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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2011 10:18:49 -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/t1324567152fjjd34zf2ut64vo.htm/, Retrieved Fri, 03 May 2024 05:57:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159587, Retrieved Fri, 03 May 2024 05:57:27 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

105

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] [95610e892c4b5c84ff80f4c898567a9d] [Current]
- R           [(Partial) Autocorrelation Function] [] [2011-12-22 15:20:17] [5a05da414fd67612c3b80d44effe0727] 
-               [(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:

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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	1 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 & 1 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159587&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159587&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159587&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	1 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.846291	6.5553	0
2	0.600571	4.652	9e-06
3	0.443643	3.4364	0.000538
4	0.418405	3.2409	0.000973
5	0.461517	3.5749	0.00035
6	0.45581	3.5307	0.000402
7	0.31514	2.4411	0.008806
8	0.10252	0.7941	0.215129
9	-0.077073	-0.597	0.276374
10	-0.140077	-1.085	0.141125
11	-0.106064	-0.8216	0.207288
12	-0.100627	-0.7795	0.219388
13	-0.22793	-1.7655	0.041281
14	-0.374703	-2.9024	0.002586
15	-0.428174	-3.3166	0.000775
16	-0.382467	-2.9626	0.002184
17	-0.319015	-2.4711	0.008164
18	-0.294484	-2.2811	0.013055
19	-0.346712	-2.6856	0.004674
20	-0.424336	-3.2869	0.000848
21	-0.46211	-3.5795	0.000345
22	-0.422398	-3.2719	0.000887
23	-0.320075	-2.4793	0.007996
24	-0.243198	-1.8838	0.03222
25	-0.257045	-1.9911	0.025517
26	-0.285769	-2.2136	0.015336
27	-0.270921	-2.0985	0.020037
28	-0.214026	-1.6578	0.051285
29	-0.154753	-1.1987	0.117677
30	-0.101676	-0.7876	0.217021
31	-0.05965	-0.4621	0.322858
32	-0.017339	-0.1343	0.446805
33	0.034147	0.2645	0.39615
34	0.095644	0.7409	0.230836
35	0.154045	1.1932	0.118738
36	0.190567	1.4761	0.072569
37	0.178724	1.3844	0.085683
38	0.177035	1.3713	0.087693
39	0.205769	1.5939	0.058109
40	0.238544	1.8478	0.034784
41	0.239134	1.8523	0.03445
42	0.218544	1.6928	0.047837
43	0.191338	1.4821	0.071774
44	0.160496	1.2432	0.109315
45	0.11795	0.9136	0.182281
46	0.081032	0.6277	0.266301
47	0.047667	0.3692	0.356629
48	0.016749	0.1297	0.448604
49	-0.020655	-0.16	0.436711
50	-0.0503	-0.3896	0.349096
51	-0.056759	-0.4397	0.330883
52	-0.057039	-0.4418	0.330104
53	-0.06922	-0.5362	0.29691
54	-0.063086	-0.4887	0.313431
55	-0.048213	-0.3735	0.355063
56	-0.036794	-0.285	0.388311
57	-0.027955	-0.2165	0.414651
58	-0.019625	-0.152	0.439843
