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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2011 10:20:17 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t13245672337ntex370ffximam.htm/, Retrieved Fri, 03 May 2024 10:46:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159591, Retrieved Fri, 03 May 2024 10:46:31 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

119

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

-     [Testing Mean with unknown Variance - Critical Value] [] [2010-10-25 13:12:27] [b98453cac15ba1066b407e146608df68]
- RMPD  [Multiple Regression] [] [2011-12-22 13:45:12] [5a05da414fd67612c3b80d44effe0727]
- RM D    [(Partial) Autocorrelation Function] [] [2011-12-22 15:18:49] [5a05da414fd67612c3b80d44effe0727]
- R           [(Partial) Autocorrelation Function] [] [2011-12-22 15:20:17] [95610e892c4b5c84ff80f4c898567a9d] [Current]
-               [(Partial) Autocorrelation Function] [] [2011-12-22 15:29:46] [5a05da414fd67612c3b80d44effe0727] 
- RM              [Variance Reduction Matrix] [] [2011-12-22 15:48:25] [5a05da414fd67612c3b80d44effe0727] 
- RM              [Variance Reduction Matrix] [] [2011-12-22 15:48:57] [5a05da414fd67612c3b80d44effe0727] 
- RM              [Spectral Analysis] [] [2011-12-22 15:57:30] [5a05da414fd67612c3b80d44effe0727] 
- RM              [Exponential Smoothing] [] [2011-12-22 16:47:54] [5a05da414fd67612c3b80d44effe0727] 
- RM                [Classical Decomposition] [] [2011-12-22 16:54:59] [5a05da414fd67612c3b80d44effe0727] 
- RM                  [Decomposition by Loess] [] [2011-12-22 17:21:01] [5a05da414fd67612c3b80d44effe0727] 
- RM                  [Structural Time Series Models] [] [2011-12-22 18:01:39] [5a05da414fd67612c3b80d44effe0727] 
- RM D                [Kendall tau Correlation Matrix] [] [2011-12-22 19:00:08] [5a05da414fd67612c3b80d44effe0727] 
- RM            [Spectral Analysis] [] [2011-12-22 15:33:22] [5a05da414fd67612c3b80d44effe0727] 
- RM              [(Partial) Autocorrelation Function] [] [2011-12-22 15:54:31] [5a05da414fd67612c3b80d44effe0727] 

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Dataseries X:

Download CSV

Histogram

Boxplots

7.9
7.9
8.0
8.0
7.9
8.0
7.7
7.2
7.5
7.3
7.0
7.0
7.0
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8.0
8.0
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6
8.7
8.5
8.3
8.0
8.0
8.8
8.7
8.5
8.1
7.8
7.6
7.4
7.1
6.9
6.7
6.6
6.5
7.1
7.2
6.9
6.7

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159591&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159591&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159591&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	2 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.842886	6.529	0
2	0.590753	4.576	1.2e-05
3	0.430751	3.3366	0.00073
4	0.406312	3.1473	0.001283
5	0.451862	3.5001	0.000442
6	0.45107	3.494	0.00045
7	0.312991	2.4244	0.009181
8	0.101165	0.7836	0.218172
9	-0.080089	-0.6204	0.268683
10	-0.14521	-1.1248	0.132578
