FreeStatistics.org

Free Statistics

of Irreproducible Research!

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 computationThu, 22 Dec 2016 18:08:50 +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/2016/Dec/22/t1482426672ofrh7ymwt65suua.htm/, Retrieved Tue, 04 Nov 2025 13:00:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302576, Retrieved Tue, 04 Nov 2025 13:00:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact281

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] [ACF1] [2016-12-22 17:08:50] [636d0f72197ac5e1dae4a755427db02a] [Current]
- R       [(Partial) Autocorrelation Function] [Acf2] [2016-12-22 19:00:45] [267314984f6394bb93cd815224aa34ba]
- RM D    [Univariate Data Series] [Plot1] [2016-12-22 19:40:19] [267314984f6394bb93cd815224aa34ba]
- R  D    [(Partial) Autocorrelation Function] [ACF3] [2016-12-22 19:42:28] [267314984f6394bb93cd815224aa34ba]
- R  D    [(Partial) Autocorrelation Function] [ACF4] [2016-12-22 19:57:56] [267314984f6394bb93cd815224aa34ba]
- R  D    [(Partial) Autocorrelation Function] [acf5] [2016-12-22 20:00:26] [267314984f6394bb93cd815224aa34ba]
- RM D    [Variance Reduction Matrix] [VRM1] [2016-12-22 20:44:22] [267314984f6394bb93cd815224aa34ba]
- RM      [Variance Reduction Matrix] [VRM2] [2016-12-22 20:59:02] [267314984f6394bb93cd815224aa34ba]
- RM      [Standard Deviation-Mean Plot] [SMP1] [2016-12-22 21:38:22] [267314984f6394bb93cd815224aa34ba]
- RM D    [Standard Deviation-Mean Plot] [SMP2] [2016-12-22 22:45:44] [267314984f6394bb93cd815224aa34ba]
- RM D    [ARIMA Backward Selection] [ARIMA1] [2016-12-23 11:27:04] [267314984f6394bb93cd815224aa34ba]
- RM D    [ARIMA Backward Selection] [ARIMA2] [2016-12-23 12:21:31] [267314984f6394bb93cd815224aa34ba]
- RM      [ARIMA Forecasting] [ARIMAF1] [2016-12-23 13:02:31] [267314984f6394bb93cd815224aa34ba]
- RM D    [ARIMA Forecasting] [ARIMAF2] [2016-12-23 14:11:47] [267314984f6394bb93cd815224aa34ba]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2601.76
2819.1
2368.84
2683.5
2649.22
2760.3
2326
2819.3
2957.02
3460.5
2873.16
3252.48
3628.52
3899.22
3049.36
3751.58
4639.42
4991.02
4076.28
4782.4
5173.8
5177.94
4048.46
4828.98
4727.62
5366.84
4597.38
4838.16
4268.2
4769.34
4223.34
4396.38
4911.6
5368.4
4665
5081.46

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302576&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [ROW]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302576&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302576&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.407212-2.40910.010695
2-0.041188-0.24370.404454
3-0.343819-2.03410.02479
40.7408714.38315.1e-05
5-0.418042-2.47320.009196
60.0429270.2540.400506
7-0.321207-1.90030.032829
80.6105143.61190.000472
9-0.267868-1.58470.061012
100.0161670.09560.462173
11-0.373981-2.21250.016775
120.4759312.81560.003971
13-0.195713-1.15790.127382
14-0.010814-0.0640.474676
15-0.281034-1.66260.05266

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.407212 & -2.4091 & 0.010695 \tabularnewline
2 & -0.041188 & -0.2437 & 0.404454 \tabularnewline
3 & -0.343819 & -2.0341 & 0.02479 \tabularnewline
4 & 0.740871 & 4.3831 & 5.1e-05 \tabularnewline
5 & -0.418042 & -2.4732 & 0.009196 \tabularnewline
6 & 0.042927 & 0.254 & 0.400506 \tabularnewline
7 & -0.321207 & -1.9003 & 0.032829 \tabularnewline
8 & 0.610514 & 3.6119 & 0.000472 \tabularnewline
9 & -0.267868 & -1.5847 & 0.061012 \tabularnewline
10 & 0.016167 & 0.0956 & 0.462173 \tabularnewline
11 & -0.373981 & -2.2125 & 0.016775 \tabularnewline
12 & 0.475931 & 2.8156 & 0.003971 \tabularnewline
13 & -0.195713 & -1.1579 & 0.127382 \tabularnewline
14 & -0.010814 & -0.064 & 0.474676 \tabularnewline
15 & -0.281034 & -1.6626 & 0.05266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302576&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]-0.407212[/C][C]-2.4091[/C][C]0.010695[/C][/ROW]
[ROW][C]2[/C][C]-0.041188[/C][C]-0.2437[/C][C]0.404454[/C][/ROW]
[ROW][C]3[/C][C]-0.343819[/C][C]-2.0341[/C][C]0.02479[/C][/ROW]
[ROW][C]4[/C][C]0.740871[/C][C]4.3831[/C][C]5.1e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.418042[/C][C]-2.4732[/C][C]0.009196[/C][/ROW]
[ROW][C]6[/C][C]0.042927[/C][C]0.254[/C][C]0.400506[/C][/ROW]
[ROW][C]7[/C][C]-0.321207[/C][C]-1.9003[/C][C]0.032829[/C][/ROW]
[ROW][C]8[/C][C]0.610514[/C][C]3.6119[/C][C]0.000472[/C][/ROW]
[ROW][C]9[/C][C]-0.267868[/C][C]-1.5847[/C][C]0.061012[/C][/ROW]
[ROW][C]10[/C][C]0.016167[/C][C]0.0956[/C][C]0.462173[/C][/ROW]
[ROW][C]11[/C][C]-0.373981[/C][C]-2.2125[/C][C]0.016775[/C][/ROW]
[ROW][C]12[/C][C]0.475931[/C][C]2.8156[/C][C]0.003971[/C][/ROW]
[ROW][C]13[/C][C]-0.195713[/C][C]-1.1579[/C][C]0.127382[/C][/ROW]
[ROW][C]14[/C][C]-0.010814[/C][C]-0.064[/C][C]0.474676[/C][/ROW]
[ROW][C]15[/C][C]-0.281034[/C][C]-1.6626[/C][C]0.05266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302576&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302576&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
1-0.407212-2.40910.010695
2-0.041188-0.24370.404454
3-0.343819-2.03410.02479
40.7408714.38315.1e-05
5-0.418042-2.47320.009196
60.0429270.2540.400506
7-0.321207-1.90030.032829
80.6105143.61190.000472
9-0.267868-1.58470.061012
100.0161670.09560.462173
11-0.373981-2.21250.016775
120.4759312.81560.003971
13-0.195713-1.15790.127382
14-0.010814-0.0640.474676
15-0.281034-1.66260.05266