59	-0.011015	-0.0853	0.466145
60	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.846291 & 6.5553 & 0 \tabularnewline
2 & 0.600571 & 4.652 & 9e-06 \tabularnewline
3 & 0.443643 & 3.4364 & 0.000538 \tabularnewline
4 & 0.418405 & 3.2409 & 0.000973 \tabularnewline
5 & 0.461517 & 3.5749 & 0.00035 \tabularnewline
6 & 0.45581 & 3.5307 & 0.000402 \tabularnewline
7 & 0.31514 & 2.4411 & 0.008806 \tabularnewline
8 & 0.10252 & 0.7941 & 0.215129 \tabularnewline
9 & -0.077073 & -0.597 & 0.276374 \tabularnewline
10 & -0.140077 & -1.085 & 0.141125 \tabularnewline
11 & -0.106064 & -0.8216 & 0.207288 \tabularnewline
12 & -0.100627 & -0.7795 & 0.219388 \tabularnewline
13 & -0.22793 & -1.7655 & 0.041281 \tabularnewline
14 & -0.374703 & -2.9024 & 0.002586 \tabularnewline
15 & -0.428174 & -3.3166 & 0.000775 \tabularnewline
16 & -0.382467 & -2.9626 & 0.002184 \tabularnewline
17 & -0.319015 & -2.4711 & 0.008164 \tabularnewline
18 & -0.294484 & -2.2811 & 0.013055 \tabularnewline
19 & -0.346712 & -2.6856 & 0.004674 \tabularnewline
20 & -0.424336 & -3.2869 & 0.000848 \tabularnewline
21 & -0.46211 & -3.5795 & 0.000345 \tabularnewline
22 & -0.422398 & -3.2719 & 0.000887 \tabularnewline
23 & -0.320075 & -2.4793 & 0.007996 \tabularnewline
24 & -0.243198 & -1.8838 & 0.03222 \tabularnewline
25 & -0.257045 & -1.9911 & 0.025517 \tabularnewline
26 & -0.285769 & -2.2136 & 0.015336 \tabularnewline
27 & -0.270921 & -2.0985 & 0.020037 \tabularnewline
28 & -0.214026 & -1.6578 & 0.051285 \tabularnewline
29 & -0.154753 & -1.1987 & 0.117677 \tabularnewline
30 & -0.101676 & -0.7876 & 0.217021 \tabularnewline
31 & -0.05965 & -0.4621 & 0.322858 \tabularnewline
32 & -0.017339 & -0.1343 & 0.446805 \tabularnewline
33 & 0.034147 & 0.2645 & 0.39615 \tabularnewline
34 & 0.095644 & 0.7409 & 0.230836 \tabularnewline
35 & 0.154045 & 1.1932 & 0.118738 \tabularnewline
36 & 0.190567 & 1.4761 & 0.072569 \tabularnewline
37 & 0.178724 & 1.3844 & 0.085683 \tabularnewline
38 & 0.177035 & 1.3713 & 0.087693 \tabularnewline
39 & 0.205769 & 1.5939 & 0.058109 \tabularnewline
40 & 0.238544 & 1.8478 & 0.034784 \tabularnewline
41 & 0.239134 & 1.8523 & 0.03445 \tabularnewline
42 & 0.218544 & 1.6928 & 0.047837 \tabularnewline
43 & 0.191338 & 1.4821 & 0.071774 \tabularnewline
44 & 0.160496 & 1.2432 & 0.109315 \tabularnewline
45 & 0.11795 & 0.9136 & 0.182281 \tabularnewline
46 & 0.081032 & 0.6277 & 0.266301 \tabularnewline
47 & 0.047667 & 0.3692 & 0.356629 \tabularnewline
48 & 0.016749 & 0.1297 & 0.448604 \tabularnewline
49 & -0.020655 & -0.16 & 0.436711 \tabularnewline
50 & -0.0503 & -0.3896 & 0.349096 \tabularnewline
51 & -0.056759 & -0.4397 & 0.330883 \tabularnewline
52 & -0.057039 & -0.4418 & 0.330104 \tabularnewline
53 & -0.06922 & -0.5362 & 0.29691 \tabularnewline
54 & -0.063086 & -0.4887 & 0.313431 \tabularnewline