11	-0.111177	-0.8612	0.196286
12	-0.103303	-0.8002	0.213382
13	-0.225887	-1.7497	0.04264
14	-0.369565	-2.8626	0.002889
15	-0.426039	-3.3001	0.000815
16	-0.386525	-2.994	0.001998
17	-0.325224	-2.5192	0.007223
18	-0.299858	-2.3227	0.011803
19	-0.347309	-2.6902	0.004617
20	-0.420603	-3.258	0.000925
21	-0.458556	-3.552	0.000376
22	-0.421535	-3.2652	0.000905
23	-0.322044	-2.4945	0.007692
24	-0.244914	-1.8971	0.031316
25	-0.256174	-1.9843	0.0259
26	-0.283561	-2.1965	0.015967
27	-0.267613	-2.0729	0.021241
28	-0.20835	-1.6139	0.055901
29	-0.146773	-1.1369	0.130051
30	-0.092635	-0.7175	0.23791
31	-0.051162	-0.3963	0.346646
32	-0.010954	-0.0849	0.466331
33	0.040393	0.3129	0.377727
34	0.106205	0.8227	0.206979
35	0.168258	1.3033	0.098722
36	0.205675	1.5932	0.058191
37	0.191783	1.4855	0.071317
38	0.184026	1.4255	0.079604
39	0.208383	1.6141	0.055874
40	0.242456	1.8781	0.032618
41	0.242772	1.8805	0.032448
42	0.219461	1.6999	0.047161
43	0.19061	1.4765	0.072525
44	0.158514	1.2278	0.112151
45	0.115712	0.8963	0.186836
46	0.07863	0.6091	0.272391
47	0.045366	0.3514	0.363259
48	0.014199	0.11	0.456393
49	-0.02502	-0.1938	0.423491
50	-0.05589	-0.4329	0.333313
51	-0.062045	-0.4806	0.316276
52	-0.06165	-0.4775	0.317357
53	-0.073622	-0.5703	0.28531
54	-0.06646	-0.5148	0.304293
55	-0.050631	-0.3922	0.348155
56	-0.037929	-0.2938	0.384965
57	-0.029124	-0.2256	0.411141
58	-0.020933	-0.1621	0.435867
59	-0.011872	-0.092	0.46352
60	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.842886 & 6.529 & 0 \tabularnewline
2 & 0.590753 & 4.576 & 1.2e-05 \tabularnewline
3 & 0.430751 & 3.3366 & 0.00073 \tabularnewline
4 & 0.406312 & 3.1473 & 0.001283 \tabularnewline
5 & 0.451862 & 3.5001 & 0.000442 \tabularnewline
6 & 0.45107 & 3.494 & 0.00045 \tabularnewline
7 & 0.312991 & 2.4244 & 0.009181 \tabularnewline
8 & 0.101165 & 0.7836 & 0.218172 \tabularnewline
9 & -0.080089 & -0.6204 & 0.268683 \tabularnewline
10 & -0.14521 & -1.1248 & 0.132578 \tabularnewline
11 & -0.111177 & -0.8612 & 0.196286 \tabularnewline
12 & -0.103303 & -0.8002 & 0.213382 \tabularnewline
13 & -0.225887 & -1.7497 & 0.04264 \tabularnewline
14 & -0.369565 & -2.8626 & 0.002889 \tabularnewline
15 & -0.426039 & -3.3001 & 0.000815 \tabularnewline
16 & -0.386525 & -2.994 & 0.001998 \tabularnewline
17 & -0.325224 & -2.5192 & 0.007223 \tabularnewline
18 & -0.299858 & -2.3227 & 0.011803 \tabularnewline
19 & -0.347309 & -2.6902 & 0.004617 \tabularnewline
20 & -0.420603 & -3.258 & 0.000925 \tabularnewline
21 & -0.458556 & -3.552 & 0.000376 \tabularnewline
22 & -0.421535 & -3.2652 & 0.000905 \tabularnewline
23 & -0.322044 & -2.4945 & 0.007692 \tabularnewline
24 & -0.244914 & -1.8971 & 0.031316 \tabularnewline
25 & -0.256174 & -1.9843 & 0.0259 \tabularnewline
26 & -0.283561 & -2.1965 & 0.015967 \tabularnewline
27 & -0.267613 & -2.0729 & 0.021241 \tabularnewline
28 & -0.20835 & -1.6139 & 0.055901 \tabularnewline
29 & -0.146773 & -1.1369 & 0.130051 \tabularnewline
30 & -0.092635 & -0.7175 & 0.23791 \tabularnewline
31 & -0.051162 & -0.3963 & 0.346646 \tabularnewline
