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Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 22 May 2015 17:16:48 +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/May/22/t1432311517tbw0jy5p26r8t4a.htm/, Retrieved Fri, 03 May 2024 05:51:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279238, Retrieved Fri, 03 May 2024 05:51:23 +0000
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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] [] [2015-05-22 16:16:48] [70e23d918d09c907c02097a361cd6415] [Current]
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Dataseries X:
3.5
4.8
6
5.9
3.6
6.8
8.7
8.4
8.1
8.9
8.7
7.8
6.3
7.5
6.8
7
8.8
8.4
7.6
7.9
7.4
8.7
8.7
8
9.4
8.5
5.8
2.8
3.3
4.8
1.8
4.8
-0.9
-6
-9
-21.1
-20.9
-23.5
-20.8
-17.3
-16.1
-13.9
-14.6
-9.2
-9.7
-7.2
-5
-8.1
-6.2
-4.8
-3.1
-1.4
0.6
-0.8
-2
0.2
-0.1
0.3
0.2
2.6
2.5
1.5
5.7
4.3
2.7
1.7
-2.2
-3.2
-0.5
-3.1
-4.8
-1.3
-1.8
-1.7
-2.8
-3.4
-4.9
-4.8
-5.4
-4.7
-6.6
-7.6
-6.8
-5.6
-5.6
-3.7
-5.1
-5.6
-4.1
-3.8
-3.1
-1.4
-2.4
-0.3
-0.3
0.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279238&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279238&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9520919.32860
20.8964898.78380
30.8210238.04430
40.7258917.11220
50.6477516.34660
60.56055.49180
70.4804884.70784e-06
80.3937173.85760.000104
90.3164723.10080.001267
100.2344572.29720.01189
110.1523141.49240.069442
120.0850770.83360.203292
130.0090120.08830.46491
14-0.052845-0.51780.302905
15-0.111079-1.08840.139582
16-0.161185-1.57930.05878
17-0.204529-2.0040.023946
18-0.241563-2.36680.009974
19-0.267189-2.61790.00514

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.952091 & 9.3286 & 0 \tabularnewline
2 & 0.896489 & 8.7838 & 0 \tabularnewline
3 & 0.821023 & 8.0443 & 0 \tabularnewline
4 & 0.725891 & 7.1122 & 0 \tabularnewline
5 & 0.647751 & 6.3466 & 0 \tabularnewline
6 & 0.5605 & 5.4918 & 0 \tabularnewline
7 & 0.480488 & 4.7078 & 4e-06 \tabularnewline
8 & 0.393717 & 3.8576 & 0.000104 \tabularnewline
9 & 0.316472 & 3.1008 & 0.001267 \tabularnewline
10 & 0.234457 & 2.2972 & 0.01189 \tabularnewline
11 & 0.152314 & 1.4924 & 0.069442 \tabularnewline
12 & 0.085077 & 0.8336 & 0.203292 \tabularnewline
13 & 0.009012 & 0.0883 & 0.46491 \tabularnewline
14 & -0.052845 & -0.5178 & 0.302905 \tabularnewline
15 & -0.111079 & -1.0884 & 0.139582 \tabularnewline
16 & -0.161185 & -1.5793 & 0.05878 \tabularnewline
17 & -0.204529 & -2.004 & 0.023946 \tabularnewline
18 & -0.241563 & -2.3668 & 0.009974 \tabularnewline
19 & -0.267189 & -2.6179 & 0.00514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279238&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]0.952091[/C][C]9.3286[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.896489[/C][C]8.7838[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.821023[/C][C]8.0443[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.725891[/C][C]7.1122[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.647751[/C][C]6.3466[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.5605[/C][C]5.4918[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.480488[/C][C]4.7078[/C][C]4e-06[/C][/ROW]
[ROW][C]8[/C][C]0.393717[/C][C]3.8576[/C][C]0.000104[/C][/ROW]
[ROW][C]9[/C][C]0.316472[/C][C]3.1008[/C][C]0.001267[/C][/ROW]
[ROW][C]10[/C][C]0.234457[/C][C]2.2972[/C][C]0.01189[/C][/ROW]
[ROW][C]11[/C][C]0.152314[/C][C]1.4924[/C][C]0.069442[/C][/ROW]
[ROW][C]12[/C][C]0.085077[/C][C]0.8336[/C][C]0.203292[/C][/ROW]
[ROW][C]13[/C][C]0.009012[/C][C]0.0883[/C][C]0.46491[/C][/ROW]
[ROW][C]14[/C][C]-0.052845[/C][C]-0.5178[/C][C]0.302905[/C][/ROW]
[ROW][C]15[/C][C]-0.111079[/C][C]-1.0884[/C][C]0.139582[/C][/ROW]
[ROW][C]16[/C][C]-0.161185[/C][C]-1.5793[/C][C]0.05878[/C][/ROW]
[ROW][C]17[/C][C]-0.204529[/C][C]-2.004[/C][C]0.023946[/C][/ROW]
[ROW][C]18[/C][C]-0.241563[/C][C]-2.3668[/C][C]0.009974[/C][/ROW]
[ROW][C]19[/C][C]-0.267189[/C][C]-2.6179[/C][C]0.00514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279238&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
10.9520919.32860
20.8964898.78380
30.8210238.04430
40.7258917.11220
50.6477516.34660
60.56055.49180
70.4804884.70784e-06
80.3937173.85760.000104
90.3164723.10080.001267
100.2344572.29720.01189
110.1523141.49240.069442
120.0850770.83360.203292
130.0090120.08830.46491
14-0.052845-0.51780.302905
15-0.111079-1.08840.139582
16-0.161185-1.57930.05878
17-0.204529-2.0040.023946
18-0.241563-2.36680.009974
19-0.267189-2.61790.00514