55 & -0.048213 & -0.3735 & 0.355063 \tabularnewline
56 & -0.036794 & -0.285 & 0.388311 \tabularnewline
57 & -0.027955 & -0.2165 & 0.414651 \tabularnewline
58 & -0.019625 & -0.152 & 0.439843 \tabularnewline
59 & -0.011015 & -0.0853 & 0.466145 \tabularnewline
60 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159587&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]0.846291[/C][C]6.5553[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.600571[/C][C]4.652[/C][C]9e-06[/C][/ROW]
[ROW][C]3[/C][C]0.443643[/C][C]3.4364[/C][C]0.000538[/C][/ROW]
[ROW][C]4[/C][C]0.418405[/C][C]3.2409[/C][C]0.000973[/C][/ROW]
[ROW][C]5[/C][C]0.461517[/C][C]3.5749[/C][C]0.00035[/C][/ROW]
[ROW][C]6[/C][C]0.45581[/C][C]3.5307[/C][C]0.000402[/C][/ROW]
[ROW][C]7[/C][C]0.31514[/C][C]2.4411[/C][C]0.008806[/C][/ROW]
[ROW][C]8[/C][C]0.10252[/C][C]0.7941[/C][C]0.215129[/C][/ROW]
[ROW][C]9[/C][C]-0.077073[/C][C]-0.597[/C][C]0.276374[/C][/ROW]
[ROW][C]10[/C][C]-0.140077[/C][C]-1.085[/C][C]0.141125[/C][/ROW]
[ROW][C]11[/C][C]-0.106064[/C][C]-0.8216[/C][C]0.207288[/C][/ROW]
[ROW][C]12[/C][C]-0.100627[/C][C]-0.7795[/C][C]0.219388[/C][/ROW]
[ROW][C]13[/C][C]-0.22793[/C][C]-1.7655[/C][C]0.041281[/C][/ROW]
[ROW][C]14[/C][C]-0.374703[/C][C]-2.9024[/C][C]0.002586[/C][/ROW]
[ROW][C]15[/C][C]-0.428174[/C][C]-3.3166[/C][C]0.000775[/C][/ROW]
[ROW][C]16[/C][C]-0.382467[/C][C]-2.9626[/C][C]0.002184[/C][/ROW]
[ROW][C]17[/C][C]-0.319015[/C][C]-2.4711[/C][C]0.008164[/C][/ROW]
[ROW][C]18[/C][C]-0.294484[/C][C]-2.2811[/C][C]0.013055[/C][/ROW]
[ROW][C]19[/C][C]-0.346712[/C][C]-2.6856[/C][C]0.004674[/C][/ROW]
[ROW][C]20[/C][C]-0.424336[/C][C]-3.2869[/C][C]0.000848[/C][/ROW]
[ROW][C]21[/C][C]-0.46211[/C][C]-3.5795[/C][C]0.000345[/C][/ROW]
[ROW][C]22[/C][C]-0.422398[/C][C]-3.2719[/C][C]0.000887[/C][/ROW]
[ROW][C]23[/C][C]-0.320075[/C][C]-2.4793[/C][C]0.007996[/C][/ROW]
[ROW][C]24[/C][C]-0.243198[/C][C]-1.8838[/C][C]0.03222[/C][/ROW]
[ROW][C]25[/C][C]-0.257045[/C][C]-1.9911[/C][C]0.025517[/C][/ROW]
[ROW][C]26[/C][C]-0.285769[/C][C]-2.2136[/C][C]0.015336[/C][/ROW]
[ROW][C]27[/C][C]-0.270921[/C][C]-2.0985[/C][C]0.020037[/C][/ROW]
[ROW][C]28[/C][C]-0.214026[/C][C]-1.6578[/C][C]0.051285[/C][/ROW]
[ROW][C]29[/C][C]-0.154753[/C][C]-1.1987[/C][C]0.117677[/C][/ROW]
[ROW][C]30[/C][C]-0.101676[/C][C]-0.7876[/C][C]0.217021[/C][/ROW]
[ROW][C]31[/C][C]-0.05965[/C][C]-0.4621[/C][C]0.322858[/C][/ROW]
[ROW][C]32[/C][C]-0.017339[/C][C]-0.1343[/C][C]0.446805[/C][/ROW]
[ROW][C]33[/C][C]0.034147[/C][C]0.2645[/C][C]0.39615[/C][/ROW]
[ROW][C]34[/C][C]0.095644[/C][C]0.7409[/C][C]0.230836[/C][/ROW]
[ROW][C]35[/C][C]0.154045[/C][C]1.1932[/C][C]0.118738[/C][/ROW]
[ROW][C]36[/C][C]0.190567[/C][C]1.4761[/C][C]0.072569[/C][/ROW]
[ROW][C]37[/C][C]0.178724[/C][C]1.3844[/C][C]0.085683[/C][/ROW]