32 & -0.010954 & -0.0849 & 0.466331 \tabularnewline
33 & 0.040393 & 0.3129 & 0.377727 \tabularnewline
34 & 0.106205 & 0.8227 & 0.206979 \tabularnewline
35 & 0.168258 & 1.3033 & 0.098722 \tabularnewline
36 & 0.205675 & 1.5932 & 0.058191 \tabularnewline
37 & 0.191783 & 1.4855 & 0.071317 \tabularnewline
38 & 0.184026 & 1.4255 & 0.079604 \tabularnewline
39 & 0.208383 & 1.6141 & 0.055874 \tabularnewline
40 & 0.242456 & 1.8781 & 0.032618 \tabularnewline
41 & 0.242772 & 1.8805 & 0.032448 \tabularnewline
42 & 0.219461 & 1.6999 & 0.047161 \tabularnewline
43 & 0.19061 & 1.4765 & 0.072525 \tabularnewline
44 & 0.158514 & 1.2278 & 0.112151 \tabularnewline
45 & 0.115712 & 0.8963 & 0.186836 \tabularnewline
46 & 0.07863 & 0.6091 & 0.272391 \tabularnewline
47 & 0.045366 & 0.3514 & 0.363259 \tabularnewline
48 & 0.014199 & 0.11 & 0.456393 \tabularnewline
49 & -0.02502 & -0.1938 & 0.423491 \tabularnewline
50 & -0.05589 & -0.4329 & 0.333313 \tabularnewline
51 & -0.062045 & -0.4806 & 0.316276 \tabularnewline
52 & -0.06165 & -0.4775 & 0.317357 \tabularnewline
53 & -0.073622 & -0.5703 & 0.28531 \tabularnewline
54 & -0.06646 & -0.5148 & 0.304293 \tabularnewline
55 & -0.050631 & -0.3922 & 0.348155 \tabularnewline
56 & -0.037929 & -0.2938 & 0.384965 \tabularnewline
57 & -0.029124 & -0.2256 & 0.411141 \tabularnewline
58 & -0.020933 & -0.1621 & 0.435867 \tabularnewline
59 & -0.011872 & -0.092 & 0.46352 \tabularnewline
60 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159591&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]0.842886[/C][C]6.529[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.590753[/C][C]4.576[/C][C]1.2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.430751[/C][C]3.3366[/C][C]0.00073[/C][/ROW]
[ROW][C]4[/C][C]0.406312[/C][C]3.1473[/C][C]0.001283[/C][/ROW]
[ROW][C]5[/C][C]0.451862[/C][C]3.5001[/C][C]0.000442[/C][/ROW]
[ROW][C]6[/C][C]0.45107[/C][C]3.494[/C][C]0.00045[/C][/ROW]
[ROW][C]7[/C][C]0.312991[/C][C]2.4244[/C][C]0.009181[/C][/ROW]
[ROW][C]8[/C][C]0.101165[/C][C]0.7836[/C][C]0.218172[/C][/ROW]
[ROW][C]9[/C][C]-0.080089[/C][C]-0.6204[/C][C]0.268683[/C][/ROW]
[ROW][C]10[/C][C]-0.14521[/C][C]-1.1248[/C][C]0.132578[/C][/ROW]
[ROW][C]11[/C][C]-0.111177[/C][C]-0.8612[/C][C]0.196286[/C][/ROW]
[ROW][C]12[/C][C]-0.103303[/C][C]-0.8002[/C][C]0.213382[/C][/ROW]
[ROW][C]13[/C][C]-0.225887[/C][C]-1.7497[/C][C]0.04264[/C][/ROW]
[ROW][C]14[/C][C]-0.369565[/C][C]-2.8626[/C][C]0.002889[/C][/ROW]
[ROW][C]15[/C][C]-0.426039[/C][C]-3.3001[/C][C]0.000815[/C][/ROW]
[ROW][C]16[/C][C]-0.386525[/C][C]-2.994[/C][C]0.001998[/C][/ROW]
[ROW][C]17[/C][C]-0.325224[/C][C]-2.5192[/C][C]0.007223[/C][/ROW]
[ROW][C]18[/C][C]-0.299858[/C][C]-2.3227[/C][C]0.011803[/C][/ROW]
[ROW][C]19[/C][C]-0.347309[/C][C]-2.6902[/C][C]0.004617[/C][/ROW]
[ROW][C]20[/C][C]-0.420603[/C][C]-3.258[/C][C]0.000925[/C][/ROW]
[ROW][C]21[/C][C]-0.458556[/C][C]-3.552[/C][C]0.000376[/C][/ROW]
[ROW][C]22[/C][C]-0.421535[/C][C]-3.2652[/C][C]0.000905[/C][/ROW]
