2.1. , . , , :
. , - :
- B
(1-L)B ( 12)
98
: a = 1
: (1-L)y = b0 + (a-1)*y(-1) +... + e
. 1- e: -0,039
(a - 1): -1,62959
: tau_c(1) = -10,1364
. - 1,21e-019
: (1-L)y = b0 + b1*t + (a-1)*y(-1) +... + e
. 1- e: -0,040
(a - 1): -1,63415
: tau_ct(1) = -10,113
. - 2,975e-020
P-value , , - . .
2.2. :
, ACF PACF . , MA- AR-.
2.3. . , , , MA- AR-, ARIMA (1,0,1) = ARMA (1,1):
4: ARMA, 1980:1-2004:4 (T = 100)
: B
. | z | P- | |||
const | 99,9953 | 0,049329 | 2027,1110 | <0,00001 | *** |
phi_1 | 0,218113 | 0,195312 | 1,1167 | 0,26410 | |
theta_1 | -0,646726 | 0,153671 | -4,2085 | 0,00003 | *** |
. | 99,99557 | . . . | 1,181085 | |
-0,003485 | . . | 1,074320 | ||
. | -149,2059 | . | 306,4117 | |
. | 316,8324 | . - | 310,6291 |
AR | 1 | 4,5848 | 0,0000 | 4,5848 | 0,0000 |
MA | 1 | 1,5462 | 0,0000 | 1,5462 | 0,0000 |
, , AR- , . , , , AR- MA- . , , ARIMA (0,0,2) = MA (2):
5: ARMA, 1980:1-2004:4 (T = 100)
: B
. | z | P- | |||
const | 99,995 | 0,0498668 | 2005,2438 | <0,00001 | *** |
theta_1 | -0,416798 | 0,0994291 | -4,1919 | 0,00003 | *** |
theta_2 | -0,125268 | 0,0990634 | -1,2645 | 0,20604 |
|
|
. | 99,99557 | . . . | 1,181085 | |
-0,003100 | . . | 1,072888 | ||
. | -149,0738 | . | 306,1477 | |
. | 316,5683 | . - | 310,3651 |
MA | 1 | 1,6152 | 0,0000 | 1,6152 | 0,0000 |
2 | -4,9424 | 0,0000 | 4,9424 | 0,5000 |
, MA . :
6: ARMA, 1980:1-2004:4 (T = 100)
: B
. | z | P- | |||
const | 99,9949 | 0,0564112 | 1772,6057 | <0,00001 | *** |
theta_1 | -0,483229 | 0,0975609 | -4,9531 | <0,00001 | *** |
. | 99,99557 | . . . | 1,181085 | |
-0,001273 | . . | 1,081344 | ||
. | -149,8473 | . | 305,6946 | |
. | 313,5101 | . - | 308,8577 |
MA | 1 | 2,0694 | 0,0000 | 2,0694 | 0,0000 |
(6) , . (6):
, , , .
* , 3 , .
, (6) ARIMA (0,0,1) = MA (1) . :
3 - ARIMA (p,k,q)
( )