[ROW][C]38[/C][C]0.177035[/C][C]1.3713[/C][C]0.087693[/C][/ROW]
[ROW][C]39[/C][C]0.205769[/C][C]1.5939[/C][C]0.058109[/C][/ROW]
[ROW][C]40[/C][C]0.238544[/C][C]1.8478[/C][C]0.034784[/C][/ROW]
[ROW][C]41[/C][C]0.239134[/C][C]1.8523[/C][C]0.03445[/C][/ROW]
[ROW][C]42[/C][C]0.218544[/C][C]1.6928[/C][C]0.047837[/C][/ROW]
[ROW][C]43[/C][C]0.191338[/C][C]1.4821[/C][C]0.071774[/C][/ROW]
[ROW][C]44[/C][C]0.160496[/C][C]1.2432[/C][C]0.109315[/C][/ROW]
[ROW][C]45[/C][C]0.11795[/C][C]0.9136[/C][C]0.182281[/C][/ROW]
[ROW][C]46[/C][C]0.081032[/C][C]0.6277[/C][C]0.266301[/C][/ROW]
[ROW][C]47[/C][C]0.047667[/C][C]0.3692[/C][C]0.356629[/C][/ROW]
[ROW][C]48[/C][C]0.016749[/C][C]0.1297[/C][C]0.448604[/C][/ROW]
[ROW][C]49[/C][C]-0.020655[/C][C]-0.16[/C][C]0.436711[/C][/ROW]
[ROW][C]50[/C][C]-0.0503[/C][C]-0.3896[/C][C]0.349096[/C][/ROW]
[ROW][C]51[/C][C]-0.056759[/C][C]-0.4397[/C][C]0.330883[/C][/ROW]
[ROW][C]52[/C][C]-0.057039[/C][C]-0.4418[/C][C]0.330104[/C][/ROW]
[ROW][C]53[/C][C]-0.06922[/C][C]-0.5362[/C][C]0.29691[/C][/ROW]
[ROW][C]54[/C][C]-0.063086[/C][C]-0.4887[/C][C]0.313431[/C][/ROW]
[ROW][C]55[/C][C]-0.048213[/C][C]-0.3735[/C][C]0.355063[/C][/ROW]
[ROW][C]56[/C][C]-0.036794[/C][C]-0.285[/C][C]0.388311[/C][/ROW]
[ROW][C]57[/C][C]-0.027955[/C][C]-0.2165[/C][C]0.414651[/C][/ROW]
[ROW][C]58[/C][C]-0.019625[/C][C]-0.152[/C][C]0.439843[/C][/ROW]
[ROW][C]59[/C][C]-0.011015[/C][C]-0.0853[/C][C]0.466145[/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=159587&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159587&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	0.846291	6.5553	0
2	0.600571	4.652	9e-06
3	0.443643	3.4364	0.000538
4	0.418405	3.2409	0.000973
5	0.461517	3.5749	0.00035
6	0.45581	3.5307	0.000402
7	0.31514	2.4411	0.008806
8	0.10252	0.7941	0.215129
9	-0.077073	-0.597	0.276374
10	-0.140077	-1.085	0.141125
11	-0.106064	-0.8216	0.207288
12	-0.100627	-0.7795	0.219388
13	-0.22793	-1.7655	0.041281
14	-0.374703	-2.9024	0.002586
15	-0.428174	-3.3166	0.000775
16	-0.382467	-2.9626	0.002184
17	-0.319015	-2.4711	0.008164
18	-0.294484	-2.2811	0.013055
19	-0.346712	-2.6856	0.004674
20	-0.424336	-3.2869	0.000848
21	-0.46211	-3.5795	0.000345
22	-0.422398	-3.2719	0.000887
23	-0.320075	-2.4793	0.007996
24	-0.243198	-1.8838	0.03222
25	-0.257045	-1.9911	0.025517
26	-0.285769	-2.2136	0.015336
27	-0.270921	-2.0985	0.020037
28	-0.214026	-1.6578	0.051285
29	-0.154753	-1.1987	0.117677
30	-0.101676	-0.7876	0.217021
31	-0.05965	-0.4621	0.322858
32	-0.017339	-0.1343	0.446805
33	0.034147	0.2645	0.39615
34	0.095644	0.7409	0.230836
35	0.154045	1.1932	0.118738
36	0.190567	1.4761	0.072569
37	0.178724	1.3844	0.085683
38	0.177035	1.3713	0.087693
39	0.205769	1.5939	0.058109
40	0.238544	1.8478	0.034784
41	0.239134	1.8523	0.03445
42	0.218544	1.6928	0.047837