[ROW][C]23[/C][C]-0.322044[/C][C]-2.4945[/C][C]0.007692[/C][/ROW]
[ROW][C]24[/C][C]-0.244914[/C][C]-1.8971[/C][C]0.031316[/C][/ROW]
[ROW][C]25[/C][C]-0.256174[/C][C]-1.9843[/C][C]0.0259[/C][/ROW]
[ROW][C]26[/C][C]-0.283561[/C][C]-2.1965[/C][C]0.015967[/C][/ROW]
[ROW][C]27[/C][C]-0.267613[/C][C]-2.0729[/C][C]0.021241[/C][/ROW]
[ROW][C]28[/C][C]-0.20835[/C][C]-1.6139[/C][C]0.055901[/C][/ROW]
[ROW][C]29[/C][C]-0.146773[/C][C]-1.1369[/C][C]0.130051[/C][/ROW]
[ROW][C]30[/C][C]-0.092635[/C][C]-0.7175[/C][C]0.23791[/C][/ROW]
[ROW][C]31[/C][C]-0.051162[/C][C]-0.3963[/C][C]0.346646[/C][/ROW]
[ROW][C]32[/C][C]-0.010954[/C][C]-0.0849[/C][C]0.466331[/C][/ROW]
[ROW][C]33[/C][C]0.040393[/C][C]0.3129[/C][C]0.377727[/C][/ROW]
[ROW][C]34[/C][C]0.106205[/C][C]0.8227[/C][C]0.206979[/C][/ROW]
[ROW][C]35[/C][C]0.168258[/C][C]1.3033[/C][C]0.098722[/C][/ROW]
[ROW][C]36[/C][C]0.205675[/C][C]1.5932[/C][C]0.058191[/C][/ROW]
[ROW][C]37[/C][C]0.191783[/C][C]1.4855[/C][C]0.071317[/C][/ROW]
[ROW][C]38[/C][C]0.184026[/C][C]1.4255[/C][C]0.079604[/C][/ROW]
[ROW][C]39[/C][C]0.208383[/C][C]1.6141[/C][C]0.055874[/C][/ROW]
[ROW][C]40[/C][C]0.242456[/C][C]1.8781[/C][C]0.032618[/C][/ROW]
[ROW][C]41[/C][C]0.242772[/C][C]1.8805[/C][C]0.032448[/C][/ROW]
[ROW][C]42[/C][C]0.219461[/C][C]1.6999[/C][C]0.047161[/C][/ROW]
[ROW][C]43[/C][C]0.19061[/C][C]1.4765[/C][C]0.072525[/C][/ROW]
[ROW][C]44[/C][C]0.158514[/C][C]1.2278[/C][C]0.112151[/C][/ROW]
[ROW][C]45[/C][C]0.115712[/C][C]0.8963[/C][C]0.186836[/C][/ROW]
[ROW][C]46[/C][C]0.07863[/C][C]0.6091[/C][C]0.272391[/C][/ROW]
[ROW][C]47[/C][C]0.045366[/C][C]0.3514[/C][C]0.363259[/C][/ROW]
[ROW][C]48[/C][C]0.014199[/C][C]0.11[/C][C]0.456393[/C][/ROW]
[ROW][C]49[/C][C]-0.02502[/C][C]-0.1938[/C][C]0.423491[/C][/ROW]
[ROW][C]50[/C][C]-0.05589[/C][C]-0.4329[/C][C]0.333313[/C][/ROW]
[ROW][C]51[/C][C]-0.062045[/C][C]-0.4806[/C][C]0.316276[/C][/ROW]
[ROW][C]52[/C][C]-0.06165[/C][C]-0.4775[/C][C]0.317357[/C][/ROW]
[ROW][C]53[/C][C]-0.073622[/C][C]-0.5703[/C][C]0.28531[/C][/ROW]
[ROW][C]54[/C][C]-0.06646[/C][C]-0.5148[/C][C]0.304293[/C][/ROW]
[ROW][C]55[/C][C]-0.050631[/C][C]-0.3922[/C][C]0.348155[/C][/ROW]
[ROW][C]56[/C][C]-0.037929[/C][C]-0.2938[/C][C]0.384965[/C][/ROW]
[ROW][C]57[/C][C]-0.029124[/C][C]-0.2256[/C][C]0.411141[/C][/ROW]
[ROW][C]58[/C][C]-0.020933[/C][C]-0.1621[/C][C]0.435867[/C][/ROW]
[ROW][C]59[/C][C]-0.011872[/C][C]-0.092[/C][C]0.46352[/C][/ROW]
[ROW][C]60[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159591&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159591&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	0.842886	6.529	0
2	0.590753	4.576	1.2e-05
3	0.430751	3.3366	0.00073
4	0.406312	3.1473	0.001283
5	0.451862	3.5001	0.000442
6	0.45107	3.494	0.00045
7	0.312991	2.4244	0.009181
8	0.101165	0.7836	0.218172
9	-0.080089	-0.6204	0.268683
10	-0.14521	-1.1248	0.132578
11	-0.111177	-0.8612	0.196286
12	-0.103303	-0.8002	0.213382
13	-0.225887	-1.7497	0.04264
14	-0.369565	-2.8626	0.002889
15	-0.426039	-3.3001	0.000815
16	-0.386525	-2.994	0.001998
