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(Partial) Autocorrelation Function

Date of computation

Mon, 17 Dec 2012 14:48:09 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t13557738220pgwyud29owjr68.htm/, Retrieved Sun, 17 Aug 2025 16:02:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201169, Retrieved Sun, 17 Aug 2025 16:02:05 +0000

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Estimated Impact

253

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- R P         [Univariate Data Series] [WS8 Time Series A...] [2010-11-30 09:10:08] [afe9379cca749d06b3d6872e02cc47ed]
- RMP           [Classical Decomposition] [] [2011-11-28 11:49:18] [77e355412ccdb651b3c7eae41c3da865]
- R               [Classical Decomposition] [] [2011-11-28 16:53:16] [aefb5c2d4042694c5b6b82f93ac1885a]
- RMPD              [Exponential Smoothing] [] [2012-11-26 19:08:13] [c6861060a9fe16fe372e7d046f8d5b70]
- RMP                 [(Partial) Autocorrelation Function] [] [2012-12-16 21:00:20] [c6861060a9fe16fe372e7d046f8d5b70]
- R P                   [(Partial) Autocorrelation Function] [] [2012-12-16 21:07:20] [c6861060a9fe16fe372e7d046f8d5b70]
-   P                     [(Partial) Autocorrelation Function] [] [2012-12-16 21:08:49] [c6861060a9fe16fe372e7d046f8d5b70]
-  M                          [(Partial) Autocorrelation Function] [] [2012-12-17 19:48:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201169&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201169&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.030498	0.5874	0.278638
2	-0.14613	-2.8147	0.002572
3	-0.254888	-4.9095	1e-06
4	-0.077666	-1.496	0.067757
5	0.26831	5.168	0
6	-0.116454	-2.2431	0.012741
7	0.237151	4.5678	3e-06
8	-0.108755	-2.0948	0.018435
9	-0.269739	-5.1955	0
10	-0.201482	-3.8808	6.2e-05
11	-0.001451	-0.0279	0.488861
12	0.759859	14.6359	0
13	-0.020891	-0.4024	0.343817
14	-0.2105	-4.0545	3.1e-05
15	-0.28356	-5.4617	0
16	-0.123045	-2.37	0.009149
17	0.226932	4.371	8e-06
18	-0.139932	-2.6953	0.003676
19	0.233959	4.5064	4e-06
20	-0.117883	-2.2706	0.011872
21	-0.243879	-4.6974	2e-06
22	-0.183068	-3.5261	0.000237
23	-0.012166	-0.2343	0.407425
24	0.720824	13.8841	0
25	-0.007937	-0.1529	0.439292
26	-0.189763	-3.6551	0.000147
27	-0.262816	-5.0622	0
28	-0.10125	-1.9502	0.025952
29	0.230583	4.4414	6e-06
30	-0.128737	-2.4796	0.006797
31	0.215015	4.1415	2.1e-05
32	-0.117502	-2.2633	0.012099
33	-0.222654	-4.2886	1.1e-05
34	-0.160545	-3.0923	0.001068
35	-0.028872	-0.5561	0.289234
36	0.688743	13.2661	0
37	-0.020199	-0.3891	0.348729
38	-0.154053	-2.9673	0.0016
39	-0.240786	-4.6379	2e-06
40	-0.093956	-1.8097	0.035574
41	0.193526	3.7276	0.000112
42	-0.120383	-2.3187	0.010476
43	0.193712	3.7312	0.00011
44	-0.105681	-2.0356	0.021253
45	-0.226142	-4.3558	9e-06
46	-0.154918	-2.9839	0.001517
47	-0.00787	-0.1516	0.439795
