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Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationWed, 20 Nov 2013 13:25:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/20/t1384971989awq3sxs6tlhjv26.htm/, Retrieved Wed, 01 May 2024 15:00:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226701, Retrieved Wed, 01 May 2024 15:00:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2013-11-20 18:25:09] [f6b0814d1ccce07ea30140b42d9cb647] [Current]
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Dataseries X:
500.48
500.49
500.50
500.51
500.52
500.53
500.54
500.55
500.56
500.57
500.58
500.59
500.60
500.61
500.62
500.63
500.64
500.65
500.66
500.67
500.68
500.69
500.70
500.71




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ yule.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 & 4 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226701&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226701&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226701&T=0

As an alternative you can also use a 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 time4 seconds
R Server'George Udny Yule' @ yule.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.8754.28660.000127
20.750873.67850.000591
30.6284783.07890.002571
40.5086962.49210.010002
50.3923911.92230.033257
60.2804351.37380.091093
70.1736960.85090.201609
80.0730430.35780.361796
9-0.020652-0.10120.460126
10-0.106522-0.52180.30328
11-0.183696-0.89990.188552
12-0.251304-1.23110.115101
13-0.308478-1.51120.071893
14-0.354348-1.73590.047699
15-0.388043-1.9010.034687
16-0.408696-2.00220.028344
17-0.415435-2.03520.026509
18-0.407391-1.99580.028712
19-0.383696-1.87970.03617
20-0.343478-1.68270.052701
21-0.28587-1.40050.087085
22-0.21-1.02880.156919
23-0.115-0.56340.2892
24NANANA

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.875 & 4.2866 & 0.000127 \tabularnewline
2 & 0.75087 & 3.6785 & 0.000591 \tabularnewline
3 & 0.628478 & 3.0789 & 0.002571 \tabularnewline
4 & 0.508696 & 2.4921 & 0.010002 \tabularnewline
5 & 0.392391 & 1.9223 & 0.033257 \tabularnewline
6 & 0.280435 & 1.3738 & 0.091093 \tabularnewline
7 & 0.173696 & 0.8509 & 0.201609 \tabularnewline
8 & 0.073043 & 0.3578 & 0.361796 \tabularnewline
9 & -0.020652 & -0.1012 & 0.460126 \tabularnewline
10 & -0.106522 & -0.5218 & 0.30328 \tabularnewline
11 & -0.183696 & -0.8999 & 0.188552 \tabularnewline
12 & -0.251304 & -1.2311 & 0.115101 \tabularnewline
13 & -0.308478 & -1.5112 & 0.071893 \tabularnewline
14 & -0.354348 & -1.7359 & 0.047699 \tabularnewline
15 & -0.388043 & -1.901 & 0.034687 \tabularnewline
16 & -0.408696 & -2.0022 & 0.028344 \tabularnewline
17 & -0.415435 & -2.0352 & 0.026509 \tabularnewline
18 & -0.407391 & -1.9958 & 0.028712 \tabularnewline
19 & -0.383696 & -1.8797 & 0.03617 \tabularnewline
20 & -0.343478 & -1.6827 & 0.052701 \tabularnewline
21 & -0.28587 & -1.4005 & 0.087085 \tabularnewline
22 & -0.21 & -1.0288 & 0.156919 \tabularnewline
23 & -0.115 & -0.5634 & 0.2892 \tabularnewline
24 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226701&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]0.875[/C][C]4.2866[/C][C]0.000127[/C][/ROW]
[ROW][C]2[/C][C]0.75087[/C][C]3.6785[/C][C]0.000591[/C][/ROW]
[ROW][C]3[/C][C]0.628478[/C][C]3.0789[/C][C]0.002571[/C][/ROW]
[ROW][C]4[/C][C]0.508696[/C][C]2.4921[/C][C]0.010002[/C][/ROW]
[ROW][C]5[/C][C]0.392391[/C][C]1.9223[/C][C]0.033257[/C][/ROW]
[ROW][C]6[/C][C]0.280435[/C][C]1.3738[/C][C]0.091093[/C][/ROW]
[ROW][C]7[/C][C]0.173696[/C][C]0.8509[/C][C]0.201609[/C][/ROW]
[ROW][C]8[/C][C]0.073043[/C][C]0.3578[/C][C]0.361796[/C][/ROW]
[ROW][C]9[/C][C]-0.020652[/C][C]-0.1012[/C][C]0.460126[/C][/ROW]
[ROW][C]10[/C][C]-0.106522[/C][C]-0.5218[/C][C]0.30328[/C][/ROW]
[ROW][C]11[/C][C]-0.183696[/C][C]-0.8999[/C][C]0.188552[/C][/ROW]
[ROW][C]12[/C][C]-0.251304[/C][C]-1.2311[/C][C]0.115101[/C][/ROW]
[ROW][C]13[/C][C]-0.308478[/C][C]-1.5112[/C][C]0.071893[/C][/ROW]
[ROW][C]14[/C][C]-0.354348[/C][C]-1.7359[/C][C]0.047699[/C][/ROW]
[ROW][C]15[/C][C]-0.388043[/C][C]-1.901[/C][C]0.034687[/C][/ROW]
[ROW][C]16[/C][C]-0.408696[/C][C]-2.0022[/C][C]0.028344[/C][/ROW]
[ROW][C]17[/C][C]-0.415435[/C][C]-2.0352[/C][C]0.026509[/C][/ROW]
[ROW][C]18[/C][C]-0.407391[/C][C]-1.9958[/C][C]0.028712[/C][/ROW]
[ROW][C]19[/C][C]-0.383696[/C][C]-1.8797[/C][C]0.03617[/C][/ROW]
[ROW][C]20[/C][C]-0.343478[/C][C]-1.6827[/C][C]0.052701[/C][/ROW]
[ROW][C]21[/C][C]-0.28587[/C][C]-1.4005[/C][C]0.087085[/C][/ROW]
[ROW][C]22[/C][C]-0.21[/C][C]-1.0288[/C][C]0.156919[/C][/ROW]
[ROW][C]23[/C][C]-0.115[/C][C]-0.5634[/C][C]0.2892[/C][/ROW]
[ROW][C]24[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226701&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226701&T=1