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9520919.32860
2-0.106811-1.04650.148971
3-0.237844-2.33040.01094
4-0.239861-2.35010.010407
50.2034091.9930.02455
6-0.093836-0.91940.180094
7-0.015798-0.15480.438657
8-0.21491-2.10570.018921
90.1397651.36940.087033
10-0.169355-1.65930.050156
11-0.015921-0.1560.438183
120.0043080.04220.483209
13-0.064304-0.63010.265079
14-0.025913-0.25390.400059
15-0.023496-0.23020.409208
160.0481150.47140.319202
17-0.088348-0.86560.194425
180.022460.22010.413144
19-0.012855-0.1260.450015

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.952091 & 9.3286 & 0 \tabularnewline
2 & -0.106811 & -1.0465 & 0.148971 \tabularnewline
3 & -0.237844 & -2.3304 & 0.01094 \tabularnewline
4 & -0.239861 & -2.3501 & 0.010407 \tabularnewline
5 & 0.203409 & 1.993 & 0.02455 \tabularnewline
6 & -0.093836 & -0.9194 & 0.180094 \tabularnewline
7 & -0.015798 & -0.1548 & 0.438657 \tabularnewline
8 & -0.21491 & -2.1057 & 0.018921 \tabularnewline
9 & 0.139765 & 1.3694 & 0.087033 \tabularnewline
10 & -0.169355 & -1.6593 & 0.050156 \tabularnewline
11 & -0.015921 & -0.156 & 0.438183 \tabularnewline
12 & 0.004308 & 0.0422 & 0.483209 \tabularnewline
13 & -0.064304 & -0.6301 & 0.265079 \tabularnewline
14 & -0.025913 & -0.2539 & 0.400059 \tabularnewline
15 & -0.023496 & -0.2302 & 0.409208 \tabularnewline
16 & 0.048115 & 0.4714 & 0.319202 \tabularnewline
17 & -0.088348 & -0.8656 & 0.194425 \tabularnewline
18 & 0.02246 & 0.2201 & 0.413144 \tabularnewline
19 & -0.012855 & -0.126 & 0.450015 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279238&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]0.952091[/C][C]9.3286[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.106811[/C][C]-1.0465[/C][C]0.148971[/C][/ROW]
[ROW][C]3[/C][C]-0.237844[/C][C]-2.3304[/C][C]0.01094[/C][/ROW]
[ROW][C]4[/C][C]-0.239861[/C][C]-2.3501[/C][C]0.010407[/C][/ROW]
[ROW][C]5[/C][C]0.203409[/C][C]1.993[/C][C]0.02455[/C][/ROW]
[ROW][C]6[/C][C]-0.093836[/C][C]-0.9194[/C][C]0.180094[/C][/ROW]
[ROW][C]7[/C][C]-0.015798[/C][C]-0.1548[/C][C]0.438657[/C][/ROW]
[ROW][C]8[/C][C]-0.21491[/C][C]-2.1057[/C][C]0.018921[/C][/ROW]
[ROW][C]9[/C][C]0.139765[/C][C]1.3694[/C][C]0.087033[/C][/ROW]
[ROW][C]10[/C][C]-0.169355[/C][C]-1.6593[/C][C]0.050156[/C][/ROW]
[ROW][C]11[/C][C]-0.015921[/C][C]-0.156[/C][C]0.438183[/C][/ROW]
[ROW][C]12[/C][C]0.004308[/C][C]0.0422[/C][C]0.483209[/C][/ROW]
[ROW][C]13[/C][C]-0.064304[/C][C]-0.6301[/C][C]0.265079[/C][/ROW]
[ROW][C]14[/C][C]-0.025913[/C][C]-0.2539[/C][C]0.400059[/C][/ROW]
[ROW][C]15[/C][C]-0.023496[/C][C]-0.2302[/C][C]0.409208[/C][/ROW]
[ROW][C]16[/C][C]0.048115[/C][C]0.4714[/C][C]0.319202[/C][/ROW]
[ROW][C]17[/C][C]-0.088348[/C][C]-0.8656[/C][C]0.194425[/C][/ROW]
[ROW][C]18[/C][C]0.02246[/C][C]0.2201[/C][C]0.413144[/C][/ROW]
[ROW][C]19[/C][C]-0.012855[/C][C]-0.126[/C][C]0.450015[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279238&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
10.9520919.32860
2-0.106811-1.04650.148971
3-0.237844-2.33040.01094
4-0.239861-2.35010.010407
50.2034091.9930.02455
6-0.093836-0.91940.180094
7-0.015798-0.15480.438657
8-0.21491-2.10570.018921
90.1397651.36940.087033
10-0.169355-1.65930.050156
11-0.015921-0.1560.438183
120.0043080.04220.483209
13-0.064304-0.63010.265079
14-0.025913-0.25390.400059
15-0.023496-0.23020.409208
160.0481150.47140.319202
17-0.088348-0.86560.194425
180.022460.22010.413144
19-0.012855-0.1260.450015



Parameters (Session):
par1 = 0.01 ; par2 = 0.09 ; par3 = 0.01 ;
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):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '2'
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')