48	0.664945	12.8077	0
49	0.014313	0.2757	0.391472
50	-0.133233	-2.5662	0.005336
51	-0.20069	-3.8656	6.5e-05
52	-0.073584	-1.4173	0.078614
53	0.205259	3.9536	4.6e-05
54	-0.10611	-2.0438	0.020839
55	0.229817	4.4266	6e-06
56	-0.08751	-1.6856	0.046361
57	-0.194829	-3.7527	0.000101
58	-0.139948	-2.6956	0.003673
59	0.004702	0.0906	0.463939
60	0.607207	11.6956	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.030498 & 0.5874 & 0.278638 \tabularnewline
2 & -0.14613 & -2.8147 & 0.002572 \tabularnewline
3 & -0.254888 & -4.9095 & 1e-06 \tabularnewline
4 & -0.077666 & -1.496 & 0.067757 \tabularnewline
5 & 0.26831 & 5.168 & 0 \tabularnewline
6 & -0.116454 & -2.2431 & 0.012741 \tabularnewline
7 & 0.237151 & 4.5678 & 3e-06 \tabularnewline
8 & -0.108755 & -2.0948 & 0.018435 \tabularnewline
9 & -0.269739 & -5.1955 & 0 \tabularnewline
10 & -0.201482 & -3.8808 & 6.2e-05 \tabularnewline
11 & -0.001451 & -0.0279 & 0.488861 \tabularnewline
12 & 0.759859 & 14.6359 & 0 \tabularnewline
13 & -0.020891 & -0.4024 & 0.343817 \tabularnewline
14 & -0.2105 & -4.0545 & 3.1e-05 \tabularnewline
15 & -0.28356 & -5.4617 & 0 \tabularnewline
16 & -0.123045 & -2.37 & 0.009149 \tabularnewline
17 & 0.226932 & 4.371 & 8e-06 \tabularnewline
18 & -0.139932 & -2.6953 & 0.003676 \tabularnewline
19 & 0.233959 & 4.5064 & 4e-06 \tabularnewline
20 & -0.117883 & -2.2706 & 0.011872 \tabularnewline
21 & -0.243879 & -4.6974 & 2e-06 \tabularnewline
22 & -0.183068 & -3.5261 & 0.000237 \tabularnewline
23 & -0.012166 & -0.2343 & 0.407425 \tabularnewline
24 & 0.720824 & 13.8841 & 0 \tabularnewline
25 & -0.007937 & -0.1529 & 0.439292 \tabularnewline
26 & -0.189763 & -3.6551 & 0.000147 \tabularnewline
27 & -0.262816 & -5.0622 & 0 \tabularnewline
28 & -0.10125 & -1.9502 & 0.025952 \tabularnewline
29 & 0.230583 & 4.4414 & 6e-06 \tabularnewline
30 & -0.128737 & -2.4796 & 0.006797 \tabularnewline
31 & 0.215015 & 4.1415 & 2.1e-05 \tabularnewline
32 & -0.117502 & -2.2633 & 0.012099 \tabularnewline
33 & -0.222654 & -4.2886 & 1.1e-05 \tabularnewline
34 & -0.160545 & -3.0923 & 0.001068 \tabularnewline
35 & -0.028872 & -0.5561 & 0.289234 \tabularnewline
36 & 0.688743 & 13.2661 & 0 \tabularnewline
37 & -0.020199 & -0.3891 & 0.348729 \tabularnewline
38 & -0.154053 & -2.9673 & 0.0016 \tabularnewline
39 & -0.240786 & -4.6379 & 2e-06 \tabularnewline
40 & -0.093956 & -1.8097 & 0.035574 \tabularnewline
41 & 0.193526 & 3.7276 & 0.000112 \tabularnewline
42 & -0.120383 & -2.3187 & 0.010476 \tabularnewline
43 & 0.193712 & 3.7312 & 0.00011 \tabularnewline
44 & -0.105681 & -2.0356 & 0.021253 \tabularnewline
45 & -0.226142 & -4.3558 & 9e-06 \tabularnewline
46 & -0.154918 & -2.9839 & 0.001517 \tabularnewline
47 & -0.00787 & -0.1516 & 0.439795 \tabularnewline
48 & 0.664945 & 12.8077 & 0 \tabularnewline
49 & 0.014313 & 0.2757 & 0.391472 \tabularnewline
