Monte Carlo AR(1) Data with Alpha = 0

Monte Carlo AR(1) data with alpha = 0.7

X=Time Y=AR(1) Series

The ARIMA Procedure Yt = 0.7Yt-1 + ut

Name of Variable = x2

Mean of Working Series -0.22223

Standard Deviation 1.589171

Number of Observations 200

Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

0 2.525463 1.00000 | |********************|

1 2.000747 0.79223 | . |**************** |

2 1.481214 0.58651 | . |************ |

3 1.061147 0.42018 | . |******** |

4 0.764765 0.30282 | . |****** |

5 0.423600 0.16773 | . |*** . |

6 0.290481 0.11502 | . |** . |

7 0.322476 0.12769 | . |*** . |

8 0.272510 0.10790 | . |** . |

9 0.195309 0.07734 | . |** . |

10 0.126098 0.04993 | . |* . |

11 0.00045990 0.00018 | . | . |

12 -0.217297 -.08604 | . **| . |

13 -0.337171 -.13351 | . ***| . |

14 -0.279029 -.11049 | . **| . |

15 -0.129674 -.05135 | . *| . |

16 0.121938 0.04828 | . |* . |

17 0.236404 0.09361 | . |** . |

18 0.301865 0.11953 | . |** . |

19 0.233485 0.09245 | . |** . |

20 0.131253 0.05197 | . |* . |

Partial Autocorrelations

Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

1 0.79223 | . |**************** |

2 -0.11042 | .**| . |

3 -0.02257 | . | . |

4 0.01423 | . | . |

5 -0.13932 | ***| . |

6 0.12842 | . |*** |

7 0.11150 | . |**. |

8 -0.10317 | .**| . |

9 0.00377 | . | . |

10 -0.02879 | . *| . |

11 -0.10391 | .**| . |

12 -0.08483 | .**| . |

13 0.02341 | . | . |

14 0.09250 | . |**. |

15 0.09371 | . |**. |

16 0.15957 | . |*** |

17 -0.11878 | .**| . |

18 -0.00073 | . | . |

19 -0.05243 | . *| . |

20 -0.04240 | . *| . |

Autocorrelation Check for White Noise

To Chi- Pr >

Lag Square DF ChiSq ------Autocorrelations------

6 261.30 6 <.0001 0.792 0.587 0.420 0.303 0.168 0.115

12 270.55 12 <.0001 0.128 0.108 0.077 0.050 0.000 -0.086

18 283.24 18 <.0001 -0.134 -0.110 -0.051 0.048 0.094 0.120

24 288.11 24 <.0001 0.092 0.052 0.016 -0.017 -0.048 -0.086

Monte Carlo AR(2) data Yt = 0.7Yt-1 - 0.49Yt-1+ ut

X=Time Y=AR(2) Series

The ARIMA Procedure

Name of Variable = y

Mean of Working Series -0.10368

Standard Deviation 1.180282

Number of Observations 200

Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

0 1.393065 1.00000 | |********************|

1 0.673948 0.48379 | . |********** |

2 -0.069432 -.04984 | . *| . |

3 -0.287630 -.20647 | ****| . |

4 -0.172808 -.12405 | . **| . |

5 0.058282 0.04184 | . |* . |

6 0.179076 0.12855 | . |***. |

7 0.157243 0.11288 | . |** . |

8 0.024019 0.01724 | . | . |

9 0.0068582 0.00492 | . | . |

10 -0.030892 -.02218 | . | . |

11 -0.055572 -.03989 | . *| . |

12 0.023867 0.01713 | . | . |

13 0.070118 0.05033 | . |* . |

14 0.052111 0.03741 | . |* . |

15 -0.021530 -.01545 | . | . |

16 0.010314 0.00740 | . | . |

17 0.059325 0.04259 | . |* . |

18 -0.053146 -.03815 | . *| . |

19 -0.114683 -.08232 | . **| . |

20 -0.096849 -.06952 | . *| . |

Partial Autocorrelations

Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

1 0.48379 | . |********** |

2 -0.37064 | *******| . |

3 0.00891 | . | . |

4 -0.01443 | . | . |

5 0.08108 | . |**. |

6 0.03143 | . |* . |

7 0.03877 | . |* . |

8 -0.03166 | . *| . |

9 0.09014 | . |**. |

10 -0.07655 | .**| . |

11 0.00655 | . | . |

12 0.04906 | . |* . |

13 -0.00388 | . | . |

14 0.00072 | . | . |

15 -0.03040 | . *| . |

16 0.07375 | . |* . |

17 0.01238 | . | . |

18 -0.12232 | .**| . |

19 0.00954 | . | . |

20 -0.02671 | . *| . |

Autocorrelation Check for White Noise

To Chi- Pr >

Lag Square DF ChiSq ------Autocorrelations------

6 63.74 6 <.0001 0.484 -0.050 -0.206 -0.124 0.042 0.129

12 66.98 12 <.0001 0.113 0.017 0.005 -0.022 -0.040 0.017

18 68.62 18 <.0001 0.050 0.037 -0.015 0.007 0.043 -0.038