43	0.191338	1.4821	0.071774
44	0.160496	1.2432	0.109315
45	0.11795	0.9136	0.182281
46	0.081032	0.6277	0.266301
47	0.047667	0.3692	0.356629
48	0.016749	0.1297	0.448604
49	-0.020655	-0.16	0.436711
50	-0.0503	-0.3896	0.349096
51	-0.056759	-0.4397	0.330883
52	-0.057039	-0.4418	0.330104
53	-0.06922	-0.5362	0.29691
54	-0.063086	-0.4887	0.313431
55	-0.048213	-0.3735	0.355063
56	-0.036794	-0.285	0.388311
57	-0.027955	-0.2165	0.414651
58	-0.019625	-0.152	0.439843
59	-0.011015	-0.0853	0.466145
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.846291	6.5553	0
2	-0.407473	-3.1563	0.00125
3	0.308974	2.3933	0.009921
4	0.179254	1.3885	0.08506
5	0.099114	0.7677	0.222828
6	-0.125206	-0.9698	0.168009
7	-0.311676	-2.4142	0.009418
8	-0.131039	-1.015	0.157085
9	-0.158724	-1.2295	0.111848
10	0.049701	0.385	0.350805
11	0.034631	0.2683	0.394713
12	-0.153487	-1.1889	0.11958
13	-0.281814	-2.1829	0.016483
14	0.218771	1.6946	0.047669
15	0.110471	0.8557	0.197784
16	-0.038953	-0.3017	0.381951
17	-0.198515	-1.5377	0.064691
18	0.028323	0.2194	0.413546
19	-0.063156	-0.4892	0.313241
20	-0.06844	-0.5301	0.298988
21	-0.163565	-1.267	0.105031
22	-0.126646	-0.981	0.165268
23	0.07278	0.5638	0.287512
24	0.012379	0.0959	0.461964
25	-0.030978	-0.24	0.405592
26	0.002388	0.0185	0.492653
27	-0.092318	-0.7151	0.238663
28	-0.039861	-0.3088	0.379286
29	-0.060423	-0.468	0.320729
30	0.014539	0.1126	0.455354
31	0.033038	0.2559	0.399447
32	0.006365	0.0493	0.48042
33	0.054926	0.4255	0.336014
34	-0.028322	-0.2194	0.413548
35	-0.042163	-0.3266	0.372557
36	0.018668	0.1446	0.442754
37	-0.120895	-0.9364	0.176398
38	0.010511	0.0814	0.46769
39	-0.089101	-0.6902	0.246372
40	0.003142	0.0243	0.490333
41	-0.052567	-0.4072	0.342662
42	-0.033044	-0.256	0.399429
43	0.012324	0.0955	0.462135
44	-0.095977	-0.7434	0.230059
45	-0.074777	-0.5792	0.282305
46	0.005939	0.046	0.481731
47	-0.08383	-0.6493	0.259298
48	-0.021208	-0.1643	0.435032
49	-0.063063	-0.4885	0.313494
50	-0.088976	-0.6892	0.246676
51	0.070109	0.5431	0.29455
52	-0.002339	-0.0181	0.492802
53	0.085519	0.6624	0.255117
54	0.047941	0.3713	0.355843
55	-0.065616	-0.5083	0.306569
56	0.004648	0.036	0.485699
57	0.016387	0.1269	0.449708
58	-0.064267	-0.4978	0.31022
59	-0.119459	-0.9253	0.179252
60	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.846291 & 6.5553 & 0 \tabularnewline
2 & -0.407473 & -3.1563 & 0.00125 \tabularnewline
3 & 0.308974 & 2.3933 & 0.009921 \tabularnewline
4 & 0.179254 & 1.3885 & 0.08506 \tabularnewline
5 & 0.099114 & 0.7677 & 0.222828 \tabularnewline
6 & -0.125206 & -0.9698 & 0.168009 \tabularnewline
7 & -0.311676 & -2.4142 & 0.009418 \tabularnewline
8 & -0.131039 & -1.015 & 0.157085 \tabularnewline
9 & -0.158724 & -1.2295 & 0.111848 \tabularnewline
10 & 0.049701 & 0.385 & 0.350805 \tabularnewline
11 & 0.034631 & 0.2683 & 0.394713 \tabularnewline