50 & -0.133233 & -2.5662 & 0.005336 \tabularnewline
51 & -0.20069 & -3.8656 & 6.5e-05 \tabularnewline
52 & -0.073584 & -1.4173 & 0.078614 \tabularnewline
53 & 0.205259 & 3.9536 & 4.6e-05 \tabularnewline
54 & -0.10611 & -2.0438 & 0.020839 \tabularnewline
55 & 0.229817 & 4.4266 & 6e-06 \tabularnewline
56 & -0.08751 & -1.6856 & 0.046361 \tabularnewline
57 & -0.194829 & -3.7527 & 0.000101 \tabularnewline
58 & -0.139948 & -2.6956 & 0.003673 \tabularnewline
59 & 0.004702 & 0.0906 & 0.463939 \tabularnewline
60 & 0.607207 & 11.6956 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201169&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.030498[/C][C]0.5874[/C][C]0.278638[/C][/ROW]
[ROW][C]2[/C][C]-0.14613[/C][C]-2.8147[/C][C]0.002572[/C][/ROW]
[ROW][C]3[/C][C]-0.254888[/C][C]-4.9095[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.077666[/C][C]-1.496[/C][C]0.067757[/C][/ROW]
[ROW][C]5[/C][C]0.26831[/C][C]5.168[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.116454[/C][C]-2.2431[/C][C]0.012741[/C][/ROW]
[ROW][C]7[/C][C]0.237151[/C][C]4.5678[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.108755[/C][C]-2.0948[/C][C]0.018435[/C][/ROW]
[ROW][C]9[/C][C]-0.269739[/C][C]-5.1955[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]-0.201482[/C][C]-3.8808[/C][C]6.2e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.001451[/C][C]-0.0279[/C][C]0.488861[/C][/ROW]
[ROW][C]12[/C][C]0.759859[/C][C]14.6359[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.020891[/C][C]-0.4024[/C][C]0.343817[/C][/ROW]
[ROW][C]14[/C][C]-0.2105[/C][C]-4.0545[/C][C]3.1e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.28356[/C][C]-5.4617[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]-0.123045[/C][C]-2.37[/C][C]0.009149[/C][/ROW]
[ROW][C]17[/C][C]0.226932[/C][C]4.371[/C][C]8e-06[/C][/ROW]
[ROW][C]18[/C][C]-0.139932[/C][C]-2.6953[/C][C]0.003676[/C][/ROW]
[ROW][C]19[/C][C]0.233959[/C][C]4.5064[/C][C]4e-06[/C][/ROW]
[ROW][C]20[/C][C]-0.117883[/C][C]-2.2706[/C][C]0.011872[/C][/ROW]
[ROW][C]21[/C][C]-0.243879[/C][C]-4.6974[/C][C]2e-06[/C][/ROW]
[ROW][C]22[/C][C]-0.183068[/C][C]-3.5261[/C][C]0.000237[/C][/ROW]
[ROW][C]23[/C][C]-0.012166[/C][C]-0.2343[/C][C]0.407425[/C][/ROW]
[ROW][C]24[/C][C]0.720824[/C][C]13.8841[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]-0.007937[/C][C]-0.1529[/C][C]0.439292[/C][/ROW]
[ROW][C]26[/C][C]-0.189763[/C][C]-3.6551[/C][C]0.000147[/C][/ROW]
[ROW][C]27[/C][C]-0.262816[/C][C]-5.0622[/C][C]0[/C][/ROW]
[ROW][C]28[/C][C]-0.10125[/C][C]-1.9502[/C][C]0.025952[/C][/ROW]
[ROW][C]29[/C][C]0.230583[/C][C]4.4414[/C][C]6e-06[/C][/ROW]
[ROW][C]30[/C][C]-0.128737[/C][C]-2.4796[/C][C]0.006797[/C][/ROW]
[ROW][C]31[/C][C]0.215015[/C][C]4.1415[/C][C]2.1e-05[/C][/ROW]
[ROW][C]32[/C][C]-0.117502[/C][C]-2.2633[/C][C]0.012099[/C][/ROW]
[ROW][C]33[/C][C]-0.222654[/C][C]-4.2886[/C][C]1.1e-05[/C][/ROW]
