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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 computationSun, 27 Dec 2009 04:04:14 -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/2009/Dec/27/t1261911938fmwy9ijam6smbmc.htm/, Retrieved Fri, 03 May 2024 00:16:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70833, Retrieved Fri, 03 May 2024 00:16:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspaper
Estimated Impact176

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Variance Reduction Matrix] [VRM] [2009-12-23 10:57:13] [5e6d255681a7853beaa91b62357037a7]
- RMP     [(Partial) Autocorrelation Function] [ACF, PACF d=1 D=1...] [2009-12-27 11:04:14] [b08f24ccf7d7e0757793cda532be96b3] [Current]
-   P       [(Partial) Autocorrelation Function] [ACF, PACF d=1 D=1...] [2009-12-27 13:55:39] [5e6d255681a7853beaa91b62357037a7]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
83.87
84.23
84.61
84.82
85.04
85.06
84.93
84.98
85.23
85.30
85.33
85.55
85.70
85.88
86.04
86.07
86.31
86.38
86.35
86.55
86.70
86.74
86.85
86.95
86.80
87.01
87.17
87.43
87.66
87.68
87.59
87.65
87.72
87.70
87.71
87.80
87.62
87.84
88.17
88.47
88.58
88.57
88.55
88.68
88.79
88.85
88.95
89.27
89.09
89.42
89.72
89.85
89.96
90.25
90.20
90.27
90.78
90.79
90.98
91.25
90.75
91.01
91.50
92.09
92.56
92.66
92.38
92.38
92.66
92.69
92.59
92.98
92.98
93.15
93.65
94.06
94.24
94.24
94.11
94.16
94.43
94.67
94.60
95.00
94.84
95.26
95.81
95.92
95.85
95.90
95.80
96.00
96.34
96.43
96.48
96.75
96.51
96.69
97.28
97.69
98.08
98.09
97.92
98.06
98.23
98.57
98.53
98.92
98.42
98.73
99.32
99.73
100.00
100.08
100.02
100.26
100.71
100.95
100.75
101.03
100.64
100.93
101.41
102.07
102.42
102.53
102.43
102.60
102.65
102.74
102.82
103.21
102.75
103.09
103.71
104.30
104.58
104.71
104.44
104.57
104.95
105.49
106.03
106.48
106.25
106.70
107.60
108.05
108.72
109.17
109.08
109.04
109.34
109.37
108.96
108.77
108.11
108.67
109.05
109.43
109.62
109.85
109.34
109.65
109.69
109.91
110.09

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70833&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70833&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70833&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'Gwilym Jenkins' @ 72.249.127.135






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.3253664.03774.2e-05
20.1608411.9960.023849
30.0045520.05650.477513
40.0045520.05650.477514
5-0.077624-0.96330.168456
60.0292950.36350.358351
70.0814451.01070.156872
80.0478870.59430.276604
90.0891351.10610.135197
10-0.044528-0.55260.290678
11-0.077897-0.96670.167611
12-0.461706-5.72960
13-0.294324-3.65250.000178
14-0.169914-2.10860.0183
15-0.033811-0.41960.337685
160.0035360.04390.482527
170.0501770.62270.267208
180.0119320.14810.441239
19-0.005095-0.06320.474834
20-0.011465-0.14230.443523
21-0.047814-0.59340.276907
22-0.006678-0.08290.467031