12 & -0.153487 & -1.1889 & 0.11958 \tabularnewline
13 & -0.281814 & -2.1829 & 0.016483 \tabularnewline
14 & 0.218771 & 1.6946 & 0.047669 \tabularnewline
15 & 0.110471 & 0.8557 & 0.197784 \tabularnewline
16 & -0.038953 & -0.3017 & 0.381951 \tabularnewline
17 & -0.198515 & -1.5377 & 0.064691 \tabularnewline
18 & 0.028323 & 0.2194 & 0.413546 \tabularnewline
19 & -0.063156 & -0.4892 & 0.313241 \tabularnewline
20 & -0.06844 & -0.5301 & 0.298988 \tabularnewline
21 & -0.163565 & -1.267 & 0.105031 \tabularnewline
22 & -0.126646 & -0.981 & 0.165268 \tabularnewline
23 & 0.07278 & 0.5638 & 0.287512 \tabularnewline
24 & 0.012379 & 0.0959 & 0.461964 \tabularnewline
25 & -0.030978 & -0.24 & 0.405592 \tabularnewline
26 & 0.002388 & 0.0185 & 0.492653 \tabularnewline
27 & -0.092318 & -0.7151 & 0.238663 \tabularnewline
28 & -0.039861 & -0.3088 & 0.379286 \tabularnewline
29 & -0.060423 & -0.468 & 0.320729 \tabularnewline
30 & 0.014539 & 0.1126 & 0.455354 \tabularnewline
31 & 0.033038 & 0.2559 & 0.399447 \tabularnewline
32 & 0.006365 & 0.0493 & 0.48042 \tabularnewline
33 & 0.054926 & 0.4255 & 0.336014 \tabularnewline
34 & -0.028322 & -0.2194 & 0.413548 \tabularnewline
35 & -0.042163 & -0.3266 & 0.372557 \tabularnewline
36 & 0.018668 & 0.1446 & 0.442754 \tabularnewline
37 & -0.120895 & -0.9364 & 0.176398 \tabularnewline
38 & 0.010511 & 0.0814 & 0.46769 \tabularnewline
39 & -0.089101 & -0.6902 & 0.246372 \tabularnewline
40 & 0.003142 & 0.0243 & 0.490333 \tabularnewline
41 & -0.052567 & -0.4072 & 0.342662 \tabularnewline
42 & -0.033044 & -0.256 & 0.399429 \tabularnewline
43 & 0.012324 & 0.0955 & 0.462135 \tabularnewline
44 & -0.095977 & -0.7434 & 0.230059 \tabularnewline
45 & -0.074777 & -0.5792 & 0.282305 \tabularnewline
46 & 0.005939 & 0.046 & 0.481731 \tabularnewline
47 & -0.08383 & -0.6493 & 0.259298 \tabularnewline
48 & -0.021208 & -0.1643 & 0.435032 \tabularnewline
49 & -0.063063 & -0.4885 & 0.313494 \tabularnewline
50 & -0.088976 & -0.6892 & 0.246676 \tabularnewline
51 & 0.070109 & 0.5431 & 0.29455 \tabularnewline
52 & -0.002339 & -0.0181 & 0.492802 \tabularnewline
53 & 0.085519 & 0.6624 & 0.255117 \tabularnewline
54 & 0.047941 & 0.3713 & 0.355843 \tabularnewline
55 & -0.065616 & -0.5083 & 0.306569 \tabularnewline
56 & 0.004648 & 0.036 & 0.485699 \tabularnewline
57 & 0.016387 & 0.1269 & 0.449708 \tabularnewline
58 & -0.064267 & -0.4978 & 0.31022 \tabularnewline
59 & -0.119459 & -0.9253 & 0.179252 \tabularnewline
60 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159587&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]0.846291[/C][C]6.5553[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.407473[/C][C]-3.1563[/C][C]0.00125[/C][/ROW]
[ROW][C]3[/C][C]0.308974[/C][C]2.3933[/C][C]0.009921[/C][/ROW]