[ROW][C]34[/C][C]-0.160545[/C][C]-3.0923[/C][C]0.001068[/C][/ROW]
[ROW][C]35[/C][C]-0.028872[/C][C]-0.5561[/C][C]0.289234[/C][/ROW]
[ROW][C]36[/C][C]0.688743[/C][C]13.2661[/C][C]0[/C][/ROW]
[ROW][C]37[/C][C]-0.020199[/C][C]-0.3891[/C][C]0.348729[/C][/ROW]
[ROW][C]38[/C][C]-0.154053[/C][C]-2.9673[/C][C]0.0016[/C][/ROW]
[ROW][C]39[/C][C]-0.240786[/C][C]-4.6379[/C][C]2e-06[/C][/ROW]
[ROW][C]40[/C][C]-0.093956[/C][C]-1.8097[/C][C]0.035574[/C][/ROW]
[ROW][C]41[/C][C]0.193526[/C][C]3.7276[/C][C]0.000112[/C][/ROW]
[ROW][C]42[/C][C]-0.120383[/C][C]-2.3187[/C][C]0.010476[/C][/ROW]
[ROW][C]43[/C][C]0.193712[/C][C]3.7312[/C][C]0.00011[/C][/ROW]
[ROW][C]44[/C][C]-0.105681[/C][C]-2.0356[/C][C]0.021253[/C][/ROW]
[ROW][C]45[/C][C]-0.226142[/C][C]-4.3558[/C][C]9e-06[/C][/ROW]
[ROW][C]46[/C][C]-0.154918[/C][C]-2.9839[/C][C]0.001517[/C][/ROW]
[ROW][C]47[/C][C]-0.00787[/C][C]-0.1516[/C][C]0.439795[/C][/ROW]
[ROW][C]48[/C][C]0.664945[/C][C]12.8077[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]0.014313[/C][C]0.2757[/C][C]0.391472[/C][/ROW]
[ROW][C]50[/C][C]-0.133233[/C][C]-2.5662[/C][C]0.005336[/C][/ROW]
[ROW][C]51[/C][C]-0.20069[/C][C]-3.8656[/C][C]6.5e-05[/C][/ROW]
[ROW][C]52[/C][C]-0.073584[/C][C]-1.4173[/C][C]0.078614[/C][/ROW]
[ROW][C]53[/C][C]0.205259[/C][C]3.9536[/C][C]4.6e-05[/C][/ROW]
[ROW][C]54[/C][C]-0.10611[/C][C]-2.0438[/C][C]0.020839[/C][/ROW]
[ROW][C]55[/C][C]0.229817[/C][C]4.4266[/C][C]6e-06[/C][/ROW]
[ROW][C]56[/C][C]-0.08751[/C][C]-1.6856[/C][C]0.046361[/C][/ROW]
[ROW][C]57[/C][C]-0.194829[/C][C]-3.7527[/C][C]0.000101[/C][/ROW]
[ROW][C]58[/C][C]-0.139948[/C][C]-2.6956[/C][C]0.003673[/C][/ROW]
[ROW][C]59[/C][C]0.004702[/C][C]0.0906[/C][C]0.463939[/C][/ROW]
[ROW][C]60[/C][C]0.607207[/C][C]11.6956[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201169&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.030498	0.5874	0.278638
2	-0.14613	-2.8147	0.002572
3	-0.254888	-4.9095	1e-06
4	-0.077666	-1.496	0.067757
5	0.26831	5.168	0
6	-0.116454	-2.2431	0.012741
7	0.237151	4.5678	3e-06
8	-0.108755	-2.0948	0.018435
9	-0.269739	-5.1955	0
10	-0.201482	-3.8808	6.2e-05
11	-0.001451	-0.0279	0.488861
12	0.759859	14.6359	0
13	-0.020891	-0.4024	0.343817
14	-0.2105	-4.0545	3.1e-05
15	-0.28356	-5.4617	0
16	-0.123045	-2.37	0.009149
17	0.226932	4.371	8e-06
18	-0.139932	-2.6953	0.003676
19	0.233959	4.5064	4e-06
20	-0.117883	-2.2706	0.011872
21	-0.243879	-4.6974	2e-06
22	-0.183068	-3.5261	0.000237
23	-0.012166	-0.2343	0.407425
24	0.720824	13.8841	0
25	-0.007937	-0.1529	0.439292
26	-0.189763	-3.6551	0.000147
27	-0.262816	-5.0622	0
28	-0.10125	-1.9502	0.025952
29	0.230583	4.4414	6e-06
30	-0.128737	-2.4796	0.006797
31	0.215015	4.1415	2.1e-05
32	-0.117502	-2.2633	0.012099
33	-0.222654	-4.2886	1.1e-05
34	-0.160545	-3.0923	0.001068
35	-0.028872	-0.5561	0.289234
36	0.688743	13.2661	0
37	-0.020199	-0.3891	0.348729