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.407212-2.40910.010695
2-0.24816-1.46810.075499
3-0.595047-3.52030.000609
40.4951472.92930.002971
5-0.145264-0.85940.197986
60.0247880.14660.442126
7-0.167107-0.98860.164818
80.0230260.13620.446213
90.2719891.60910.058288
10-0.078183-0.46250.32328
11-0.172668-1.02150.15701
12-0.239734-1.41830.082475
13-0.175861-1.04040.152642
14-0.169053-1.00010.162056
15-0.046833-0.27710.391679

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.407212 & -2.4091 & 0.010695 \tabularnewline
2 & -0.24816 & -1.4681 & 0.075499 \tabularnewline
3 & -0.595047 & -3.5203 & 0.000609 \tabularnewline
4 & 0.495147 & 2.9293 & 0.002971 \tabularnewline
5 & -0.145264 & -0.8594 & 0.197986 \tabularnewline
6 & 0.024788 & 0.1466 & 0.442126 \tabularnewline
7 & -0.167107 & -0.9886 & 0.164818 \tabularnewline
8 & 0.023026 & 0.1362 & 0.446213 \tabularnewline
9 & 0.271989 & 1.6091 & 0.058288 \tabularnewline
10 & -0.078183 & -0.4625 & 0.32328 \tabularnewline
11 & -0.172668 & -1.0215 & 0.15701 \tabularnewline
12 & -0.239734 & -1.4183 & 0.082475 \tabularnewline
13 & -0.175861 & -1.0404 & 0.152642 \tabularnewline
14 & -0.169053 & -1.0001 & 0.162056 \tabularnewline
15 & -0.046833 & -0.2771 & 0.391679 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302576&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]-0.407212[/C][C]-2.4091[/C][C]0.010695[/C][/ROW]
[ROW][C]2[/C][C]-0.24816[/C][C]-1.4681[/C][C]0.075499[/C][/ROW]
[ROW][C]3[/C][C]-0.595047[/C][C]-3.5203[/C][C]0.000609[/C][/ROW]
[ROW][C]4[/C][C]0.495147[/C][C]2.9293[/C][C]0.002971[/C][/ROW]
[ROW][C]5[/C][C]-0.145264[/C][C]-0.8594[/C][C]0.197986[/C][/ROW]
[ROW][C]6[/C][C]0.024788[/C][C]0.1466[/C][C]0.442126[/C][/ROW]
[ROW][C]7[/C][C]-0.167107[/C][C]-0.9886[/C][C]0.164818[/C][/ROW]
[ROW][C]8[/C][C]0.023026[/C][C]0.1362[/C][C]0.446213[/C][/ROW]
[ROW][C]9[/C][C]0.271989[/C][C]1.6091[/C][C]0.058288[/C][/ROW]
[ROW][C]10[/C][C]-0.078183[/C][C]-0.4625[/C][C]0.32328[/C][/ROW]
[ROW][C]11[/C][C]-0.172668[/C][C]-1.0215[/C][C]0.15701[/C][/ROW]
[ROW][C]12[/C][C]-0.239734[/C][C]-1.4183[/C][C]0.082475[/C][/ROW]
[ROW][C]13[/C][C]-0.175861[/C][C]-1.0404[/C][C]0.152642[/C][/ROW]
[ROW][C]14[/C][C]-0.169053[/C][C]-1.0001[/C][C]0.162056[/C][/ROW]
[ROW][C]15[/C][C]-0.046833[/C][C]-0.2771[/C][C]0.391679[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302576&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302576&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
1-0.407212-2.40910.010695
2-0.24816-1.46810.075499
3-0.595047-3.52030.000609
40.4951472.92930.002971
5-0.145264-0.85940.197986
60.0247880.14660.442126
7-0.167107-0.98860.164818
80.0230260.13620.446213
90.2719891.60910.058288
10-0.078183-0.46250.32328
11-0.172668-1.02150.15701
12-0.239734-1.41830.082475
13-0.175861-1.04040.152642
14-0.169053-1.00010.162056
15-0.046833-0.27710.391679


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = -0.3 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; 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 <- 'Default'
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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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')