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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 14 Dec 2007 08:29:38 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/14/t1197645234hbr2ee16872d8fr.htm/, Retrieved Thu, 02 May 2024 17:33:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3920, Retrieved Thu, 02 May 2024 17:33:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact172

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] [VRM G29] [2007-12-14 15:29:38] [8e05505c645e933583b5ad9ab4281af9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
145,3
143,6
142,8
155,9
156,2
149,8
152,7
155,5
159,3
143
141,4
142,8
146,4
152,3
164,3
168
171,3
162,7
150,2
142,5
138,2
138
145,1
138,4
131,8
130,8
126,3
123
124
120,8
122,1
106,5
104,3
108,7
113,8
112,5
106,1
98,4
96
99,3
97,5
95,3
88
94,7
99,4
98,9
96,4
95,3
99,5
101,6
103,9
106,6
108,3
102
93,8
91,6
97,7
94,8
98
103,8
97,8
91,2
89,3
87,5
90,4
94,2
102,2
101,3
96
90,8
93,2
90,9
91,1
90,2
94,3
96
99
103,3
113,1
112,8
112,1
107,4
111
110,5
110,8
112,4
111,5
116,2
122,5
121,3
113,9
110,7
120,8
141,1
147,4
148
158,1
165
187
190,3
182,4
168,8
151,2
120,1
112,5
106,2
107,1
108,5
106,5
108,3
125,6
124
127,2
136,9
135,8
124,3
115,4
113,6
114,4
118,4
117
116,5
115,4
113,6
117,4
116,9
116,4
111,1
110,2
118,9
131,8
130,6
138,3
148,4
148,7
144,3
152,5
162,9
167,2
166,5
185,6

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3920&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3920&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3920&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Autocorrelation Function
Time lag kACF(k)T-STATP-value
0111.83220
10.3615434.27781.7e-05
20.0245650.29070.385872
3-0.043699-0.51710.697035
40.0062660.07410.470501
5-0.078834-0.93280.823731
6-0.066641-0.78850.784132
7-0.113011-1.33720.908331
8-0.007844-0.09280.536908
9-0.122629-1.4510.925486
10-0.102094-1.2080.885456
110.0490260.58010.281395
120.0696870.82460.205514
130.0547320.64760.259153
140.0914991.08260.140416
150.0131630.15570.438228
160.0016330.01930.492304
17-0.032453-0.3840.649215
180.0383550.45380.325329
190.0731930.8660.193977
200.0514440.60870.271857