38	-0.154053	-2.9673	0.0016
39	-0.240786	-4.6379	2e-06
40	-0.093956	-1.8097	0.035574
41	0.193526	3.7276	0.000112
42	-0.120383	-2.3187	0.010476
43	0.193712	3.7312	0.00011
44	-0.105681	-2.0356	0.021253
45	-0.226142	-4.3558	9e-06
46	-0.154918	-2.9839	0.001517
47	-0.00787	-0.1516	0.439795
48	0.664945	12.8077	0
49	0.014313	0.2757	0.391472
50	-0.133233	-2.5662	0.005336
51	-0.20069	-3.8656	6.5e-05
52	-0.073584	-1.4173	0.078614
53	0.205259	3.9536	4.6e-05
54	-0.10611	-2.0438	0.020839
55	0.229817	4.4266	6e-06
56	-0.08751	-1.6856	0.046361
57	-0.194829	-3.7527	0.000101
58	-0.139948	-2.6956	0.003673
59	0.004702	0.0906	0.463939
60	0.607207	11.6956	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.030498	0.5874	0.278638
2	-0.147197	-2.8352	0.002415
3	-0.250952	-4.8337	1e-06
4	-0.099073	-1.9083	0.028564
5	0.213671	4.1156	2.4e-05
6	-0.229321	-4.417	7e-06
7	0.319489	6.1538	0
8	-0.108402	-2.088	0.018741
9	-0.295783	-5.6972	0
10	-0.189546	-3.6509	0.000149
11	0.053272	1.0261	0.152758
12	0.637002	12.2695	0
13	-0.152635	-2.94	0.001744
14	-0.220834	-4.2536	1.3e-05
15	-0.061034	-1.1756	0.120255
16	-0.163243	-3.1443	9e-04
17	-0.089865	-1.7309	0.042149
18	-0.089665	-1.7271	0.042494
19	0.08468	1.631	0.051864
20	-0.044248	-0.8523	0.197305
21	0.00323	0.0622	0.475209
22	0.020675	0.3982	0.345344
23	-0.085334	-1.6436	0.050548
24	0.214348	4.1286	2.3e-05
25	-0.011253	-0.2167	0.414261
26	-0.088796	-1.7103	0.044021
27	-0.01174	-0.2261	0.410614
28	-0.020782	-0.4003	0.344585
29	-0.058745	-1.1315	0.129286
30	-0.070939	-1.3664	0.086325
31	-0.04759	-0.9166	0.179961
32	-0.057698	-1.1113	0.133569
33	-0.008413	-0.162	0.435678
34	0.041499	0.7993	0.212304
35	-0.075142	-1.4473	0.074325
36	0.127509	2.456	0.007253
37	-0.042765	-0.8237	0.205317
38	0.026773	0.5157	0.303188
39	0.018049	0.3476	0.364154
40	-0.055476	-1.0685	0.142985
41	-0.161702	-3.1146	0.000993
42	0.0151	0.2909	0.385663
43	-0.075803	-1.4601	0.072558
44	-0.030211	-0.5819	0.280491
45	-0.071316	-1.3736	0.08519
46	0.007752	0.1493	0.440693
47	0.046162	0.8892	0.187249
48	0.10469	2.0165	0.022236
49	0.057529	1.1081	0.13427
50	-0.001197	-0.023	0.490813
51	0.043952	0.8466	0.198888
52	0.014767	0.2844	0.388119
53	-0.049461	-0.9527	0.170683
54	-0.005899	-0.1136	0.454796
55	0.061869	1.1917	0.117073
56	0.003246	0.0625	0.475092
57	-0.003959	-0.0763	0.469629
58	0.018637	0.359	0.359906
59	0.024576	0.4734	0.318116
60	-0.052034	-1.0022	0.158439

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.030498 & 0.5874 & 0.278638 \tabularnewline
2 & -0.147197 & -2.8352 & 0.002415 \tabularnewline
3 & -0.250952 & -4.8337 & 1e-06 \tabularnewline
4 & -0.099073 & -1.9083 & 0.028564 \tabularnewline
5 & 0.213671 & 4.1156 & 2.4e-05 \tabularnewline
6 & -0.229321 & -4.417 & 7e-06 \tabularnewline
7 & 0.319489 & 6.1538 & 0 \tabularnewline
8 & -0.108402 & -2.088 & 0.018741 \tabularnewline
