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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationMon, 19 Oct 2009 13:36:49 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/19/t1255981036jaiv8n9wufj3ox3.htm/, Retrieved Mon, 29 Apr 2024 19:17:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48154, Retrieved Mon, 29 Apr 2024 19:17:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [WS3partial] [2009-10-19 19:36:49] [87085ce7f5378f281469a8b1f0969170] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87.28
87.28
87.09
86.92
87.59
90.72
90.69
90.3
89.55
88.94
88.41
87.82
87.07
86.82
86.4
86.02
85.66
85.32
85
84.67
83.94
82.83
81.95
81.19
80.48
78.86
69.47
68.77
70.06
73.95
75.8
77.79
81.57
83.07
84.34
85.1
85.25
84.26
83.63
86.44
85.3
84.1
83.36
82.48
81.58
80.47
79.34
82.13
81.69
80.7
79.88
79.16
78.38
77.42
76.47
75.46
74.48
78.27
80.7
79.91
78.75
77.78
81.14
81.08
80.03
78.91
78.01
76.9
75.97
81.93
80.27
78.67
77.42
76.16
74.7
76.39
76.04
74.65
73.29
71.79
74.39
74.91
74.54
73.08
72.75
71.32
70.38
70.35
70.01
69.36
67.77
69.26
69.8
68.38
67.62
68.39
66.95
65.21
66.64
63.45
60.66
62.34
60.32
58.64
60.46
58.59
61.87
61.85
67.44
77.06
91.74
93.15
94.15
93.11
91.51
89.96
88.16
86.98
88.03
86.24
84.65
83.23
81.7
80.25
78.8
77.51
76.2
75.04
74
75.49
77.14
76.15
76.27
78.19
76.49
77.31
76.65
74.99
73.51
72.07
70.59
71.96
76.29
74.86
74.93
71.9
71.01
77.47
75.78
76.6
76.07
74.57
73.02
72.65
73.16
71.53
69.78
67.98
69.96
72.16
70.47
68.86
67.37
65.87
72.16
71.34
69.93
68.44
67.16
66.01
67.25
70.91
69.75
68.59
67.48
66.31
64.81
66.58
65.97
64.7
64.7
60.94
59.08
58.42
57.77
57.11
53.31
49.96
49.4
48.84
48.3
47.74
47.24
46.76
46.29
48.9
49.23
48.53
48.03
54.34
53.79
53.24
52.96
52.17
51.7
58.55
78.2
77.03
76.19
77.15
75.87
95.47
109.67
112.28
112.01
107.93
105.96
105.06
102.98
102.2
105.23
101.85
99.89
96.23
94.76
91.51
91.63
91.54
85.23
87.83
87.38
84.44
85.19
84.03
86.73
102.52
104.45
106.98
107.02
99.26
94.45
113.44
157.33
147.38
171.89
171.95
132.71
126.02
121.18
115.45
110.48
117.85
117.63
124.65
109.59
111.27
99.78
98.21
99.2
97.97
89.55
87.91
93.34
94.42
93.2
90.29
91.46
89.98
88.35
88.41
82.44
79.89
75.69
75.66
84.5
96.73
87.48
82.39
83.48
79.31
78.16
72.77
72.45
68.46
67.62
68.76
70.07
68.55
65.3
58.96
59.17
62.37
66.28
55.62
55.23
55.85
56.75
50.89
53.88
52.95
55.08
53.61
58.78
61.85
55.91
53.32
46.41
44.57
50
50
53.36
46.23
50.45
49.07
45.85
48.45
49.96
46.53
50.51
47.58
48.05
46.84
47.67
49.16
55.54
55.82
58.22
56.19
57.77
63.19
54.76
55.74
62.54
61.39
69.6
79.23
80
93.68
107.63
100.18
97.3
90.45
80.64
80.58
75.82
85.59
89.35
89.42
104.73
95.32
89.27
90.44
86.97
79.98
81.22
87.35
83.64
82.22
94.4
102.18

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48154&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48154&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.95582718.13550
20.903217.1370
30.85380816.19990
40.7981515.14380
50.7595314.41110
60.73513813.94830
70.70738113.42160
80.67191512.74870
90.63425912.03420
100.59380911.26670
110.5483210.40370
120.4980389.44960
130.4578048.68620
140.4179687.93040
150.383037.26750
160.3571036.77550
170.3327116.31270
180.3094545.87150
190.288415.47220
200.2763715.24380
210.2644635.01780
220.2504554.75211e-06
230.2342564.44476e-06
240.2166534.11072.4e-05
250.1925623.65360.000149