[ROW][C]4[/C][C]0.179254[/C][C]1.3885[/C][C]0.08506[/C][/ROW]
[ROW][C]5[/C][C]0.099114[/C][C]0.7677[/C][C]0.222828[/C][/ROW]
[ROW][C]6[/C][C]-0.125206[/C][C]-0.9698[/C][C]0.168009[/C][/ROW]
[ROW][C]7[/C][C]-0.311676[/C][C]-2.4142[/C][C]0.009418[/C][/ROW]
[ROW][C]8[/C][C]-0.131039[/C][C]-1.015[/C][C]0.157085[/C][/ROW]
[ROW][C]9[/C][C]-0.158724[/C][C]-1.2295[/C][C]0.111848[/C][/ROW]
[ROW][C]10[/C][C]0.049701[/C][C]0.385[/C][C]0.350805[/C][/ROW]
[ROW][C]11[/C][C]0.034631[/C][C]0.2683[/C][C]0.394713[/C][/ROW]
[ROW][C]12[/C][C]-0.153487[/C][C]-1.1889[/C][C]0.11958[/C][/ROW]
[ROW][C]13[/C][C]-0.281814[/C][C]-2.1829[/C][C]0.016483[/C][/ROW]
[ROW][C]14[/C][C]0.218771[/C][C]1.6946[/C][C]0.047669[/C][/ROW]
[ROW][C]15[/C][C]0.110471[/C][C]0.8557[/C][C]0.197784[/C][/ROW]
[ROW][C]16[/C][C]-0.038953[/C][C]-0.3017[/C][C]0.381951[/C][/ROW]
[ROW][C]17[/C][C]-0.198515[/C][C]-1.5377[/C][C]0.064691[/C][/ROW]
[ROW][C]18[/C][C]0.028323[/C][C]0.2194[/C][C]0.413546[/C][/ROW]
[ROW][C]19[/C][C]-0.063156[/C][C]-0.4892[/C][C]0.313241[/C][/ROW]
[ROW][C]20[/C][C]-0.06844[/C][C]-0.5301[/C][C]0.298988[/C][/ROW]
[ROW][C]21[/C][C]-0.163565[/C][C]-1.267[/C][C]0.105031[/C][/ROW]
[ROW][C]22[/C][C]-0.126646[/C][C]-0.981[/C][C]0.165268[/C][/ROW]
[ROW][C]23[/C][C]0.07278[/C][C]0.5638[/C][C]0.287512[/C][/ROW]
[ROW][C]24[/C][C]0.012379[/C][C]0.0959[/C][C]0.461964[/C][/ROW]
[ROW][C]25[/C][C]-0.030978[/C][C]-0.24[/C][C]0.405592[/C][/ROW]
[ROW][C]26[/C][C]0.002388[/C][C]0.0185[/C][C]0.492653[/C][/ROW]
[ROW][C]27[/C][C]-0.092318[/C][C]-0.7151[/C][C]0.238663[/C][/ROW]
[ROW][C]28[/C][C]-0.039861[/C][C]-0.3088[/C][C]0.379286[/C][/ROW]
[ROW][C]29[/C][C]-0.060423[/C][C]-0.468[/C][C]0.320729[/C][/ROW]
[ROW][C]30[/C][C]0.014539[/C][C]0.1126[/C][C]0.455354[/C][/ROW]
[ROW][C]31[/C][C]0.033038[/C][C]0.2559[/C][C]0.399447[/C][/ROW]
[ROW][C]32[/C][C]0.006365[/C][C]0.0493[/C][C]0.48042[/C][/ROW]
[ROW][C]33[/C][C]0.054926[/C][C]0.4255[/C][C]0.336014[/C][/ROW]
[ROW][C]34[/C][C]-0.028322[/C][C]-0.2194[/C][C]0.413548[/C][/ROW]
[ROW][C]35[/C][C]-0.042163[/C][C]-0.3266[/C][C]0.372557[/C][/ROW]
[ROW][C]36[/C][C]0.018668[/C][C]0.1446[/C][C]0.442754[/C][/ROW]
[ROW][C]37[/C][C]-0.120895[/C][C]-0.9364[/C][C]0.176398[/C][/ROW]
[ROW][C]38[/C][C]0.010511[/C][C]0.0814[/C][C]0.46769[/C][/ROW]
[ROW][C]39[/C][C]-0.089101[/C][C]-0.6902[/C][C]0.246372[/C][/ROW]
[ROW][C]40[/C][C]0.003142[/C][C]0.0243[/C][C]0.490333[/C][/ROW]
[ROW][C]41[/C][C]-0.052567[/C][C]-0.4072[/C][C]0.342662[/C][/ROW]
[ROW][C]42[/C][C]-0.033044[/C][C]-0.256[/C][C]0.399429[/C][/ROW]
[ROW][C]43[/C][C]0.012324[/C][C]0.0955[/C][C]0.462135[/C][/ROW]
[ROW][C]44[/C][C]-0.095977[/C][C]-0.7434[/C][C]0.230059[/C][/ROW]
[ROW][C]45[/C][C]-0.074777[/C][C]-0.5792[/C][C]0.282305[/C][/ROW]
[ROW][C]46[/C][C]0.005939[/C][C]0.046[/C][C]0.481731[/C][/ROW]