9 & -0.295783 & -5.6972 & 0 \tabularnewline
10 & -0.189546 & -3.6509 & 0.000149 \tabularnewline
11 & 0.053272 & 1.0261 & 0.152758 \tabularnewline
12 & 0.637002 & 12.2695 & 0 \tabularnewline
13 & -0.152635 & -2.94 & 0.001744 \tabularnewline
14 & -0.220834 & -4.2536 & 1.3e-05 \tabularnewline
15 & -0.061034 & -1.1756 & 0.120255 \tabularnewline
16 & -0.163243 & -3.1443 & 9e-04 \tabularnewline
17 & -0.089865 & -1.7309 & 0.042149 \tabularnewline
18 & -0.089665 & -1.7271 & 0.042494 \tabularnewline
19 & 0.08468 & 1.631 & 0.051864 \tabularnewline
20 & -0.044248 & -0.8523 & 0.197305 \tabularnewline
21 & 0.00323 & 0.0622 & 0.475209 \tabularnewline
22 & 0.020675 & 0.3982 & 0.345344 \tabularnewline
23 & -0.085334 & -1.6436 & 0.050548 \tabularnewline
24 & 0.214348 & 4.1286 & 2.3e-05 \tabularnewline
25 & -0.011253 & -0.2167 & 0.414261 \tabularnewline
26 & -0.088796 & -1.7103 & 0.044021 \tabularnewline
27 & -0.01174 & -0.2261 & 0.410614 \tabularnewline
28 & -0.020782 & -0.4003 & 0.344585 \tabularnewline
29 & -0.058745 & -1.1315 & 0.129286 \tabularnewline
30 & -0.070939 & -1.3664 & 0.086325 \tabularnewline
31 & -0.04759 & -0.9166 & 0.179961 \tabularnewline
32 & -0.057698 & -1.1113 & 0.133569 \tabularnewline
33 & -0.008413 & -0.162 & 0.435678 \tabularnewline
34 & 0.041499 & 0.7993 & 0.212304 \tabularnewline
35 & -0.075142 & -1.4473 & 0.074325 \tabularnewline
36 & 0.127509 & 2.456 & 0.007253 \tabularnewline
37 & -0.042765 & -0.8237 & 0.205317 \tabularnewline
38 & 0.026773 & 0.5157 & 0.303188 \tabularnewline
39 & 0.018049 & 0.3476 & 0.364154 \tabularnewline
40 & -0.055476 & -1.0685 & 0.142985 \tabularnewline
41 & -0.161702 & -3.1146 & 0.000993 \tabularnewline
42 & 0.0151 & 0.2909 & 0.385663 \tabularnewline
43 & -0.075803 & -1.4601 & 0.072558 \tabularnewline
44 & -0.030211 & -0.5819 & 0.280491 \tabularnewline
45 & -0.071316 & -1.3736 & 0.08519 \tabularnewline
46 & 0.007752 & 0.1493 & 0.440693 \tabularnewline
47 & 0.046162 & 0.8892 & 0.187249 \tabularnewline
48 & 0.10469 & 2.0165 & 0.022236 \tabularnewline
49 & 0.057529 & 1.1081 & 0.13427 \tabularnewline
50 & -0.001197 & -0.023 & 0.490813 \tabularnewline
51 & 0.043952 & 0.8466 & 0.198888 \tabularnewline
52 & 0.014767 & 0.2844 & 0.388119 \tabularnewline
53 & -0.049461 & -0.9527 & 0.170683 \tabularnewline
54 & -0.005899 & -0.1136 & 0.454796 \tabularnewline
55 & 0.061869 & 1.1917 & 0.117073 \tabularnewline
56 & 0.003246 & 0.0625 & 0.475092 \tabularnewline
57 & -0.003959 & -0.0763 & 0.469629 \tabularnewline
58 & 0.018637 & 0.359 & 0.359906 \tabularnewline
59 & 0.024576 & 0.4734 & 0.318116 \tabularnewline
60 & -0.052034 & -1.0022 & 0.158439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201169&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.030498[/C][C]0.5874[/C][C]0.278638[/C][/ROW]
[ROW][C]2[/C][C]-0.147197[/C][C]-2.8352[/C][C]0.002415[/C][/ROW]