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.325366 & 4.0377 & 4.2e-05 \tabularnewline
2 & 0.160841 & 1.996 & 0.023849 \tabularnewline
3 & 0.004552 & 0.0565 & 0.477513 \tabularnewline
4 & 0.004552 & 0.0565 & 0.477514 \tabularnewline
5 & -0.077624 & -0.9633 & 0.168456 \tabularnewline
6 & 0.029295 & 0.3635 & 0.358351 \tabularnewline
7 & 0.081445 & 1.0107 & 0.156872 \tabularnewline
8 & 0.047887 & 0.5943 & 0.276604 \tabularnewline
9 & 0.089135 & 1.1061 & 0.135197 \tabularnewline
10 & -0.044528 & -0.5526 & 0.290678 \tabularnewline
11 & -0.077897 & -0.9667 & 0.167611 \tabularnewline
12 & -0.461706 & -5.7296 & 0 \tabularnewline
13 & -0.294324 & -3.6525 & 0.000178 \tabularnewline
14 & -0.169914 & -2.1086 & 0.0183 \tabularnewline
15 & -0.033811 & -0.4196 & 0.337685 \tabularnewline
16 & 0.003536 & 0.0439 & 0.482527 \tabularnewline
17 & 0.050177 & 0.6227 & 0.267208 \tabularnewline
18 & 0.011932 & 0.1481 & 0.441239 \tabularnewline
19 & -0.005095 & -0.0632 & 0.474834 \tabularnewline
20 & -0.011465 & -0.1423 & 0.443523 \tabularnewline
21 & -0.047814 & -0.5934 & 0.276907 \tabularnewline
22 & -0.006678 & -0.0829 & 0.467031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70833&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]0.325366[/C][C]4.0377[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.160841[/C][C]1.996[/C][C]0.023849[/C][/ROW]
[ROW][C]3[/C][C]0.004552[/C][C]0.0565[/C][C]0.477513[/C][/ROW]
[ROW][C]4[/C][C]0.004552[/C][C]0.0565[/C][C]0.477514[/C][/ROW]
[ROW][C]5[/C][C]-0.077624[/C][C]-0.9633[/C][C]0.168456[/C][/ROW]
[ROW][C]6[/C][C]0.029295[/C][C]0.3635[/C][C]0.358351[/C][/ROW]
[ROW][C]7[/C][C]0.081445[/C][C]1.0107[/C][C]0.156872[/C][/ROW]
[ROW][C]8[/C][C]0.047887[/C][C]0.5943[/C][C]0.276604[/C][/ROW]
[ROW][C]9[/C][C]0.089135[/C][C]1.1061[/C][C]0.135197[/C][/ROW]
[ROW][C]10[/C][C]-0.044528[/C][C]-0.5526[/C][C]0.290678[/C][/ROW]
[ROW][C]11[/C][C]-0.077897[/C][C]-0.9667[/C][C]0.167611[/C][/ROW]
[ROW][C]12[/C][C]-0.461706[/C][C]-5.7296[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.294324[/C][C]-3.6525[/C][C]0.000178[/C][/ROW]
[ROW][C]14[/C][C]-0.169914[/C][C]-2.1086[/C][C]0.0183[/C][/ROW]
[ROW][C]15[/C][C]-0.033811[/C][C]-0.4196[/C][C]0.337685[/C][/ROW]
[ROW][C]16[/C][C]0.003536[/C][C]0.0439[/C][C]0.482527[/C][/ROW]
[ROW][C]17[/C][C]0.050177[/C][C]0.6227[/C][C]0.267208[/C][/ROW]
[ROW][C]18[/C][C]0.011932[/C][C]0.1481[/C][C]0.441239[/C][/ROW]
[ROW][C]19[/C][C]-0.005095[/C][C]-0.0632[/C][C]0.474834[/C][/ROW]
[ROW][C]20[/C][C]-0.011465[/C][C]-0.1423[/C][C]0.443523[/C][/ROW]
[ROW][C]21[/C][C]-0.047814[/C][C]-0.5934[/C][C]0.276907[/C][/ROW]
[ROW][C]22[/C][C]-0.006678[/C][C]-0.0829[/C][C]0.467031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70833&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70833&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
10.3253664.03774.2e-05
20.1608411.9960.023849
30.0045520.05650.477513
40.0045520.05650.477514
5-0.077624-0.96330.168456
60.0292950.36350.358351
70.0814451.01070.156872
80.0478870.59430.276604
90.0891351.10610.135197
10-0.044528-0.55260.290678
11-0.077897-0.96670.167611
12-0.461706-5.72960
13-0.294324-3.65250.000178
14-0.169914-2.10860.0183
15-0.033811-0.41960.337685
160.0035360.04390.482527
170.0501770.62270.267208
180.0119320.14810.441239
19-0.005095-0.06320.474834
20-0.011465-0.14230.443523
21-0.047814-0.59340.276907
22-0.006678-0.08290.467031






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.3253664.03774.2e-05
20.0614880.7630.223302
3-0.072487-0.89950.184884
40.0149830.18590.42637
5-0.081144-1.0070.157764
60.083441.03550.151038
70.077790.96530.167942
8-0.022509-0.27930.390182
90.076520.94960.171903
10-0.114543-1.42140.078604
11-0.050249-0.62360.266916
12-0.452431-5.61450
13-0.047547-0.590.278014
140.0353150.43830.330909
150.0026960.03350.486677
160.046540.57750.282209
17-0.027483-0.34110.366763
180.0260570.32340.373429
190.0760740.94410.173311
200.0011750.01460.494191
210.0457230.56740.285631
22-0.029491-0.3660.357442

