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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, 23 Oct 2015 09:46:53 +0100
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/Oct/23/t1445590059q6ha7o9zicrpiq6.htm/, Retrieved Tue, 14 May 2024 15:15:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282842, Retrieved Tue, 14 May 2024 15:15:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

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] [] [2015-10-23 08:46:53] [5460c453892b15ffecb85c645e1cdda5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
94,3
94,6
94,9
95,6
95,4
97,4
98,4
100,5
106,6
106,7
106,8
109
109,3
110,5
113,4
113
113,6
121,2
120,5
120,9
125,8
125,4
125,7
127,7
128,1
130
130,5
130,1
129,6
128,8
128,4
128,3
127,6
127,3
127,7
126,9
125,1
119
118,7
118,9
116,9
117
117
115,5
115,6
117,5
117,6
117,8
119,3
120
120,2
109,4
109
108,8
96,3
96,9
97
111,4
111,8
111,7

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282842&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282842&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282842&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9231367.15060
20.8413126.51680
30.7566685.86110
40.6594385.1082e-06
50.5614584.3492.7e-05
60.4673473.62010.000303
70.3966623.07250.001595
80.3305412.56040.006496
90.2758592.13680.018351
100.2171111.68170.048909
110.1572011.21770.114058
120.0969870.75130.227716
130.0302230.23410.40785
14-0.032766-0.25380.400257
15-0.097586-0.75590.226334
16-0.167831-1.30.099284
17-0.23756-1.84010.035348

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923136 & 7.1506 & 0 \tabularnewline
2 & 0.841312 & 6.5168 & 0 \tabularnewline
3 & 0.756668 & 5.8611 & 0 \tabularnewline
4 & 0.659438 & 5.108 & 2e-06 \tabularnewline
5 & 0.561458 & 4.349 & 2.7e-05 \tabularnewline
6 & 0.467347 & 3.6201 & 0.000303 \tabularnewline
7 & 0.396662 & 3.0725 & 0.001595 \tabularnewline
8 & 0.330541 & 2.5604 & 0.006496 \tabularnewline
9 & 0.275859 & 2.1368 & 0.018351 \tabularnewline
10 & 0.217111 & 1.6817 & 0.048909 \tabularnewline
11 & 0.157201 & 1.2177 & 0.114058 \tabularnewline
12 & 0.096987 & 0.7513 & 0.227716 \tabularnewline
13 & 0.030223 & 0.2341 & 0.40785 \tabularnewline
14 & -0.032766 & -0.2538 & 0.400257 \tabularnewline
15 & -0.097586 & -0.7559 & 0.226334 \tabularnewline
16 & -0.167831 & -1.3 & 0.099284 \tabularnewline
17 & -0.23756 & -1.8401 & 0.035348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282842&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]0.923136[/C][C]7.1506[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.841312[/C][C]6.5168[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.756668[/C][C]5.8611[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.659438[/C][C]5.108[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.561458[/C][C]4.349[/C][C]2.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.467347[/C][C]3.6201[/C][C]0.000303[/C][/ROW]
[ROW][C]7[/C][C]0.396662[/C][C]3.0725[/C][C]0.001595[/C][/ROW]
[ROW][C]8[/C][C]0.330541[/C][C]2.5604[/C][C]0.006496[/C][/ROW]
[ROW][C]9[/C][C]0.275859[/C][C]2.1368[/C][C]0.018351[/C][/ROW]
[ROW][C]10[/C][C]0.217111[/C][C]1.6817[/C][C]0.048909[/C][/ROW]
[ROW][C]11[/C][C]0.157201[/C][C]1.2177[/C][C]0.114058[/C][/ROW]
[ROW][C]12[/C][C]0.096987[/C][C]0.7513[/C][C]0.227716[/C][/ROW]
[ROW][C]13[/C][C]0.030223[/C][C]0.2341[/C][C]0.40785[/C][/ROW]
[ROW][C]14[/C][C]-0.032766[/C][C]-0.2538[/C][C]0.400257[/C][/ROW]
[ROW][C]15[/C][C]-0.097586[/C][C]-0.7559[/C][C]0.226334[/C][/ROW]
[ROW][C]16[/C][C]-0.167831[/C][C]-1.3[/C][C]0.099284[/C][/ROW]
[ROW][C]17[/C][C]-0.23756[/C][C]-1.8401[/C][C]0.035348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282842&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282842&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
10.9231367.15060
20.8413126.51680
30.7566685.86110
40.6594385.1082e-06
50.5614584.3492.7e-05
60.4673473.62010.000303
70.3966623.07250.001595
80.3305412.56040.006496
90.2758592.13680.018351
100.2171111.68170.048909
110.1572011.21770.114058
120.0969870.75130.227716
130.0302230.23410.40785
14-0.032766-0.25380.400257
15-0.097586-0.75590.226334
16-0.167831-1.30.099284
17-0.23756-1.84010.035348






