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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 computationFri, 16 Jan 2015 10:17:32 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jan/16/t14214034590pcwjkex4t27o62.htm/, Retrieved Wed, 15 May 2024 17:39:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=273878, Retrieved Wed, 15 May 2024 17:39:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact49

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] [] [2015-01-16 10:17:32] [8145b3fe416df466b077d26de89041cd] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
67
72
74
62
56
66
65
59
61
69
74
69
66
68
58
64
66
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73
61
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57
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57
67
81
79
76
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74
67
84
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79
82
87
90
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82
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79
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72
65
73
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73
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74
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93
87
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75
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77
71
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67
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82
64
71
81
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77
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68

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' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273878&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273878&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' @ jenkins.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.7623819.05280
20.6370467.56450
30.5528776.56510
40.4231135.02421e-06
50.3151323.7420.000132
60.1896062.25140.012952
70.0856531.01710.155431
8-0.028141-0.33420.369381
9-0.127198-1.51040.066591
10-0.224796-2.66930.004246
11-0.350216-4.15862.8e-05
12-0.512374-6.08410
13-0.446467-5.30150
14-0.42897-5.09371e-06
15-0.399707-4.74633e-06
16-0.325228-3.86198.5e-05
17-0.309385-3.67370.000169
18-0.216367-2.56920.005616
19-0.138518-1.64480.051118
20-0.108076-1.28330.10074
21-0.035705-0.4240.336116

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.762381 & 9.0528 & 0 \tabularnewline
2 & 0.637046 & 7.5645 & 0 \tabularnewline
3 & 0.552877 & 6.5651 & 0 \tabularnewline
4 & 0.423113 & 5.0242 & 1e-06 \tabularnewline
5 & 0.315132 & 3.742 & 0.000132 \tabularnewline
6 & 0.189606 & 2.2514 & 0.012952 \tabularnewline
7 & 0.085653 & 1.0171 & 0.155431 \tabularnewline
8 & -0.028141 & -0.3342 & 0.369381 \tabularnewline
9 & -0.127198 & -1.5104 & 0.066591 \tabularnewline
10 & -0.224796 & -2.6693 & 0.004246 \tabularnewline
11 & -0.350216 & -4.1586 & 2.8e-05 \tabularnewline
12 & -0.512374 & -6.0841 & 0 \tabularnewline
13 & -0.446467 & -5.3015 & 0 \tabularnewline
14 & -0.42897 & -5.0937 & 1e-06 \tabularnewline
15 & -0.399707 & -4.7463 & 3e-06 \tabularnewline
16 & -0.325228 & -3.8619 & 8.5e-05 \tabularnewline
17 & -0.309385 & -3.6737 & 0.000169 \tabularnewline
18 & -0.216367 & -2.5692 & 0.005616 \tabularnewline
19 & -0.138518 & -1.6448 & 0.051118 \tabularnewline
20 & -0.108076 & -1.2833 & 0.10074 \tabularnewline
21 & -0.035705 & -0.424 & 0.336116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273878&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]0.762381[/C][C]9.0528[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.637046[/C][C]7.5645[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.552877[/C][C]6.5651[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.423113[/C][C]5.0242[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.315132[/C][C]3.742[/C][C]0.000132[/C][/ROW]
[ROW][C]6[/C][C]0.189606[/C][C]2.2514[/C][C]0.012952[/C][/ROW]
[ROW][C]7[/C][C]0.085653[/C][C]1.0171[/C][C]0.155431[/C][/ROW]
[ROW][C]8[/C][C]-0.028141[/C][C]-0.3342[/C][C]0.369381[/C][/ROW]
[ROW][C]9[/C][C]-0.127198[/C][C]-1.5104[/C][C]0.066591[/C][/ROW]
[ROW][C]10[/C][C]-0.224796[/C][C]-2.6693[/C][C]0.004246[/C][/ROW]
[ROW][C]11[/C][C]-0.350216[/C][C]-4.1586[/C][C]2.8e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.512374[/C][C]-6.0841[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.446467[/C][C]-5.3015[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.42897[/C][C]-5.0937[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]-0.399707[/C][C]-4.7463[/C][C]3e-06[/C][/ROW]
[ROW][C]16[/C][C]-0.325228[/C][C]-3.8619[/C][C]8.5e-05[/C][/ROW]
[ROW][C]17[/C][C]-0.309385[/C][C]-3.6737[/C][C]0.000169[/C][/ROW]
[ROW][C]18[/C][C]-0.216367[/C][C]-2.5692[/C][C]0.005616[/C][/ROW]
[ROW][C]19[/C][C]-0.138518[/C][C]-1.6448[/C][C]0.051118[/C][/ROW]
[ROW][C]20[/C][C]-0.108076[/C][C]-1.2833[/C][C]0.10074[/C][/ROW]
[ROW][C]21[/C][C]-0.035705[/C][C]-0.424[/C][C]0.336116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273878&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
10.7623819.05280
20.6370467.56450
30.5528776.56510
40.4231135.02421e-06
50.3151323.7420.000132
60.1896062.25140.012952
70.0856531.01710.155431
8-0.028141-0.33420.369381
9-0.127198-1.51040.066591
10-0.224796-2.66930.004246
11-0.350216-4.15862.8e-05
12-0.512374-6.08410
13-0.446467-5.30150
14-0.42897-5.09371e-06
15-0.399707-4.74633e-06
16-0.325228-3.86198.5e-05
17-0.309385-3.67370.000169
18-0.216367-2.56920.005616
19-0.138518-1.64480.051118
20-0.108076-1.28330.10074
21-0.035705-0.4240.336116