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.325366 & 4.0377 & 4.2e-05 \tabularnewline
2 & 0.061488 & 0.763 & 0.223302 \tabularnewline
3 & -0.072487 & -0.8995 & 0.184884 \tabularnewline
4 & 0.014983 & 0.1859 & 0.42637 \tabularnewline
5 & -0.081144 & -1.007 & 0.157764 \tabularnewline
6 & 0.08344 & 1.0355 & 0.151038 \tabularnewline
7 & 0.07779 & 0.9653 & 0.167942 \tabularnewline
8 & -0.022509 & -0.2793 & 0.390182 \tabularnewline
9 & 0.07652 & 0.9496 & 0.171903 \tabularnewline
10 & -0.114543 & -1.4214 & 0.078604 \tabularnewline
11 & -0.050249 & -0.6236 & 0.266916 \tabularnewline
12 & -0.452431 & -5.6145 & 0 \tabularnewline
13 & -0.047547 & -0.59 & 0.278014 \tabularnewline
14 & 0.035315 & 0.4383 & 0.330909 \tabularnewline
15 & 0.002696 & 0.0335 & 0.486677 \tabularnewline
16 & 0.04654 & 0.5775 & 0.282209 \tabularnewline
17 & -0.027483 & -0.3411 & 0.366763 \tabularnewline
18 & 0.026057 & 0.3234 & 0.373429 \tabularnewline
19 & 0.076074 & 0.9441 & 0.173311 \tabularnewline
20 & 0.001175 & 0.0146 & 0.494191 \tabularnewline
21 & 0.045723 & 0.5674 & 0.285631 \tabularnewline
22 & -0.029491 & -0.366 & 0.357442 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70833&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]0.325366[/C][C]4.0377[/C][C]4.2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.061488[/C][C]0.763[/C][C]0.223302[/C][/ROW]
[ROW][C]3[/C][C]-0.072487[/C][C]-0.8995[/C][C]0.184884[/C][/ROW]
[ROW][C]4[/C][C]0.014983[/C][C]0.1859[/C][C]0.42637[/C][/ROW]
[ROW][C]5[/C][C]-0.081144[/C][C]-1.007[/C][C]0.157764[/C][/ROW]
[ROW][C]6[/C][C]0.08344[/C][C]1.0355[/C][C]0.151038[/C][/ROW]
[ROW][C]7[/C][C]0.07779[/C][C]0.9653[/C][C]0.167942[/C][/ROW]
[ROW][C]8[/C][C]-0.022509[/C][C]-0.2793[/C][C]0.390182[/C][/ROW]
[ROW][C]9[/C][C]0.07652[/C][C]0.9496[/C][C]0.171903[/C][/ROW]
[ROW][C]10[/C][C]-0.114543[/C][C]-1.4214[/C][C]0.078604[/C][/ROW]
[ROW][C]11[/C][C]-0.050249[/C][C]-0.6236[/C][C]0.266916[/C][/ROW]
[ROW][C]12[/C][C]-0.452431[/C][C]-5.6145[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.047547[/C][C]-0.59[/C][C]0.278014[/C][/ROW]
[ROW][C]14[/C][C]0.035315[/C][C]0.4383[/C][C]0.330909[/C][/ROW]
[ROW][C]15[/C][C]0.002696[/C][C]0.0335[/C][C]0.486677[/C][/ROW]
[ROW][C]16[/C][C]0.04654[/C][C]0.5775[/C][C]0.282209[/C][/ROW]
[ROW][C]17[/C][C]-0.027483[/C][C]-0.3411[/C][C]0.366763[/C][/ROW]
[ROW][C]18[/C][C]0.026057[/C][C]0.3234[/C][C]0.373429[/C][/ROW]
[ROW][C]19[/C][C]0.076074[/C][C]0.9441[/C][C]0.173311[/C][/ROW]
[ROW][C]20[/C][C]0.001175[/C][C]0.0146[/C][C]0.494191[/C][/ROW]
[ROW][C]21[/C][C]0.045723[/C][C]0.5674[/C][C]0.285631[/C][/ROW]
[ROW][C]22[/C][C]-0.029491[/C][C]-0.366[/C][C]0.357442[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70833&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70833&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
10.3253664.03774.2e-05
20.0614880.7630.223302
3-0.072487-0.89950.184884
40.0149830.18590.42637
5-0.081144-1.0070.157764
60.083441.03550.151038
70.077790.96530.167942
8-0.022509-0.27930.390182
90.076520.94960.171903
10-0.114543-1.42140.078604
11-0.050249-0.62360.266916
12-0.452431-5.61450
13-0.047547-0.590.278014
140.0353150.43830.330909
150.0026960.03350.486677
160.046540.57750.282209
17-0.027483-0.34110.366763
180.0260570.32340.373429
190.0760740.94410.173311
200.0011750.01460.494191
210.0457230.56740.285631
22-0.029491-0.3660.357442


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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')