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9231367.15060
2-0.073522-0.56950.285572
3-0.062627-0.48510.314684
4-0.133075-1.03080.153388
5-0.059739-0.46270.322615
6-0.034033-0.26360.396487
70.1046290.81050.210442
8-0.026842-0.20790.417999
90.0195160.15120.440173
10-0.108157-0.83780.20274
11-0.0678-0.52520.300699
12-0.065997-0.51120.30554
13-0.073664-0.57060.285202
14-0.024839-0.19240.424038
15-0.057509-0.44550.328794
16-0.116484-0.90230.185259
17-0.085602-0.66310.254914

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.923136 & 7.1506 & 0 \tabularnewline
2 & -0.073522 & -0.5695 & 0.285572 \tabularnewline
3 & -0.062627 & -0.4851 & 0.314684 \tabularnewline
4 & -0.133075 & -1.0308 & 0.153388 \tabularnewline
5 & -0.059739 & -0.4627 & 0.322615 \tabularnewline
6 & -0.034033 & -0.2636 & 0.396487 \tabularnewline
7 & 0.104629 & 0.8105 & 0.210442 \tabularnewline
8 & -0.026842 & -0.2079 & 0.417999 \tabularnewline
9 & 0.019516 & 0.1512 & 0.440173 \tabularnewline
10 & -0.108157 & -0.8378 & 0.20274 \tabularnewline
11 & -0.0678 & -0.5252 & 0.300699 \tabularnewline
12 & -0.065997 & -0.5112 & 0.30554 \tabularnewline
13 & -0.073664 & -0.5706 & 0.285202 \tabularnewline
14 & -0.024839 & -0.1924 & 0.424038 \tabularnewline
15 & -0.057509 & -0.4455 & 0.328794 \tabularnewline
16 & -0.116484 & -0.9023 & 0.185259 \tabularnewline
17 & -0.085602 & -0.6631 & 0.254914 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282842&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]0.923136[/C][C]7.1506[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.073522[/C][C]-0.5695[/C][C]0.285572[/C][/ROW]
[ROW][C]3[/C][C]-0.062627[/C][C]-0.4851[/C][C]0.314684[/C][/ROW]
[ROW][C]4[/C][C]-0.133075[/C][C]-1.0308[/C][C]0.153388[/C][/ROW]
[ROW][C]5[/C][C]-0.059739[/C][C]-0.4627[/C][C]0.322615[/C][/ROW]
[ROW][C]6[/C][C]-0.034033[/C][C]-0.2636[/C][C]0.396487[/C][/ROW]
[ROW][C]7[/C][C]0.104629[/C][C]0.8105[/C][C]0.210442[/C][/ROW]
[ROW][C]8[/C][C]-0.026842[/C][C]-0.2079[/C][C]0.417999[/C][/ROW]
[ROW][C]9[/C][C]0.019516[/C][C]0.1512[/C][C]0.440173[/C][/ROW]
[ROW][C]10[/C][C]-0.108157[/C][C]-0.8378[/C][C]0.20274[/C][/ROW]
[ROW][C]11[/C][C]-0.0678[/C][C]-0.5252[/C][C]0.300699[/C][/ROW]
[ROW][C]12[/C][C]-0.065997[/C][C]-0.5112[/C][C]0.30554[/C][/ROW]
[ROW][C]13[/C][C]-0.073664[/C][C]-0.5706[/C][C]0.285202[/C][/ROW]
[ROW][C]14[/C][C]-0.024839[/C][C]-0.1924[/C][C]0.424038[/C][/ROW]
[ROW][C]15[/C][C]-0.057509[/C][C]-0.4455[/C][C]0.328794[/C][/ROW]
[ROW][C]16[/C][C]-0.116484[/C][C]-0.9023[/C][C]0.185259[/C][/ROW]
[ROW][C]17[/C][C]-0.085602[/C][C]-0.6631[/C][C]0.254914[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282842&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282842&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
10.9231367.15060
2-0.073522-0.56950.285572
3-0.062627-0.48510.314684
4-0.133075-1.03080.153388
5-0.059739-0.46270.322615
6-0.034033-0.26360.396487
70.1046290.81050.210442
8-0.026842-0.20790.417999
90.0195160.15120.440173
10-0.108157-0.83780.20274
11-0.0678-0.52520.300699
12-0.065997-0.51120.30554
13-0.073664-0.57060.285202
14-0.024839-0.19240.424038
15-0.057509-0.44550.328794
16-0.116484-0.90230.185259
17-0.085602-0.66310.254914


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 ; 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')