[ROW][C]3[/C][C]-0.250952[/C][C]-4.8337[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.099073[/C][C]-1.9083[/C][C]0.028564[/C][/ROW]
[ROW][C]5[/C][C]0.213671[/C][C]4.1156[/C][C]2.4e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.229321[/C][C]-4.417[/C][C]7e-06[/C][/ROW]
[ROW][C]7[/C][C]0.319489[/C][C]6.1538[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.108402[/C][C]-2.088[/C][C]0.018741[/C][/ROW]
[ROW][C]9[/C][C]-0.295783[/C][C]-5.6972[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]-0.189546[/C][C]-3.6509[/C][C]0.000149[/C][/ROW]
[ROW][C]11[/C][C]0.053272[/C][C]1.0261[/C][C]0.152758[/C][/ROW]
[ROW][C]12[/C][C]0.637002[/C][C]12.2695[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.152635[/C][C]-2.94[/C][C]0.001744[/C][/ROW]
[ROW][C]14[/C][C]-0.220834[/C][C]-4.2536[/C][C]1.3e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.061034[/C][C]-1.1756[/C][C]0.120255[/C][/ROW]
[ROW][C]16[/C][C]-0.163243[/C][C]-3.1443[/C][C]9e-04[/C][/ROW]
[ROW][C]17[/C][C]-0.089865[/C][C]-1.7309[/C][C]0.042149[/C][/ROW]
[ROW][C]18[/C][C]-0.089665[/C][C]-1.7271[/C][C]0.042494[/C][/ROW]
[ROW][C]19[/C][C]0.08468[/C][C]1.631[/C][C]0.051864[/C][/ROW]
[ROW][C]20[/C][C]-0.044248[/C][C]-0.8523[/C][C]0.197305[/C][/ROW]
[ROW][C]21[/C][C]0.00323[/C][C]0.0622[/C][C]0.475209[/C][/ROW]
[ROW][C]22[/C][C]0.020675[/C][C]0.3982[/C][C]0.345344[/C][/ROW]
[ROW][C]23[/C][C]-0.085334[/C][C]-1.6436[/C][C]0.050548[/C][/ROW]
[ROW][C]24[/C][C]0.214348[/C][C]4.1286[/C][C]2.3e-05[/C][/ROW]
[ROW][C]25[/C][C]-0.011253[/C][C]-0.2167[/C][C]0.414261[/C][/ROW]
[ROW][C]26[/C][C]-0.088796[/C][C]-1.7103[/C][C]0.044021[/C][/ROW]
[ROW][C]27[/C][C]-0.01174[/C][C]-0.2261[/C][C]0.410614[/C][/ROW]
[ROW][C]28[/C][C]-0.020782[/C][C]-0.4003[/C][C]0.344585[/C][/ROW]
[ROW][C]29[/C][C]-0.058745[/C][C]-1.1315[/C][C]0.129286[/C][/ROW]
[ROW][C]30[/C][C]-0.070939[/C][C]-1.3664[/C][C]0.086325[/C][/ROW]
[ROW][C]31[/C][C]-0.04759[/C][C]-0.9166[/C][C]0.179961[/C][/ROW]
[ROW][C]32[/C][C]-0.057698[/C][C]-1.1113[/C][C]0.133569[/C][/ROW]
[ROW][C]33[/C][C]-0.008413[/C][C]-0.162[/C][C]0.435678[/C][/ROW]
[ROW][C]34[/C][C]0.041499[/C][C]0.7993[/C][C]0.212304[/C][/ROW]
[ROW][C]35[/C][C]-0.075142[/C][C]-1.4473[/C][C]0.074325[/C][/ROW]
[ROW][C]36[/C][C]0.127509[/C][C]2.456[/C][C]0.007253[/C][/ROW]
[ROW][C]37[/C][C]-0.042765[/C][C]-0.8237[/C][C]0.205317[/C][/ROW]
[ROW][C]38[/C][C]0.026773[/C][C]0.5157[/C][C]0.303188[/C][/ROW]
[ROW][C]39[/C][C]0.018049[/C][C]0.3476[/C][C]0.364154[/C][/ROW]
[ROW][C]40[/C][C]-0.055476[/C][C]-1.0685[/C][C]0.142985[/C][/ROW]
[ROW][C]41[/C][C]-0.161702[/C][C]-3.1146[/C][C]0.000993[/C][/ROW]
[ROW][C]42[/C][C]0.0151[/C][C]0.2909[/C][C]0.385663[/C][/ROW]
[ROW][C]43[/C][C]-0.075803[/C][C]-1.4601[/C][C]0.072558[/C][/ROW]
[ROW][C]44[/C][C]-0.030211[/C][C]-0.5819[/C][C]0.280491[/C][/ROW]
[ROW][C]45[/C][C]-0.071316[/C][C]-1.3736[/C][C]0.08519[/C][/ROW]
