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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 computationSun, 12 Jan 2014 20:25:38 -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/2014/Jan/12/t1389576448qmi2ss3c4fd95qv.htm/, Retrieved Sun, 19 May 2024 08:02:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233098, Retrieved Sun, 19 May 2024 08:02:04 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKarel De Grote-Hogeschool Valérie Weyts
Estimated Impact90

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Mean Plot] [Mean plot NWWZ Ma...] [2014-01-13 00:02:57] [ba0d20b2fbb0c8f9ef8b1828cc8a0bda]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelatie ge...] [2014-01-13 01:25:38] [feb2df3f24188fb89c42f3077ec68a56] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233098&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]3 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=233098&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233098&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.5379166.38740
20.0856321.01680.155489
30.0698270.82910.204211
40.0603890.71710.237254
50.0509520.6050.273069
60.0415140.4930.311405
70.0320770.38090.351928
80.0226390.26880.394227
90.0132020.15680.437827
100.0547080.64960.258495
110.1041751.2370.10907
120.0992651.17870.12025
130.1166431.38510.084111
140.1212851.44020.076016
150.1244591.47790.070836
160.1148981.36430.087318
170.1117041.32640.093424
180.108511.28850.099843
190.1053171.25060.106582
200.1021231.21260.113647
210.0989291.17470.121043

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.537916 & 6.3874 & 0 \tabularnewline
2 & 0.085632 & 1.0168 & 0.155489 \tabularnewline
3 & 0.069827 & 0.8291 & 0.204211 \tabularnewline
4 & 0.060389 & 0.7171 & 0.237254 \tabularnewline
5 & 0.050952 & 0.605 & 0.273069 \tabularnewline
6 & 0.041514 & 0.493 & 0.311405 \tabularnewline
7 & 0.032077 & 0.3809 & 0.351928 \tabularnewline
8 & 0.022639 & 0.2688 & 0.394227 \tabularnewline
9 & 0.013202 & 0.1568 & 0.437827 \tabularnewline
10 & 0.054708 & 0.6496 & 0.258495 \tabularnewline
11 & 0.104175 & 1.237 & 0.10907 \tabularnewline
12 & 0.099265 & 1.1787 & 0.12025 \tabularnewline
13 & 0.116643 & 1.3851 & 0.084111 \tabularnewline
14 & 0.121285 & 1.4402 & 0.076016 \tabularnewline
15 & 0.124459 & 1.4779 & 0.070836 \tabularnewline
16 & 0.114898 & 1.3643 & 0.087318 \tabularnewline
17 & 0.111704 & 1.3264 & 0.093424 \tabularnewline
18 & 0.10851 & 1.2885 & 0.099843 \tabularnewline
19 & 0.105317 & 1.2506 & 0.106582 \tabularnewline
20 & 0.102123 & 1.2126 & 0.113647 \tabularnewline
21 & 0.098929 & 1.1747 & 0.121043 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233098&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]0.537916[/C][C]6.3874[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.085632[/C][C]1.0168[/C][C]0.155489[/C][/ROW]
[ROW][C]3[/C][C]0.069827[/C][C]0.8291[/C][C]0.204211[/C][/ROW]
[ROW][C]4[/C][C]0.060389[/C][C]0.7171[/C][C]0.237254[/C][/ROW]
[ROW][C]5[/C][C]0.050952[/C][C]0.605[/C][C]0.273069[/C][/ROW]
[ROW][C]6[/C][C]0.041514[/C][C]0.493[/C][C]0.311405[/C][/ROW]
[ROW][C]7[/C][C]0.032077[/C][C]0.3809[/C][C]0.351928[/C][/ROW]
[ROW][C]8[/C][C]0.022639[/C][C]0.2688[/C][C]0.394227[/C][/ROW]
[ROW][C]9[/C][C]0.013202[/C][C]0.1568[/C][C]0.437827[/C][/ROW]
[ROW][C]10[/C][C]0.054708[/C][C]0.6496[/C][C]0.258495[/C][/ROW]
[ROW][C]11[/C][C]0.104175[/C][C]1.237[/C][C]0.10907[/C][/ROW]
[ROW][C]12[/C][C]0.099265[/C][C]1.1787[/C][C]0.12025[/C][/ROW]
[ROW][C]13[/C][C]0.116643[/C][C]1.3851[/C][C]0.084111[/C][/ROW]
[ROW][C]14[/C][C]0.121285[/C][C]1.4402[/C][C]0.076016[/C][/ROW]
[ROW][C]15[/C][C]0.124459[/C][C]1.4779[/C][C]0.070836[/C][/ROW]
[ROW][C]16[/C][C]0.114898[/C][C]1.3643[/C][C]0.087318[/C][/ROW]
[ROW][C]17[/C][C]0.111704[/C][C]1.3264[/C][C]0.093424[/C][/ROW]
[ROW][C]18[/C][C]0.10851[/C][C]1.2885[/C][C]0.099843[/C][/ROW]
[ROW][C]19[/C][C]0.105317[/C][C]1.2506[/C][C]0.106582[/C][/ROW]
[ROW][C]20[/C][C]0.102123[/C][C]1.2126[/C][C]0.113647[/C][/ROW]
[ROW][C]21[/C][C]0.098929[/C][C]1.1747[/C][C]0.121043[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233098&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233098&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
10.5379166.38740
20.0856321.01680.155489
30.0698270.82910.204211
40.0603890.71710.237254
50.0509520.6050.273069
60.0415140.4930.311405
70.0320770.38090.351928
80.0226390.26880.394227
90.0132020.15680.437827
100.0547080.64960.258495
110.1041751.2370.10907
120.0992651.17870.12025
130.1166431.38510.084111
140.1212851.44020.076016
150.1244591.47790.070836
160.1148981.36430.087318
170.1117041.32640.093424
180.108511.28850.099843
190.1053171.25060.106582
200.1021231.21260.113647
210.0989291.17470.121043