24 73.17 24 <.0001 -0.082 -0.070 -0.071 -0.059 0.011 -0.002

Monte Carlo MA(1) data with theta(1) = 0.8 Yt-1 = ut+0.8ut-1

X=Time Y=MA(1) Series

The ARIMA Procedure

Name of Variable = y

Mean of Working Series 0.024985

Standard Deviation 1.177461

Number of Observations 200

Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

0 1.386414 1.00000 | |********************|

1 0.617518 0.44541 | . |********* |

2 -0.102013 -.07358 | . *| . |

3 -0.039333 -.02837 | . *| . |

4 0.075957 0.05479 | . |* . |

5 0.076722 0.05534 | . |* . |

6 0.024612 0.01775 | . | . |

7 0.071660 0.05169 | . |* . |

8 0.086203 0.06218 | . |* . |

9 0.149339 0.10772 | . |**. |

10 0.104206 0.07516 | . |**. |

11 -0.023733 -.01712 | . | . |

12 0.038651 0.02788 | . |* . |

13 0.093707 0.06759 | . |* . |

14 0.052088 0.03757 | . |* . |

15 0.159412 0.11498 | . |**. |

16 0.294483 0.21241 | . |**** |

17 0.183905 0.13265 | . |***. |

18 0.055823 0.04026 | . |* . |

19 0.103898 0.07494 | . |* . |

20 0.059887 0.04320 | . |* . |

Partial Autocorrelations

Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

1 0.44541 | . |********* |

2 -0.33928 | *******| . |

3 0.23492 | . |***** |

4 -0.09839 | .**| . |

5 0.10259 | . |**. |

6 -0.05952 | . *| . |

7 0.12402 | . |**. |

8 -0.05180 | . *| . |

9 0.18240 | . |**** |

10 -0.11637 | .**| . |

11 0.06511 | . |* . |

12 0.02013 | . | . |

13 0.02433 | . | . |

14 -0.01123 | . | . |

15 0.19687 | . |**** |

16 0.04651 | . |* . |

17 0.02853 | . |* . |

18 0.03517 | . |* . |

19 0.07181 | . |* . |

20 -0.08323 | .**| . |

Autocorrelation Check for White Noise

To Chi- Pr >

Lag Square DF ChiSq ------Autocorrelations------

6 42.86 6 <.0001 0.445 -0.074 -0.028 0.055 0.055 0.018

12 48.12 12 <.0001 0.052 0.062 0.108 0.075 -0.017 0.028

18 66.45 18 <.0001 0.068 0.038 0.115 0.212 0.133 0.040

24 70.28 24 <.0001 0.075 0.043 -0.075 -0.058 0.006 0.021

Monte Carlo MA(2) Yt-1 = ut + 0.8ut-1 – 0.4ut-2

X=Time Y=MA(2) Series

The ARIMA Procedure

Name of Variable = y

Mean of Working Series -0.00455

Standard Deviation 1.333815

Number of Observations 200

Autocorrelations

Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

0 1.779064 1.00000 | |********************|

1 0.480413 0.27004 | . |***** |

2 -0.381847 -.21463 | ****| . |

3 0.044064 0.02477 | . | . |

4 -0.049282 -.02770 | . *| . |

5 -0.110860 -.06231 | . *| . |

6 0.027674 0.01556 | . | . |

7 0.090107 0.05065 | . |* . |

8 0.054117 0.03042 | . |* . |

9 -0.031377 -.01764 | . | . |

10 -0.153138 -.08608 | .**| . |

11 -0.087647 -.04927 | . *| . |

12 -0.046587 -.02619 | . *| . |

13 -0.046934 -.02638 | . *| . |

14 0.224168 0.12600 | . |*** |

15 0.117552 0.06608 | . |* . |

16 -0.071001 -.03991 | . *| . |

17 0.121724 0.06842 | . |* . |

18 0.096163 0.05405 | . |* . |

19 0.093289 0.05244 | . |* . |

20 0.120107 0.06751 | . |* . |

Partial Autocorrelations

Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

1 0.27004 | . |***** |

2 -0.31017 | ******| . |

3 0.22015 | . |**** |

4 -0.22689 | *****| . |

5 0.12117 | . |**. |

6 -0.09463 | .**| . |

7 0.12221 | . |**. |

8 -0.05831 | . *| . |

9 0.03196 | . |* . |

10 -0.13000 | ***| . |

11 0.05601 | . |* . |

12 -0.11492 | .**| . |

13 0.06755 | . |* . |

14 0.09337 | . |**. |

15 -0.04957 | . *| . |

16 0.05922 | . |* . |

17 0.04454 | . |* . |

18 0.02478 | . | . |

19 0.11539 | . |**. |

20 -0.02065 | . | . |

Autocorrelation Check for White Noise

To Chi- Pr >

Lag Square DF ChiSq ------Autocorrelations------

6 25.34 6 0.0003 0.270 -0.215 0.025 -0.028 -0.062 0.016

12 28.38 12 0.0049 0.051 0.030 -0.018 -0.086 -0.049 -0.026

18 34.97 18 0.0095 -0.026 0.126 0.066 -0.040 0.068 0.054

24 41.17 24 0.0160 0.052 0.068 -0.075 -0.020 0.049 -0.107