17	-0.325224	-2.5192	0.007223
18	-0.299858	-2.3227	0.011803
19	-0.347309	-2.6902	0.004617
20	-0.420603	-3.258	0.000925
21	-0.458556	-3.552	0.000376
22	-0.421535	-3.2652	0.000905
23	-0.322044	-2.4945	0.007692
24	-0.244914	-1.8971	0.031316
25	-0.256174	-1.9843	0.0259
26	-0.283561	-2.1965	0.015967
27	-0.267613	-2.0729	0.021241
28	-0.20835	-1.6139	0.055901
29	-0.146773	-1.1369	0.130051
30	-0.092635	-0.7175	0.23791
31	-0.051162	-0.3963	0.346646
32	-0.010954	-0.0849	0.466331
33	0.040393	0.3129	0.377727
34	0.106205	0.8227	0.206979
35	0.168258	1.3033	0.098722
36	0.205675	1.5932	0.058191
37	0.191783	1.4855	0.071317
38	0.184026	1.4255	0.079604
39	0.208383	1.6141	0.055874
40	0.242456	1.8781	0.032618
41	0.242772	1.8805	0.032448
42	0.219461	1.6999	0.047161
43	0.19061	1.4765	0.072525
44	0.158514	1.2278	0.112151
45	0.115712	0.8963	0.186836
46	0.07863	0.6091	0.272391
47	0.045366	0.3514	0.363259
48	0.014199	0.11	0.456393
49	-0.02502	-0.1938	0.423491
50	-0.05589	-0.4329	0.333313
51	-0.062045	-0.4806	0.316276
52	-0.06165	-0.4775	0.317357
53	-0.073622	-0.5703	0.28531
54	-0.06646	-0.5148	0.304293
55	-0.050631	-0.3922	0.348155
56	-0.037929	-0.2938	0.384965
57	-0.029124	-0.2256	0.411141
58	-0.020933	-0.1621	0.435867
59	-0.011872	-0.092	0.46352
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.842886	6.529	0
2	-0.413425	-3.2024	0.001091
3	0.314193	2.4337	0.00897
4	0.174312	1.3502	0.091009
5	0.099946	0.7742	0.220932
6	-0.107021	-0.829	0.2052
7	-0.31577	-2.4459	0.008698
8	-0.115872	-0.8975	0.186509
9	-0.171196	-1.3261	0.09492
10	0.048881	0.3786	0.35315
11	0.028066	0.2174	0.414319
12	-0.160524	-1.2434	0.109276
13	-0.260964	-2.0214	0.023852
14	0.205419	1.5912	0.058413
15	0.081231	0.6292	0.2658
16	-0.037004	-0.2866	0.38769
17	-0.169211	-1.3107	0.097477
18	0.00767	0.0594	0.476411
19	-0.053066	-0.411	0.341251
20	-0.07533	-0.5835	0.28087
21	-0.145959	-1.1306	0.131363
22	-0.1174	-0.9094	0.183394
23	0.058103	0.4501	0.327143
24	-0.006908	-0.0535	0.478753
25	-0.051744	-0.4008	0.344992
26	0.011329	0.0878	0.465182
27	-0.064905	-0.5028	0.30849
28	-0.031872	-0.2469	0.402923
29	-0.088127	-0.6826	0.248734
30	0.015541	0.1204	0.452293
31	0.032552	0.2521	0.400894
32	0.00757	0.0586	0.476718
33	0.058307	0.4516	0.326576
34	-0.020641	-0.1599	0.436755
35	-0.048422	-0.3751	0.354464
36	0.026141	0.2025	0.42011
37	-0.117438	-0.9097	0.183319
38	0.002597	0.0201	0.492009
39	-0.093402	-0.7235	0.236095
40	-0.007855	-0.0608	0.475842
41	-0.068021	-0.5269	0.300106
42	-0.021699	-0.1681	0.433542
43	0.034987	0.271	0.393659
44	-0.098488	-0.7629	0.224261
45	-0.083035	-0.6432	0.261276
46	-0.015452	-0.1197	0.452564
47	-0.06176	-0.4784	0.317056
48	-0.016669	-0.1291	0.448848
49	-0.073474	-0.5691	0.285698
50	-0.085434	-0.6618	0.255325
51	0.049661	0.3847	0.35092
52	-0.016356	-0.1267	0.449804
53	0.090842	0.7037	0.242184
54	0.058234	0.4511	0.326778
55	-0.08148	-0.6311	0.265172
56	0.028428	0.2202	0.413231
57	0.011207	0.0868	0.465556
58	-0.038455	-0.2979	0.383414
59	-0.109017	-0.8444	0.200888