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.955827 & 18.1355 & 0 \tabularnewline
2 & 0.9032 & 17.137 & 0 \tabularnewline
3 & 0.853808 & 16.1999 & 0 \tabularnewline
4 & 0.79815 & 15.1438 & 0 \tabularnewline
5 & 0.75953 & 14.4111 & 0 \tabularnewline
6 & 0.735138 & 13.9483 & 0 \tabularnewline
7 & 0.707381 & 13.4216 & 0 \tabularnewline
8 & 0.671915 & 12.7487 & 0 \tabularnewline
9 & 0.634259 & 12.0342 & 0 \tabularnewline
10 & 0.593809 & 11.2667 & 0 \tabularnewline
11 & 0.54832 & 10.4037 & 0 \tabularnewline
12 & 0.498038 & 9.4496 & 0 \tabularnewline
13 & 0.457804 & 8.6862 & 0 \tabularnewline
14 & 0.417968 & 7.9304 & 0 \tabularnewline
15 & 0.38303 & 7.2675 & 0 \tabularnewline
16 & 0.357103 & 6.7755 & 0 \tabularnewline
17 & 0.332711 & 6.3127 & 0 \tabularnewline
18 & 0.309454 & 5.8715 & 0 \tabularnewline
19 & 0.28841 & 5.4722 & 0 \tabularnewline
20 & 0.276371 & 5.2438 & 0 \tabularnewline
21 & 0.264463 & 5.0178 & 0 \tabularnewline
22 & 0.250455 & 4.7521 & 1e-06 \tabularnewline
23 & 0.234256 & 4.4447 & 6e-06 \tabularnewline
24 & 0.216653 & 4.1107 & 2.4e-05 \tabularnewline
25 & 0.192562 & 3.6536 & 0.000149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48154&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]0.955827[/C][C]18.1355[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.9032[/C][C]17.137[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.853808[/C][C]16.1999[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.79815[/C][C]15.1438[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.75953[/C][C]14.4111[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.735138[/C][C]13.9483[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.707381[/C][C]13.4216[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.671915[/C][C]12.7487[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.634259[/C][C]12.0342[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.593809[/C][C]11.2667[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.54832[/C][C]10.4037[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.498038[/C][C]9.4496[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.457804[/C][C]8.6862[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.417968[/C][C]7.9304[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.38303[/C][C]7.2675[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.357103[/C][C]6.7755[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.332711[/C][C]6.3127[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.309454[/C][C]5.8715[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.28841[/C][C]5.4722[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.276371[/C][C]5.2438[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.264463[/C][C]5.0178[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.250455[/C][C]4.7521[/C][C]1e-06[/C][/ROW]
[ROW][C]23[/C][C]0.234256[/C][C]4.4447[/C][C]6e-06[/C][/ROW]
[ROW][C]24[/C][C]0.216653[/C][C]4.1107[/C][C]2.4e-05[/C][/ROW]
[ROW][C]25[/C][C]0.192562[/C][C]3.6536[/C][C]0.000149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48154&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.95582718.13550
20.903217.1370
30.85380816.19990
40.7981515.14380
50.7595314.41110
60.73513813.94830
70.70738113.42160
80.67191512.74870
90.63425912.03420
100.59380911.26670
110.5483210.40370
120.4980389.44960
130.4578048.68620
140.4179687.93040
150.383037.26750
160.3571036.77550
170.3327116.31270
180.3094545.87150
190.288415.47220
200.2763715.24380
210.2644635.01780
220.2504554.75211e-06
230.2342564.44476e-06
240.2166534.11072.4e-05
250.1925623.65360.000149






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.95582718.13550
2-0.120452-2.28540.011434
30.0193750.36760.35669
4-0.108344-2.05570.020267
50.1885373.57720.000197
60.0974821.84960.032595
7-0.061251-1.16220.122971
8-0.128123-2.4310.007773
9-0.018108-0.34360.365681
100.0045130.08560.465905
11-0.063258-1.20020.11542
12-0.129721-2.46130.007156
130.0769671.46030.072534
14-0.034258-0.650.258053
150.0488980.92780.177071
160.0055420.10510.458159
170.0158230.30020.382089
180.0249150.47270.318349
190.0197840.37540.353798
200.1136872.15710.015831
21-0.013963-0.26490.395607
22-0.036355-0.68980.245384
23-0.063126-1.19770.115904
240.0030340.05760.477067
25-0.065817-1.24880.106277