[ROW][C]47[/C][C]-0.08383[/C][C]-0.6493[/C][C]0.259298[/C][/ROW]
[ROW][C]48[/C][C]-0.021208[/C][C]-0.1643[/C][C]0.435032[/C][/ROW]
[ROW][C]49[/C][C]-0.063063[/C][C]-0.4885[/C][C]0.313494[/C][/ROW]
[ROW][C]50[/C][C]-0.088976[/C][C]-0.6892[/C][C]0.246676[/C][/ROW]
[ROW][C]51[/C][C]0.070109[/C][C]0.5431[/C][C]0.29455[/C][/ROW]
[ROW][C]52[/C][C]-0.002339[/C][C]-0.0181[/C][C]0.492802[/C][/ROW]
[ROW][C]53[/C][C]0.085519[/C][C]0.6624[/C][C]0.255117[/C][/ROW]
[ROW][C]54[/C][C]0.047941[/C][C]0.3713[/C][C]0.355843[/C][/ROW]
[ROW][C]55[/C][C]-0.065616[/C][C]-0.5083[/C][C]0.306569[/C][/ROW]
[ROW][C]56[/C][C]0.004648[/C][C]0.036[/C][C]0.485699[/C][/ROW]
[ROW][C]57[/C][C]0.016387[/C][C]0.1269[/C][C]0.449708[/C][/ROW]
[ROW][C]58[/C][C]-0.064267[/C][C]-0.4978[/C][C]0.31022[/C][/ROW]
[ROW][C]59[/C][C]-0.119459[/C][C]-0.9253[/C][C]0.179252[/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=159587&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159587&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	0.846291	6.5553	0
2	-0.407473	-3.1563	0.00125
3	0.308974	2.3933	0.009921
4	0.179254	1.3885	0.08506
5	0.099114	0.7677	0.222828
6	-0.125206	-0.9698	0.168009
7	-0.311676	-2.4142	0.009418
8	-0.131039	-1.015	0.157085
9	-0.158724	-1.2295	0.111848
10	0.049701	0.385	0.350805
11	0.034631	0.2683	0.394713
12	-0.153487	-1.1889	0.11958
13	-0.281814	-2.1829	0.016483
14	0.218771	1.6946	0.047669
15	0.110471	0.8557	0.197784
16	-0.038953	-0.3017	0.381951
17	-0.198515	-1.5377	0.064691
18	0.028323	0.2194	0.413546
19	-0.063156	-0.4892	0.313241
20	-0.06844	-0.5301	0.298988
21	-0.163565	-1.267	0.105031
22	-0.126646	-0.981	0.165268
23	0.07278	0.5638	0.287512
24	0.012379	0.0959	0.461964
25	-0.030978	-0.24	0.405592
26	0.002388	0.0185	0.492653
27	-0.092318	-0.7151	0.238663
28	-0.039861	-0.3088	0.379286
29	-0.060423	-0.468	0.320729
30	0.014539	0.1126	0.455354
31	0.033038	0.2559	0.399447
32	0.006365	0.0493	0.48042
33	0.054926	0.4255	0.336014
34	-0.028322	-0.2194	0.413548
35	-0.042163	-0.3266	0.372557
36	0.018668	0.1446	0.442754
37	-0.120895	-0.9364	0.176398
38	0.010511	0.0814	0.46769
39	-0.089101	-0.6902	0.246372
40	0.003142	0.0243	0.490333
41	-0.052567	-0.4072	0.342662
42	-0.033044	-0.256	0.399429
43	0.012324	0.0955	0.462135
44	-0.095977	-0.7434	0.230059
45	-0.074777	-0.5792	0.282305
46	0.005939	0.046	0.481731
47	-0.08383	-0.6493	0.259298
48	-0.021208	-0.1643	0.435032
49	-0.063063	-0.4885	0.313494
50	-0.088976	-0.6892	0.246676
51	0.070109	0.5431	0.29455
52	-0.002339	-0.0181	0.492802
53	0.085519	0.6624	0.255117
54	0.047941	0.3713	0.355843
55	-0.065616	-0.5083	0.306569
56	0.004648	0.036	0.485699
57	0.016387	0.1269	0.449708
58	-0.064267	-0.4978	0.31022
59	-0.119459	-0.9253	0.179252
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 = 2.0 ; 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