60	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.842886 & 6.529 & 0 \tabularnewline
2 & -0.413425 & -3.2024 & 0.001091 \tabularnewline
3 & 0.314193 & 2.4337 & 0.00897 \tabularnewline
4 & 0.174312 & 1.3502 & 0.091009 \tabularnewline
5 & 0.099946 & 0.7742 & 0.220932 \tabularnewline
6 & -0.107021 & -0.829 & 0.2052 \tabularnewline
7 & -0.31577 & -2.4459 & 0.008698 \tabularnewline
8 & -0.115872 & -0.8975 & 0.186509 \tabularnewline
9 & -0.171196 & -1.3261 & 0.09492 \tabularnewline
10 & 0.048881 & 0.3786 & 0.35315 \tabularnewline
11 & 0.028066 & 0.2174 & 0.414319 \tabularnewline
12 & -0.160524 & -1.2434 & 0.109276 \tabularnewline
13 & -0.260964 & -2.0214 & 0.023852 \tabularnewline
14 & 0.205419 & 1.5912 & 0.058413 \tabularnewline
15 & 0.081231 & 0.6292 & 0.2658 \tabularnewline
16 & -0.037004 & -0.2866 & 0.38769 \tabularnewline
17 & -0.169211 & -1.3107 & 0.097477 \tabularnewline
18 & 0.00767 & 0.0594 & 0.476411 \tabularnewline
19 & -0.053066 & -0.411 & 0.341251 \tabularnewline
20 & -0.07533 & -0.5835 & 0.28087 \tabularnewline
21 & -0.145959 & -1.1306 & 0.131363 \tabularnewline
22 & -0.1174 & -0.9094 & 0.183394 \tabularnewline
23 & 0.058103 & 0.4501 & 0.327143 \tabularnewline
24 & -0.006908 & -0.0535 & 0.478753 \tabularnewline
25 & -0.051744 & -0.4008 & 0.344992 \tabularnewline
26 & 0.011329 & 0.0878 & 0.465182 \tabularnewline
27 & -0.064905 & -0.5028 & 0.30849 \tabularnewline
28 & -0.031872 & -0.2469 & 0.402923 \tabularnewline
29 & -0.088127 & -0.6826 & 0.248734 \tabularnewline
30 & 0.015541 & 0.1204 & 0.452293 \tabularnewline
31 & 0.032552 & 0.2521 & 0.400894 \tabularnewline
32 & 0.00757 & 0.0586 & 0.476718 \tabularnewline
33 & 0.058307 & 0.4516 & 0.326576 \tabularnewline
34 & -0.020641 & -0.1599 & 0.436755 \tabularnewline
35 & -0.048422 & -0.3751 & 0.354464 \tabularnewline
36 & 0.026141 & 0.2025 & 0.42011 \tabularnewline
37 & -0.117438 & -0.9097 & 0.183319 \tabularnewline
38 & 0.002597 & 0.0201 & 0.492009 \tabularnewline
39 & -0.093402 & -0.7235 & 0.236095 \tabularnewline
40 & -0.007855 & -0.0608 & 0.475842 \tabularnewline
41 & -0.068021 & -0.5269 & 0.300106 \tabularnewline
42 & -0.021699 & -0.1681 & 0.433542 \tabularnewline
43 & 0.034987 & 0.271 & 0.393659 \tabularnewline
44 & -0.098488 & -0.7629 & 0.224261 \tabularnewline
45 & -0.083035 & -0.6432 & 0.261276 \tabularnewline
46 & -0.015452 & -0.1197 & 0.452564 \tabularnewline
47 & -0.06176 & -0.4784 & 0.317056 \tabularnewline
48 & -0.016669 & -0.1291 & 0.448848 \tabularnewline
49 & -0.073474 & -0.5691 & 0.285698 \tabularnewline
50 & -0.085434 & -0.6618 & 0.255325 \tabularnewline
51 & 0.049661 & 0.3847 & 0.35092 \tabularnewline
52 & -0.016356 & -0.1267 & 0.449804 \tabularnewline
53 & 0.090842 & 0.7037 & 0.242184 \tabularnewline
54 & 0.058234 & 0.4511 & 0.326778 \tabularnewline
55 & -0.08148 & -0.6311 & 0.265172 \tabularnewline
56 & 0.028428 & 0.2202 & 0.413231 \tabularnewline
57 & 0.011207 & 0.0868 & 0.465556 \tabularnewline
58 & -0.038455 & -0.2979 & 0.383414 \tabularnewline
59 & -0.109017 & -0.8444 & 0.200888 \tabularnewline