As an alternative you can also use a QR Code:  

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

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.8754.28660.000127
20.750873.67850.000591
30.6284783.07890.002571
40.5086962.49210.010002
50.3923911.92230.033257
60.2804351.37380.091093
70.1736960.85090.201609
80.0730430.35780.361796
9-0.020652-0.10120.460126
10-0.106522-0.52180.30328
11-0.183696-0.89990.188552
12-0.251304-1.23110.115101
13-0.308478-1.51120.071893
14-0.354348-1.73590.047699
15-0.388043-1.9010.034687
16-0.408696-2.00220.028344
17-0.415435-2.03520.026509
18-0.407391-1.99580.028712
19-0.383696-1.87970.03617
20-0.343478-1.68270.052701
21-0.28587-1.40050.087085
22-0.21-1.02880.156919
23-0.115-0.56340.2892
24NANANA







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.8754.28660.000127
2-0.062957-0.30840.380211
3-0.063436-0.31080.37933
4-0.063901-0.3130.378474
5-0.064309-0.3150.377724
6-0.064608-0.31650.377174
7-0.064735-0.31710.376942
8-0.064611-0.31650.377169
9-0.064139-0.31420.378035
10-0.063202-0.30960.379759
11-0.061653-0.3020.382613
12-0.059317-0.29060.38693
13-0.055981-0.27430.393119
14-0.051399-0.25180.401668
15-0.045287-0.22190.41315
16-0.03733-0.18290.428214
17-0.027195-0.13320.447563
18-0.014542-0.07120.471899
190.0009570.00470.498148
200.0196180.09610.462116
210.0417730.20460.419787
220.0678720.33250.371198
230.0987090.48360.316535
24NANANA