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 11.8322 & 0 \tabularnewline
1 & 0.361543 & 4.2778 & 1.7e-05 \tabularnewline
2 & 0.024565 & 0.2907 & 0.385872 \tabularnewline
3 & -0.043699 & -0.5171 & 0.697035 \tabularnewline
4 & 0.006266 & 0.0741 & 0.470501 \tabularnewline
5 & -0.078834 & -0.9328 & 0.823731 \tabularnewline
6 & -0.066641 & -0.7885 & 0.784132 \tabularnewline
7 & -0.113011 & -1.3372 & 0.908331 \tabularnewline
8 & -0.007844 & -0.0928 & 0.536908 \tabularnewline
9 & -0.122629 & -1.451 & 0.925486 \tabularnewline
10 & -0.102094 & -1.208 & 0.885456 \tabularnewline
11 & 0.049026 & 0.5801 & 0.281395 \tabularnewline
12 & 0.069687 & 0.8246 & 0.205514 \tabularnewline
13 & 0.054732 & 0.6476 & 0.259153 \tabularnewline
14 & 0.091499 & 1.0826 & 0.140416 \tabularnewline
15 & 0.013163 & 0.1557 & 0.438228 \tabularnewline
16 & 0.001633 & 0.0193 & 0.492304 \tabularnewline
17 & -0.032453 & -0.384 & 0.649215 \tabularnewline
18 & 0.038355 & 0.4538 & 0.325329 \tabularnewline
19 & 0.073193 & 0.866 & 0.193977 \tabularnewline
20 & 0.051444 & 0.6087 & 0.271857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3920&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]0[/C][C]1[/C][C]11.8322[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.361543[/C][C]4.2778[/C][C]1.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.024565[/C][C]0.2907[/C][C]0.385872[/C][/ROW]
[ROW][C]3[/C][C]-0.043699[/C][C]-0.5171[/C][C]0.697035[/C][/ROW]
[ROW][C]4[/C][C]0.006266[/C][C]0.0741[/C][C]0.470501[/C][/ROW]
[ROW][C]5[/C][C]-0.078834[/C][C]-0.9328[/C][C]0.823731[/C][/ROW]
[ROW][C]6[/C][C]-0.066641[/C][C]-0.7885[/C][C]0.784132[/C][/ROW]
[ROW][C]7[/C][C]-0.113011[/C][C]-1.3372[/C][C]0.908331[/C][/ROW]
[ROW][C]8[/C][C]-0.007844[/C][C]-0.0928[/C][C]0.536908[/C][/ROW]
[ROW][C]9[/C][C]-0.122629[/C][C]-1.451[/C][C]0.925486[/C][/ROW]
[ROW][C]10[/C][C]-0.102094[/C][C]-1.208[/C][C]0.885456[/C][/ROW]
[ROW][C]11[/C][C]0.049026[/C][C]0.5801[/C][C]0.281395[/C][/ROW]
[ROW][C]12[/C][C]0.069687[/C][C]0.8246[/C][C]0.205514[/C][/ROW]
[ROW][C]13[/C][C]0.054732[/C][C]0.6476[/C][C]0.259153[/C][/ROW]
[ROW][C]14[/C][C]0.091499[/C][C]1.0826[/C][C]0.140416[/C][/ROW]
[ROW][C]15[/C][C]0.013163[/C][C]0.1557[/C][C]0.438228[/C][/ROW]
[ROW][C]16[/C][C]0.001633[/C][C]0.0193[/C][C]0.492304[/C][/ROW]
[ROW][C]17[/C][C]-0.032453[/C][C]-0.384[/C][C]0.649215[/C][/ROW]
[ROW][C]18[/C][C]0.038355[/C][C]0.4538[/C][C]0.325329[/C][/ROW]
[ROW][C]19[/C][C]0.073193[/C][C]0.866[/C][C]0.193977[/C][/ROW]
[ROW][C]20[/C][C]0.051444[/C][C]0.6087[/C][C]0.271857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3920&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3920&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
0111.83220
10.3615434.27781.7e-05
20.0245650.29070.385872
3-0.043699-0.51710.697035
40.0062660.07410.470501
5-0.078834-0.93280.823731
6-0.066641-0.78850.784132
7-0.113011-1.33720.908331
8-0.007844-0.09280.536908
9-0.122629-1.4510.925486
10-0.102094-1.2080.885456
110.0490260.58010.281395
120.0696870.82460.205514
130.0547320.64760.259153
140.0914991.08260.140416
150.0131630.15570.438228
160.0016330.01930.492304
17-0.032453-0.3840.649215
180.0383550.45380.325329
190.0731930.8660.193977
200.0514440.60870.271857






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
00.3615434.27781.7e-05
1-0.12211-1.44480.924629
2-0.011114-0.13150.552217
30.0360220.42620.335303
4-0.115444-1.3660.912928
50.0051370.06080.475808
6-0.10669-1.26240.895542
70.0704180.83320.203078
8-0.17918-2.12010.982119
9-0.004324-0.05120.520364
100.1110581.31410.095489
11-0.046778-0.55350.709591
120.0712990.84360.20016
130.0405490.47980.316064
14-0.056044-0.66310.74583
150.0126630.14980.440559
16-0.03889-0.46020.67694
170.0964931.14170.127759
180.0118720.14050.444243
190.0395150.46760.320416
20-0.008443-0.09990.539718