[ROW][C]46[/C][C]0.007752[/C][C]0.1493[/C][C]0.440693[/C][/ROW]
[ROW][C]47[/C][C]0.046162[/C][C]0.8892[/C][C]0.187249[/C][/ROW]
[ROW][C]48[/C][C]0.10469[/C][C]2.0165[/C][C]0.022236[/C][/ROW]
[ROW][C]49[/C][C]0.057529[/C][C]1.1081[/C][C]0.13427[/C][/ROW]
[ROW][C]50[/C][C]-0.001197[/C][C]-0.023[/C][C]0.490813[/C][/ROW]
[ROW][C]51[/C][C]0.043952[/C][C]0.8466[/C][C]0.198888[/C][/ROW]
[ROW][C]52[/C][C]0.014767[/C][C]0.2844[/C][C]0.388119[/C][/ROW]
[ROW][C]53[/C][C]-0.049461[/C][C]-0.9527[/C][C]0.170683[/C][/ROW]
[ROW][C]54[/C][C]-0.005899[/C][C]-0.1136[/C][C]0.454796[/C][/ROW]
[ROW][C]55[/C][C]0.061869[/C][C]1.1917[/C][C]0.117073[/C][/ROW]
[ROW][C]56[/C][C]0.003246[/C][C]0.0625[/C][C]0.475092[/C][/ROW]
[ROW][C]57[/C][C]-0.003959[/C][C]-0.0763[/C][C]0.469629[/C][/ROW]
[ROW][C]58[/C][C]0.018637[/C][C]0.359[/C][C]0.359906[/C][/ROW]
[ROW][C]59[/C][C]0.024576[/C][C]0.4734[/C][C]0.318116[/C][/ROW]
[ROW][C]60[/C][C]-0.052034[/C][C]-1.0022[/C][C]0.158439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201169&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.030498	0.5874	0.278638
2	-0.147197	-2.8352	0.002415
3	-0.250952	-4.8337	1e-06
4	-0.099073	-1.9083	0.028564
5	0.213671	4.1156	2.4e-05
6	-0.229321	-4.417	7e-06
7	0.319489	6.1538	0
8	-0.108402	-2.088	0.018741
9	-0.295783	-5.6972	0
10	-0.189546	-3.6509	0.000149
11	0.053272	1.0261	0.152758
12	0.637002	12.2695	0
13	-0.152635	-2.94	0.001744
14	-0.220834	-4.2536	1.3e-05
15	-0.061034	-1.1756	0.120255
16	-0.163243	-3.1443	9e-04
17	-0.089865	-1.7309	0.042149
18	-0.089665	-1.7271	0.042494
19	0.08468	1.631	0.051864
20	-0.044248	-0.8523	0.197305
21	0.00323	0.0622	0.475209
22	0.020675	0.3982	0.345344
23	-0.085334	-1.6436	0.050548
24	0.214348	4.1286	2.3e-05
25	-0.011253	-0.2167	0.414261
26	-0.088796	-1.7103	0.044021
27	-0.01174	-0.2261	0.410614
28	-0.020782	-0.4003	0.344585
29	-0.058745	-1.1315	0.129286
30	-0.070939	-1.3664	0.086325
31	-0.04759	-0.9166	0.179961
32	-0.057698	-1.1113	0.133569
33	-0.008413	-0.162	0.435678
34	0.041499	0.7993	0.212304
35	-0.075142	-1.4473	0.074325
36	0.127509	2.456	0.007253
37	-0.042765	-0.8237	0.205317
38	0.026773	0.5157	0.303188
39	0.018049	0.3476	0.364154
40	-0.055476	-1.0685	0.142985
41	-0.161702	-3.1146	0.000993
42	0.0151	0.2909	0.385663
43	-0.075803	-1.4601	0.072558
44	-0.030211	-0.5819	0.280491
45	-0.071316	-1.3736	0.08519
46	0.007752	0.1493	0.440693
47	0.046162	0.8892	0.187249
48	0.10469	2.0165	0.022236
49	0.057529	1.1081	0.13427
50	-0.001197	-0.023	0.490813
51	0.043952	0.8466	0.198888
52	0.014767	0.2844	0.388119
53	-0.049461	-0.9527	0.170683
54	-0.005899	-0.1136	0.454796
55	0.061869	1.1917	0.117073
56	0.003246	0.0625	0.475092
57	-0.003959	-0.0763	0.469629
58	0.018637	0.359	0.359906
59	0.024576	0.4734	0.318116
60	-0.052034	-1.0022	0.158439

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code