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.875 & 4.2866 & 0.000127 \tabularnewline
2 & -0.062957 & -0.3084 & 0.380211 \tabularnewline
3 & -0.063436 & -0.3108 & 0.37933 \tabularnewline
4 & -0.063901 & -0.313 & 0.378474 \tabularnewline
5 & -0.064309 & -0.315 & 0.377724 \tabularnewline
6 & -0.064608 & -0.3165 & 0.377174 \tabularnewline
7 & -0.064735 & -0.3171 & 0.376942 \tabularnewline
8 & -0.064611 & -0.3165 & 0.377169 \tabularnewline
9 & -0.064139 & -0.3142 & 0.378035 \tabularnewline
10 & -0.063202 & -0.3096 & 0.379759 \tabularnewline
11 & -0.061653 & -0.302 & 0.382613 \tabularnewline
12 & -0.059317 & -0.2906 & 0.38693 \tabularnewline
13 & -0.055981 & -0.2743 & 0.393119 \tabularnewline
14 & -0.051399 & -0.2518 & 0.401668 \tabularnewline
15 & -0.045287 & -0.2219 & 0.41315 \tabularnewline
16 & -0.03733 & -0.1829 & 0.428214 \tabularnewline
17 & -0.027195 & -0.1332 & 0.447563 \tabularnewline
18 & -0.014542 & -0.0712 & 0.471899 \tabularnewline
19 & 0.000957 & 0.0047 & 0.498148 \tabularnewline
20 & 0.019618 & 0.0961 & 0.462116 \tabularnewline
21 & 0.041773 & 0.2046 & 0.419787 \tabularnewline
22 & 0.067872 & 0.3325 & 0.371198 \tabularnewline
23 & 0.098709 & 0.4836 & 0.316535 \tabularnewline
24 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226701&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]0.875[/C][C]4.2866[/C][C]0.000127[/C][/ROW]
[ROW][C]2[/C][C]-0.062957[/C][C]-0.3084[/C][C]0.380211[/C][/ROW]
[ROW][C]3[/C][C]-0.063436[/C][C]-0.3108[/C][C]0.37933[/C][/ROW]
[ROW][C]4[/C][C]-0.063901[/C][C]-0.313[/C][C]0.378474[/C][/ROW]
[ROW][C]5[/C][C]-0.064309[/C][C]-0.315[/C][C]0.377724[/C][/ROW]
[ROW][C]6[/C][C]-0.064608[/C][C]-0.3165[/C][C]0.377174[/C][/ROW]
[ROW][C]7[/C][C]-0.064735[/C][C]-0.3171[/C][C]0.376942[/C][/ROW]
[ROW][C]8[/C][C]-0.064611[/C][C]-0.3165[/C][C]0.377169[/C][/ROW]
[ROW][C]9[/C][C]-0.064139[/C][C]-0.3142[/C][C]0.378035[/C][/ROW]
[ROW][C]10[/C][C]-0.063202[/C][C]-0.3096[/C][C]0.379759[/C][/ROW]
[ROW][C]11[/C][C]-0.061653[/C][C]-0.302[/C][C]0.382613[/C][/ROW]
[ROW][C]12[/C][C]-0.059317[/C][C]-0.2906[/C][C]0.38693[/C][/ROW]
[ROW][C]13[/C][C]-0.055981[/C][C]-0.2743[/C][C]0.393119[/C][/ROW]
[ROW][C]14[/C][C]-0.051399[/C][C]-0.2518[/C][C]0.401668[/C][/ROW]
[ROW][C]15[/C][C]-0.045287[/C][C]-0.2219[/C][C]0.41315[/C][/ROW]
[ROW][C]16[/C][C]-0.03733[/C][C]-0.1829[/C][C]0.428214[/C][/ROW]
[ROW][C]17[/C][C]-0.027195[/C][C]-0.1332[/C][C]0.447563[/C][/ROW]
[ROW][C]18[/C][C]-0.014542[/C][C]-0.0712[/C][C]0.471899[/C][/ROW]
[ROW][C]19[/C][C]0.000957[/C][C]0.0047[/C][C]0.498148[/C][/ROW]
[ROW][C]20[/C][C]0.019618[/C][C]0.0961[/C][C]0.462116[/C][/ROW]
[ROW][C]21[/C][C]0.041773[/C][C]0.2046[/C][C]0.419787[/C][/ROW]
[ROW][C]22[/C][C]0.067872[/C][C]0.3325[/C][C]0.371198[/C][/ROW]
[ROW][C]23[/C][C]0.098709[/C][C]0.4836[/C][C]0.316535[/C][/ROW]
[ROW][C]24[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226701&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226701&T=2

As an alternative you can also use a QR Code:  

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

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.8754.28660.000127
2-0.062957-0.30840.380211
3-0.063436-0.31080.37933
4-0.063901-0.3130.378474
5-0.064309-0.3150.377724
6-0.064608-0.31650.377174
7-0.064735-0.31710.376942
8-0.064611-0.31650.377169
9-0.064139-0.31420.378035
10-0.063202-0.30960.379759
11-0.061653-0.3020.382613
12-0.059317-0.29060.38693
13-0.055981-0.27430.393119
14-0.051399-0.25180.401668
15-0.045287-0.22190.41315
16-0.03733-0.18290.428214
17-0.027195-0.13320.447563
18-0.014542-0.07120.471899
190.0009570.00470.498148
200.0196180.09610.462116
210.0417730.20460.419787
220.0678720.33250.371198
230.0987090.48360.316535
24NANANA



Parameters (Session):
par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 24 ; 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):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- '48'
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')