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.955827 & 18.1355 & 0 \tabularnewline
2 & -0.120452 & -2.2854 & 0.011434 \tabularnewline
3 & 0.019375 & 0.3676 & 0.35669 \tabularnewline
4 & -0.108344 & -2.0557 & 0.020267 \tabularnewline
5 & 0.188537 & 3.5772 & 0.000197 \tabularnewline
6 & 0.097482 & 1.8496 & 0.032595 \tabularnewline
7 & -0.061251 & -1.1622 & 0.122971 \tabularnewline
8 & -0.128123 & -2.431 & 0.007773 \tabularnewline
9 & -0.018108 & -0.3436 & 0.365681 \tabularnewline
10 & 0.004513 & 0.0856 & 0.465905 \tabularnewline
11 & -0.063258 & -1.2002 & 0.11542 \tabularnewline
12 & -0.129721 & -2.4613 & 0.007156 \tabularnewline
13 & 0.076967 & 1.4603 & 0.072534 \tabularnewline
14 & -0.034258 & -0.65 & 0.258053 \tabularnewline
15 & 0.048898 & 0.9278 & 0.177071 \tabularnewline
16 & 0.005542 & 0.1051 & 0.458159 \tabularnewline
17 & 0.015823 & 0.3002 & 0.382089 \tabularnewline
18 & 0.024915 & 0.4727 & 0.318349 \tabularnewline
19 & 0.019784 & 0.3754 & 0.353798 \tabularnewline
20 & 0.113687 & 2.1571 & 0.015831 \tabularnewline
21 & -0.013963 & -0.2649 & 0.395607 \tabularnewline
22 & -0.036355 & -0.6898 & 0.245384 \tabularnewline
23 & -0.063126 & -1.1977 & 0.115904 \tabularnewline
24 & 0.003034 & 0.0576 & 0.477067 \tabularnewline
25 & -0.065817 & -1.2488 & 0.106277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48154&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]0.955827[/C][C]18.1355[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.120452[/C][C]-2.2854[/C][C]0.011434[/C][/ROW]
[ROW][C]3[/C][C]0.019375[/C][C]0.3676[/C][C]0.35669[/C][/ROW]
[ROW][C]4[/C][C]-0.108344[/C][C]-2.0557[/C][C]0.020267[/C][/ROW]
[ROW][C]5[/C][C]0.188537[/C][C]3.5772[/C][C]0.000197[/C][/ROW]
[ROW][C]6[/C][C]0.097482[/C][C]1.8496[/C][C]0.032595[/C][/ROW]
[ROW][C]7[/C][C]-0.061251[/C][C]-1.1622[/C][C]0.122971[/C][/ROW]
[ROW][C]8[/C][C]-0.128123[/C][C]-2.431[/C][C]0.007773[/C][/ROW]
[ROW][C]9[/C][C]-0.018108[/C][C]-0.3436[/C][C]0.365681[/C][/ROW]
[ROW][C]10[/C][C]0.004513[/C][C]0.0856[/C][C]0.465905[/C][/ROW]
[ROW][C]11[/C][C]-0.063258[/C][C]-1.2002[/C][C]0.11542[/C][/ROW]
[ROW][C]12[/C][C]-0.129721[/C][C]-2.4613[/C][C]0.007156[/C][/ROW]
[ROW][C]13[/C][C]0.076967[/C][C]1.4603[/C][C]0.072534[/C][/ROW]
[ROW][C]14[/C][C]-0.034258[/C][C]-0.65[/C][C]0.258053[/C][/ROW]
[ROW][C]15[/C][C]0.048898[/C][C]0.9278[/C][C]0.177071[/C][/ROW]
[ROW][C]16[/C][C]0.005542[/C][C]0.1051[/C][C]0.458159[/C][/ROW]
[ROW][C]17[/C][C]0.015823[/C][C]0.3002[/C][C]0.382089[/C][/ROW]
[ROW][C]18[/C][C]0.024915[/C][C]0.4727[/C][C]0.318349[/C][/ROW]
[ROW][C]19[/C][C]0.019784[/C][C]0.3754[/C][C]0.353798[/C][/ROW]
[ROW][C]20[/C][C]0.113687[/C][C]2.1571[/C][C]0.015831[/C][/ROW]
[ROW][C]21[/C][C]-0.013963[/C][C]-0.2649[/C][C]0.395607[/C][/ROW]
[ROW][C]22[/C][C]-0.036355[/C][C]-0.6898[/C][C]0.245384[/C][/ROW]
[ROW][C]23[/C][C]-0.063126[/C][C]-1.1977[/C][C]0.115904[/C][/ROW]
[ROW][C]24[/C][C]0.003034[/C][C]0.0576[/C][C]0.477067[/C][/ROW]
[ROW][C]25[/C][C]-0.065817[/C][C]-1.2488[/C][C]0.106277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48154&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48154&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.95582718.13550
2-0.120452-2.28540.011434
30.0193750.36760.35669
4-0.108344-2.05570.020267
50.1885373.57720.000197
60.0974821.84960.032595
7-0.061251-1.16220.122971
8-0.128123-2.4310.007773
9-0.018108-0.34360.365681
100.0045130.08560.465905
11-0.063258-1.20020.11542
12-0.129721-2.46130.007156
130.0769671.46030.072534
14-0.034258-0.650.258053
150.0488980.92780.177071
160.0055420.10510.458159
170.0158230.30020.382089
180.0249150.47270.318349
190.0197840.37540.353798
200.1136872.15710.015831
21-0.013963-0.26490.395607
22-0.036355-0.68980.245384
23-0.063126-1.19770.115904
240.0030340.05760.477067
25-0.065817-1.24880.106277


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')