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.361543 & 4.2778 & 1.7e-05 \tabularnewline
1 & -0.12211 & -1.4448 & 0.924629 \tabularnewline
2 & -0.011114 & -0.1315 & 0.552217 \tabularnewline
3 & 0.036022 & 0.4262 & 0.335303 \tabularnewline
4 & -0.115444 & -1.366 & 0.912928 \tabularnewline
5 & 0.005137 & 0.0608 & 0.475808 \tabularnewline
6 & -0.10669 & -1.2624 & 0.895542 \tabularnewline
7 & 0.070418 & 0.8332 & 0.203078 \tabularnewline
8 & -0.17918 & -2.1201 & 0.982119 \tabularnewline
9 & -0.004324 & -0.0512 & 0.520364 \tabularnewline
10 & 0.111058 & 1.3141 & 0.095489 \tabularnewline
11 & -0.046778 & -0.5535 & 0.709591 \tabularnewline
12 & 0.071299 & 0.8436 & 0.20016 \tabularnewline
13 & 0.040549 & 0.4798 & 0.316064 \tabularnewline
14 & -0.056044 & -0.6631 & 0.74583 \tabularnewline
15 & 0.012663 & 0.1498 & 0.440559 \tabularnewline
16 & -0.03889 & -0.4602 & 0.67694 \tabularnewline
17 & 0.096493 & 1.1417 & 0.127759 \tabularnewline
18 & 0.011872 & 0.1405 & 0.444243 \tabularnewline
19 & 0.039515 & 0.4676 & 0.320416 \tabularnewline
20 & -0.008443 & -0.0999 & 0.539718 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3920&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]0[/C][C]0.361543[/C][C]4.2778[/C][C]1.7e-05[/C][/ROW]
[ROW][C]1[/C][C]-0.12211[/C][C]-1.4448[/C][C]0.924629[/C][/ROW]
[ROW][C]2[/C][C]-0.011114[/C][C]-0.1315[/C][C]0.552217[/C][/ROW]
[ROW][C]3[/C][C]0.036022[/C][C]0.4262[/C][C]0.335303[/C][/ROW]
[ROW][C]4[/C][C]-0.115444[/C][C]-1.366[/C][C]0.912928[/C][/ROW]
[ROW][C]5[/C][C]0.005137[/C][C]0.0608[/C][C]0.475808[/C][/ROW]
[ROW][C]6[/C][C]-0.10669[/C][C]-1.2624[/C][C]0.895542[/C][/ROW]
[ROW][C]7[/C][C]0.070418[/C][C]0.8332[/C][C]0.203078[/C][/ROW]
[ROW][C]8[/C][C]-0.17918[/C][C]-2.1201[/C][C]0.982119[/C][/ROW]
[ROW][C]9[/C][C]-0.004324[/C][C]-0.0512[/C][C]0.520364[/C][/ROW]
[ROW][C]10[/C][C]0.111058[/C][C]1.3141[/C][C]0.095489[/C][/ROW]
[ROW][C]11[/C][C]-0.046778[/C][C]-0.5535[/C][C]0.709591[/C][/ROW]
[ROW][C]12[/C][C]0.071299[/C][C]0.8436[/C][C]0.20016[/C][/ROW]
[ROW][C]13[/C][C]0.040549[/C][C]0.4798[/C][C]0.316064[/C][/ROW]
[ROW][C]14[/C][C]-0.056044[/C][C]-0.6631[/C][C]0.74583[/C][/ROW]
[ROW][C]15[/C][C]0.012663[/C][C]0.1498[/C][C]0.440559[/C][/ROW]
[ROW][C]16[/C][C]-0.03889[/C][C]-0.4602[/C][C]0.67694[/C][/ROW]
[ROW][C]17[/C][C]0.096493[/C][C]1.1417[/C][C]0.127759[/C][/ROW]
[ROW][C]18[/C][C]0.011872[/C][C]0.1405[/C][C]0.444243[/C][/ROW]
[ROW][C]19[/C][C]0.039515[/C][C]0.4676[/C][C]0.320416[/C][/ROW]
[ROW][C]20[/C][C]-0.008443[/C][C]-0.0999[/C][C]0.539718[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3920&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3920&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
00.3615434.27781.7e-05
1-0.12211-1.44480.924629
2-0.011114-0.13150.552217
30.0360220.42620.335303
4-0.115444-1.3660.912928
50.0051370.06080.475808
6-0.10669-1.26240.895542
70.0704180.83320.203078
8-0.17918-2.12010.982119
9-0.004324-0.05120.520364
100.1110581.31410.095489
11-0.046778-0.55350.709591
120.0712990.84360.20016
130.0405490.47980.316064
14-0.056044-0.66310.74583
150.0126630.14980.440559
16-0.03889-0.46020.67694
170.0964931.14170.127759
180.0118720.14050.444243
190.0395150.46760.320416
20-0.008443-0.09990.539718


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;
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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')