60 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159591&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]0.842886[/C][C]6.529[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.413425[/C][C]-3.2024[/C][C]0.001091[/C][/ROW]
[ROW][C]3[/C][C]0.314193[/C][C]2.4337[/C][C]0.00897[/C][/ROW]
[ROW][C]4[/C][C]0.174312[/C][C]1.3502[/C][C]0.091009[/C][/ROW]
[ROW][C]5[/C][C]0.099946[/C][C]0.7742[/C][C]0.220932[/C][/ROW]
[ROW][C]6[/C][C]-0.107021[/C][C]-0.829[/C][C]0.2052[/C][/ROW]
[ROW][C]7[/C][C]-0.31577[/C][C]-2.4459[/C][C]0.008698[/C][/ROW]
[ROW][C]8[/C][C]-0.115872[/C][C]-0.8975[/C][C]0.186509[/C][/ROW]
[ROW][C]9[/C][C]-0.171196[/C][C]-1.3261[/C][C]0.09492[/C][/ROW]
[ROW][C]10[/C][C]0.048881[/C][C]0.3786[/C][C]0.35315[/C][/ROW]
[ROW][C]11[/C][C]0.028066[/C][C]0.2174[/C][C]0.414319[/C][/ROW]
[ROW][C]12[/C][C]-0.160524[/C][C]-1.2434[/C][C]0.109276[/C][/ROW]
[ROW][C]13[/C][C]-0.260964[/C][C]-2.0214[/C][C]0.023852[/C][/ROW]
[ROW][C]14[/C][C]0.205419[/C][C]1.5912[/C][C]0.058413[/C][/ROW]
[ROW][C]15[/C][C]0.081231[/C][C]0.6292[/C][C]0.2658[/C][/ROW]
[ROW][C]16[/C][C]-0.037004[/C][C]-0.2866[/C][C]0.38769[/C][/ROW]
[ROW][C]17[/C][C]-0.169211[/C][C]-1.3107[/C][C]0.097477[/C][/ROW]
[ROW][C]18[/C][C]0.00767[/C][C]0.0594[/C][C]0.476411[/C][/ROW]
[ROW][C]19[/C][C]-0.053066[/C][C]-0.411[/C][C]0.341251[/C][/ROW]
[ROW][C]20[/C][C]-0.07533[/C][C]-0.5835[/C][C]0.28087[/C][/ROW]
[ROW][C]21[/C][C]-0.145959[/C][C]-1.1306[/C][C]0.131363[/C][/ROW]
[ROW][C]22[/C][C]-0.1174[/C][C]-0.9094[/C][C]0.183394[/C][/ROW]
[ROW][C]23[/C][C]0.058103[/C][C]0.4501[/C][C]0.327143[/C][/ROW]
[ROW][C]24[/C][C]-0.006908[/C][C]-0.0535[/C][C]0.478753[/C][/ROW]
[ROW][C]25[/C][C]-0.051744[/C][C]-0.4008[/C][C]0.344992[/C][/ROW]
[ROW][C]26[/C][C]0.011329[/C][C]0.0878[/C][C]0.465182[/C][/ROW]
[ROW][C]27[/C][C]-0.064905[/C][C]-0.5028[/C][C]0.30849[/C][/ROW]
[ROW][C]28[/C][C]-0.031872[/C][C]-0.2469[/C][C]0.402923[/C][/ROW]
[ROW][C]29[/C][C]-0.088127[/C][C]-0.6826[/C][C]0.248734[/C][/ROW]
[ROW][C]30[/C][C]0.015541[/C][C]0.1204[/C][C]0.452293[/C][/ROW]
[ROW][C]31[/C][C]0.032552[/C][C]0.2521[/C][C]0.400894[/C][/ROW]
[ROW][C]32[/C][C]0.00757[/C][C]0.0586[/C][C]0.476718[/C][/ROW]
[ROW][C]33[/C][C]0.058307[/C][C]0.4516[/C][C]0.326576[/C][/ROW]
[ROW][C]34[/C][C]-0.020641[/C][C]-0.1599[/C][C]0.436755[/C][/ROW]
[ROW][C]35[/C][C]-0.048422[/C][C]-0.3751[/C][C]0.354464[/C][/ROW]
[ROW][C]36[/C][C]0.026141[/C][C]0.2025[/C][C]0.42011[/C][/ROW]
[ROW][C]37[/C][C]-0.117438[/C][C]-0.9097[/C][C]0.183319[/C][/ROW]
[ROW][C]38[/C][C]0.002597[/C][C]0.0201[/C][C]0.492009[/C][/ROW]
[ROW][C]39[/C][C]-0.093402[/C][C]-0.7235[/C][C]0.236095[/C][/ROW]
[ROW][C]40[/C][C]-0.007855[/C][C]-0.0608[/C][C]0.475842[/C][/ROW]
[ROW][C]41[/C][C]-0.068021[/C][C]-0.5269[/C][C]0.300106[/C][/ROW]
[ROW][C]42[/C][C]-0.021699[/C][C]-0.1681[/C][C]0.433542[/C][/ROW]
[ROW][C]43[/C][C]0.034987[/C][C]0.271[/C][C]0.393659[/C][/ROW]
[ROW][C]44[/C][C]-0.098488[/C][C]-0.7629[/C][C]0.224261[/C][/ROW]
