08554 | * |
theta_2 | 0,279339 | 0,554187 | 0,5041 | 0,61423 |
|
|
. | 0,124087 | . . . | 1,484416 | |
-0,011494 | . . | 1,157414 | ||
. | -153,9798 | . | 319,9595 | |
. | 335,4693 | . - | 326,2329 |
AR | 1 | 1,0061 | -2,1508 | 2,3745 | -0,1804 |
2 | 1,0061 | 2,1508 | 2,3745 | 0,1804 | |
MA | 1 | 1,3333 | 0,0000 | 1,3333 | 0,0000 |
2 | 2,6850 | 0,0000 | 2,6850 | 0,0000 |
(2) (1) : -, , -, . , (1).
(1), . . (3):
3: ARIMA, 1981:3-2004:4 (T = 94)
: (1-Ls) d_d_A
. | z | P- | |||
const | 0,00731114 | 0,00119846 | 6,1004 | <0,00001 | *** |
theta_1 | -1 | 0,0532804 | -18,7686 | <0,00001 | *** |
Theta_1 | -0,999986 | 0,216516 | -4,6185 | <0,00001 | *** |
. | 0,038700 | . . . | 1,995767 | |
0,019520 | . . | 1,087806 | ||
. | -151,9717 | . | 311,9435 | |
. | 322,1166 | . - | 316,0527 |
MA | 1 | 1,0000 | 0,0000 | 1,0000 | 0,0000 |
MA () | 1 | 1,0000 | 0,0000 | 1,0000 | 0,0000 |
(3) (1), , 1% . (3), ( 20 ):
, , , . , (3), ARIMA (0,2,1) , . :