Problem 9 (no need to show details of your work) Consider the Sample Autocorrelation (SAC) and Sample Partial Autocorrelation (SPAC) functions given below. Circle the most-appropriate tentative model. I. a. Nonseasonal AR(2): z₁= 8+0₁Z₁-1+0₂²₁-2+A₁ b. Nonseasonal ARIMA(1,1): z₁ = 8+₁2₁-1+ a₁0₁ a₁-1 c. Nonseasonal MA(1): z= 8 + a₁-0₁a₁-1 d. Nonseasonal MA(2): z; = 8 + a₁−0₁a₁-1-0₂a₁-2 e. The time series is nonstationary. SAC Lag AutoCorr -8-6-4-20 .2.4.6.8 Lag 0 0 1 2 3 4 5 6 -0.0549 7 0.1572 8 -0.0332 9 0.0217 10 -0.0055 11 -0.0253 12 -0.0708 -0.0342 0.1978 -0.1726 13 14 15 16 17 18 19 Autocorrelation 1.0 0.8 0.6 0.4 0.2 0.0 -02 1.0000 -0.4936 -0.4 -06 -0.8 -10 0.0831 -0.0736 1 0.0010 -0.0415 0.0366 0.0059 II. a. Nonseasonal AR(2): zt = 8 +0₁Z₁-1+0₂Z₁-2+A₁ b. Nonseasonal ARIMA(1,1): z; = 8 +Ø₁²₁-1 + a₁−0₁a₁-1 c. Nonseasonal AR(1): z₁ = 8+0₁ Z₁-1 + a₂ d. Nonseasonal MA(2): z₁ = 8 + a₁−0₁a₁-1-0₂ a₁-2 e. The time series is nonstationary. 0.1068 -0.1301 SAC SPAC Partial -.8-6-4-2 0 .2.4.6.8 1.0000 1 -0.4936 2 -0.2122 3 -0.1781 Lag 20 4 -0.1535 5 -0.1769 6 -0.2616 7 -0.0493 8 0.0180 9 0.0420 10 0.0686 11 0.0453 12 -0.0552 13 -0.1404 14 0.1159 15 -0.0446 Autocorrelation Function for z (with 5% significance limits for the autocorrelations) 25 16 -0.1443 17 -0.1299 18 0.0705 19 0.0111 35 Partial Autocorrelation 1.0 0.8 0.6 0.4 02 0.0 -0.2 -0.4 -0.6 -0.8 -10 Partial Autocorrelation Function for z (with 5% significance limits for the partial autocorrelations) Lag 20 SPAC 35
Problem 9 (no need to show details of your work) Consider the Sample Autocorrelation (SAC) and Sample Partial Autocorrelation (SPAC) functions given below. Circle the most-appropriate tentative model. I. a. Nonseasonal AR(2): z₁= 8+0₁Z₁-1+0₂²₁-2+A₁ b. Nonseasonal ARIMA(1,1): z₁ = 8+₁2₁-1+ a₁0₁ a₁-1 c. Nonseasonal MA(1): z= 8 + a₁-0₁a₁-1 d. Nonseasonal MA(2): z; = 8 + a₁−0₁a₁-1-0₂a₁-2 e. The time series is nonstationary. SAC Lag AutoCorr -8-6-4-20 .2.4.6.8 Lag 0 0 1 2 3 4 5 6 -0.0549 7 0.1572 8 -0.0332 9 0.0217 10 -0.0055 11 -0.0253 12 -0.0708 -0.0342 0.1978 -0.1726 13 14 15 16 17 18 19 Autocorrelation 1.0 0.8 0.6 0.4 0.2 0.0 -02 1.0000 -0.4936 -0.4 -06 -0.8 -10 0.0831 -0.0736 1 0.0010 -0.0415 0.0366 0.0059 II. a. Nonseasonal AR(2): zt = 8 +0₁Z₁-1+0₂Z₁-2+A₁ b. Nonseasonal ARIMA(1,1): z; = 8 +Ø₁²₁-1 + a₁−0₁a₁-1 c. Nonseasonal AR(1): z₁ = 8+0₁ Z₁-1 + a₂ d. Nonseasonal MA(2): z₁ = 8 + a₁−0₁a₁-1-0₂ a₁-2 e. The time series is nonstationary. 0.1068 -0.1301 SAC SPAC Partial -.8-6-4-2 0 .2.4.6.8 1.0000 1 -0.4936 2 -0.2122 3 -0.1781 Lag 20 4 -0.1535 5 -0.1769 6 -0.2616 7 -0.0493 8 0.0180 9 0.0420 10 0.0686 11 0.0453 12 -0.0552 13 -0.1404 14 0.1159 15 -0.0446 Autocorrelation Function for z (with 5% significance limits for the autocorrelations) 25 16 -0.1443 17 -0.1299 18 0.0705 19 0.0111 35 Partial Autocorrelation 1.0 0.8 0.6 0.4 02 0.0 -0.2 -0.4 -0.6 -0.8 -10 Partial Autocorrelation Function for z (with 5% significance limits for the partial autocorrelations) Lag 20 SPAC 35
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:Problem 9 (no need to show details of your work)
Consider the Sample Autocorrelation (SAC) and Sample Partial Autocorrelation (SPAC)
functions given below. Circle the most-appropriate tentative model.
I. a. Nonseasonal AR(2): zt = 8 + 0₁Z₁-1+0₂ ²1-2+A₁
b. Nonseasonal ARIMA(1,1): z = 8 +0₁Z₁-1+ a₁0₁ a₁-1
c. Nonseasonal MA(1): z= 8+ a₁-0₁a₁-1
d. Nonseasonal MA(2): z₁= 8+ a₁0₁ a₁-1-0₂a₁-2
e. The time series is nonstationary.
SAC
SPAC
Lag AutoCorr -8-.6-.4-.2 0.2.4.6.8 Lag Partial -8-.6-.4-.2 0 .2.4.6.8
0 1.0000
0 1.0000
1
-0.4936
1
-0.4936
0.0831
-0.0736
2
3
4
5
6
-0.0549
7 0.1572
8 -0.0332
9 0.0217
10
-0.0055
11
-0.0253
12
-0.0708
13
-0.0342
14
15
16
17
18
19
Autocorrelation
1.0
0.0010
-0.0415
0.8
0.6
0.4
II. a. Nonseasonal AR(2): z: = 8+0₁ 2₁-1+0₂2₁-2+ at
b. Nonseasonal ARIMA(1,1): zt = 8 + ₁²₁-₁ + a₁-0₁a₁-1
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0.1978
-0.1726
0.0366
0.0059
0.1068
-0.1301
-1.0
c. Nonseasonal AR(1): z₁ = 8+₁ Z₁-1 + a₂
d. Nonseasonal MA(2): z₁ = 8+ a₁-0₁a₁-1-0₂ a₁-2
e. The time series is nonstationary.
10
Autocorrelation Function for z
(with 5% significance limits for the autocorrelations)
15
2 -0.2122
3 -0.1781
SAC
4 -0.1535
5
-0.1769
6 -0.2616
7 -0.0493
8
0.0180
9
0.0420
10
0.0686
11 0.0453
12 -0.0552
13 -0.1404
14 0.1159
15 -0.0446
16 -0.1443
17 -0.1299
18
19
Lag
20
0.0705
0.0111
35
Partial Autocorrelation
1.0
0.8
0.6
0.4
02
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Partial Autocorrelation Function for z
(with 5% significance limits for the partial autocorrelations)
15
Lag
20
SPAC
25
30
35
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