[ROW][C]45[/C][C]-0.083035[/C][C]-0.6432[/C][C]0.261276[/C][/ROW]
[ROW][C]46[/C][C]-0.015452[/C][C]-0.1197[/C][C]0.452564[/C][/ROW]
[ROW][C]47[/C][C]-0.06176[/C][C]-0.4784[/C][C]0.317056[/C][/ROW]
[ROW][C]48[/C][C]-0.016669[/C][C]-0.1291[/C][C]0.448848[/C][/ROW]
[ROW][C]49[/C][C]-0.073474[/C][C]-0.5691[/C][C]0.285698[/C][/ROW]
[ROW][C]50[/C][C]-0.085434[/C][C]-0.6618[/C][C]0.255325[/C][/ROW]
[ROW][C]51[/C][C]0.049661[/C][C]0.3847[/C][C]0.35092[/C][/ROW]
[ROW][C]52[/C][C]-0.016356[/C][C]-0.1267[/C][C]0.449804[/C][/ROW]
[ROW][C]53[/C][C]0.090842[/C][C]0.7037[/C][C]0.242184[/C][/ROW]
[ROW][C]54[/C][C]0.058234[/C][C]0.4511[/C][C]0.326778[/C][/ROW]
[ROW][C]55[/C][C]-0.08148[/C][C]-0.6311[/C][C]0.265172[/C][/ROW]
[ROW][C]56[/C][C]0.028428[/C][C]0.2202[/C][C]0.413231[/C][/ROW]
[ROW][C]57[/C][C]0.011207[/C][C]0.0868[/C][C]0.465556[/C][/ROW]
[ROW][C]58[/C][C]-0.038455[/C][C]-0.2979[/C][C]0.383414[/C][/ROW]
[ROW][C]59[/C][C]-0.109017[/C][C]-0.8444[/C][C]0.200888[/C][/ROW]
[ROW][C]60[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159591&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159591&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	0.842886	6.529	0
2	-0.413425	-3.2024	0.001091
3	0.314193	2.4337	0.00897
4	0.174312	1.3502	0.091009
5	0.099946	0.7742	0.220932
6	-0.107021	-0.829	0.2052
7	-0.31577	-2.4459	0.008698
8	-0.115872	-0.8975	0.186509
9	-0.171196	-1.3261	0.09492
10	0.048881	0.3786	0.35315
11	0.028066	0.2174	0.414319
12	-0.160524	-1.2434	0.109276
13	-0.260964	-2.0214	0.023852
14	0.205419	1.5912	0.058413
15	0.081231	0.6292	0.2658
16	-0.037004	-0.2866	0.38769
17	-0.169211	-1.3107	0.097477
18	0.00767	0.0594	0.476411
19	-0.053066	-0.411	0.341251
20	-0.07533	-0.5835	0.28087
21	-0.145959	-1.1306	0.131363
22	-0.1174	-0.9094	0.183394
23	0.058103	0.4501	0.327143
24	-0.006908	-0.0535	0.478753
25	-0.051744	-0.4008	0.344992
26	0.011329	0.0878	0.465182
27	-0.064905	-0.5028	0.30849
28	-0.031872	-0.2469	0.402923
29	-0.088127	-0.6826	0.248734
30	0.015541	0.1204	0.452293
31	0.032552	0.2521	0.400894
32	0.00757	0.0586	0.476718
33	0.058307	0.4516	0.326576
34	-0.020641	-0.1599	0.436755
35	-0.048422	-0.3751	0.354464
36	0.026141	0.2025	0.42011
37	-0.117438	-0.9097	0.183319
38	0.002597	0.0201	0.492009
39	-0.093402	-0.7235	0.236095
40	-0.007855	-0.0608	0.475842
41	-0.068021	-0.5269	0.300106
42	-0.021699	-0.1681	0.433542
43	0.034987	0.271	0.393659
44	-0.098488	-0.7629	0.224261
45	-0.083035	-0.6432	0.261276
46	-0.015452	-0.1197	0.452564
47	-0.06176	-0.4784	0.317056
48	-0.016669	-0.1291	0.448848
49	-0.073474	-0.5691	0.285698
50	-0.085434	-0.6618	0.255325
51	0.049661	0.3847	0.35092
52	-0.016356	-0.1267	0.449804
53	0.090842	0.7037	0.242184
54	0.058234	0.4511	0.326778
55	-0.08148	-0.6311	0.265172
56	0.028428	0.2202	0.413231
57	0.011207	0.0868	0.465556
58	-0.038455	-0.2979	0.383414
59	-0.109017	-0.8444	0.200888
60	NA	NA	NA

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 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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