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.7623819.05280
20.1332971.58280.057852
30.0737140.87530.191448
4-0.114539-1.36010.087988
5-0.057254-0.67990.248856
6-0.129207-1.53430.063604
7-0.058238-0.69150.245182
8-0.118696-1.40940.080454
9-0.075023-0.89080.187265
10-0.114351-1.35780.088341
11-0.193069-2.29260.011676
12-0.326356-3.87538.1e-05
130.307753.65430.000181
140.0346470.41140.340698
150.1073291.27450.102298
160.0315190.37430.354383
17-0.108576-1.28930.099708
180.0686220.81480.208269
190.0490260.58210.280698
20-0.137321-1.63060.052604
210.0621650.73820.230818

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.762381 & 9.0528 & 0 \tabularnewline
2 & 0.133297 & 1.5828 & 0.057852 \tabularnewline
3 & 0.073714 & 0.8753 & 0.191448 \tabularnewline
4 & -0.114539 & -1.3601 & 0.087988 \tabularnewline
5 & -0.057254 & -0.6799 & 0.248856 \tabularnewline
6 & -0.129207 & -1.5343 & 0.063604 \tabularnewline
7 & -0.058238 & -0.6915 & 0.245182 \tabularnewline
8 & -0.118696 & -1.4094 & 0.080454 \tabularnewline
9 & -0.075023 & -0.8908 & 0.187265 \tabularnewline
10 & -0.114351 & -1.3578 & 0.088341 \tabularnewline
11 & -0.193069 & -2.2926 & 0.011676 \tabularnewline
12 & -0.326356 & -3.8753 & 8.1e-05 \tabularnewline
13 & 0.30775 & 3.6543 & 0.000181 \tabularnewline
14 & 0.034647 & 0.4114 & 0.340698 \tabularnewline
15 & 0.107329 & 1.2745 & 0.102298 \tabularnewline
16 & 0.031519 & 0.3743 & 0.354383 \tabularnewline
17 & -0.108576 & -1.2893 & 0.099708 \tabularnewline
18 & 0.068622 & 0.8148 & 0.208269 \tabularnewline
19 & 0.049026 & 0.5821 & 0.280698 \tabularnewline
20 & -0.137321 & -1.6306 & 0.052604 \tabularnewline
21 & 0.062165 & 0.7382 & 0.230818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=273878&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]0.762381[/C][C]9.0528[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.133297[/C][C]1.5828[/C][C]0.057852[/C][/ROW]
[ROW][C]3[/C][C]0.073714[/C][C]0.8753[/C][C]0.191448[/C][/ROW]
[ROW][C]4[/C][C]-0.114539[/C][C]-1.3601[/C][C]0.087988[/C][/ROW]
[ROW][C]5[/C][C]-0.057254[/C][C]-0.6799[/C][C]0.248856[/C][/ROW]
[ROW][C]6[/C][C]-0.129207[/C][C]-1.5343[/C][C]0.063604[/C][/ROW]
[ROW][C]7[/C][C]-0.058238[/C][C]-0.6915[/C][C]0.245182[/C][/ROW]
[ROW][C]8[/C][C]-0.118696[/C][C]-1.4094[/C][C]0.080454[/C][/ROW]
[ROW][C]9[/C][C]-0.075023[/C][C]-0.8908[/C][C]0.187265[/C][/ROW]
[ROW][C]10[/C][C]-0.114351[/C][C]-1.3578[/C][C]0.088341[/C][/ROW]
[ROW][C]11[/C][C]-0.193069[/C][C]-2.2926[/C][C]0.011676[/C][/ROW]
[ROW][C]12[/C][C]-0.326356[/C][C]-3.8753[/C][C]8.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.30775[/C][C]3.6543[/C][C]0.000181[/C][/ROW]
[ROW][C]14[/C][C]0.034647[/C][C]0.4114[/C][C]0.340698[/C][/ROW]
[ROW][C]15[/C][C]0.107329[/C][C]1.2745[/C][C]0.102298[/C][/ROW]
[ROW][C]16[/C][C]0.031519[/C][C]0.3743[/C][C]0.354383[/C][/ROW]
[ROW][C]17[/C][C]-0.108576[/C][C]-1.2893[/C][C]0.099708[/C][/ROW]
[ROW][C]18[/C][C]0.068622[/C][C]0.8148[/C][C]0.208269[/C][/ROW]
[ROW][C]19[/C][C]0.049026[/C][C]0.5821[/C][C]0.280698[/C][/ROW]
[ROW][C]20[/C][C]-0.137321[/C][C]-1.6306[/C][C]0.052604[/C][/ROW]
[ROW][C]21[/C][C]0.062165[/C][C]0.7382[/C][C]0.230818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=273878&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=273878&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
10.7623819.05280
20.1332971.58280.057852
30.0737140.87530.191448
4-0.114539-1.36010.087988
5-0.057254-0.67990.248856
6-0.129207-1.53430.063604
7-0.058238-0.69150.245182
8-0.118696-1.40940.080454
9-0.075023-0.89080.187265
10-0.114351-1.35780.088341
11-0.193069-2.29260.011676
12-0.326356-3.87538.1e-05
130.307753.65430.000181
140.0346470.41140.340698
150.1073291.27450.102298
160.0315190.37430.354383
17-0.108576-1.28930.099708
180.0686220.81480.208269
190.0490260.58210.280698
20-0.137321-1.63060.052604
210.0621650.73820.230818


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1.6 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1.6 ; par3 = 0 ; par4 = 1 ; 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')