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.5379166.38740
2-0.28667-3.4040.000432
30.252612.99960.001599
4-0.14634-1.73770.042225
50.145591.72880.043018
6-0.088697-1.05320.147022
70.0864571.02660.153178
8-0.059905-0.71130.239027
90.0487080.57840.281965
100.0438570.52080.30167
110.0632030.75050.227104
120.0140660.1670.433795
130.1035471.22950.110457
14-0.008856-0.10520.458198
150.1127971.33940.0913
16-0.032303-0.38360.350935
170.1161941.37970.084927
18-0.034941-0.41490.339422
190.1106531.31390.095501
20-0.027756-0.32960.371101
210.0931981.10670.135162

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.537916 & 6.3874 & 0 \tabularnewline
2 & -0.28667 & -3.404 & 0.000432 \tabularnewline
3 & 0.25261 & 2.9996 & 0.001599 \tabularnewline
4 & -0.14634 & -1.7377 & 0.042225 \tabularnewline
5 & 0.14559 & 1.7288 & 0.043018 \tabularnewline
6 & -0.088697 & -1.0532 & 0.147022 \tabularnewline
7 & 0.086457 & 1.0266 & 0.153178 \tabularnewline
8 & -0.059905 & -0.7113 & 0.239027 \tabularnewline
9 & 0.048708 & 0.5784 & 0.281965 \tabularnewline
10 & 0.043857 & 0.5208 & 0.30167 \tabularnewline
11 & 0.063203 & 0.7505 & 0.227104 \tabularnewline
12 & 0.014066 & 0.167 & 0.433795 \tabularnewline
13 & 0.103547 & 1.2295 & 0.110457 \tabularnewline
14 & -0.008856 & -0.1052 & 0.458198 \tabularnewline
15 & 0.112797 & 1.3394 & 0.0913 \tabularnewline
16 & -0.032303 & -0.3836 & 0.350935 \tabularnewline
17 & 0.116194 & 1.3797 & 0.084927 \tabularnewline
18 & -0.034941 & -0.4149 & 0.339422 \tabularnewline
19 & 0.110653 & 1.3139 & 0.095501 \tabularnewline
20 & -0.027756 & -0.3296 & 0.371101 \tabularnewline
21 & 0.093198 & 1.1067 & 0.135162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233098&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]0.537916[/C][C]6.3874[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.28667[/C][C]-3.404[/C][C]0.000432[/C][/ROW]
[ROW][C]3[/C][C]0.25261[/C][C]2.9996[/C][C]0.001599[/C][/ROW]
[ROW][C]4[/C][C]-0.14634[/C][C]-1.7377[/C][C]0.042225[/C][/ROW]
[ROW][C]5[/C][C]0.14559[/C][C]1.7288[/C][C]0.043018[/C][/ROW]
[ROW][C]6[/C][C]-0.088697[/C][C]-1.0532[/C][C]0.147022[/C][/ROW]
[ROW][C]7[/C][C]0.086457[/C][C]1.0266[/C][C]0.153178[/C][/ROW]
[ROW][C]8[/C][C]-0.059905[/C][C]-0.7113[/C][C]0.239027[/C][/ROW]
[ROW][C]9[/C][C]0.048708[/C][C]0.5784[/C][C]0.281965[/C][/ROW]
[ROW][C]10[/C][C]0.043857[/C][C]0.5208[/C][C]0.30167[/C][/ROW]
[ROW][C]11[/C][C]0.063203[/C][C]0.7505[/C][C]0.227104[/C][/ROW]
[ROW][C]12[/C][C]0.014066[/C][C]0.167[/C][C]0.433795[/C][/ROW]
[ROW][C]13[/C][C]0.103547[/C][C]1.2295[/C][C]0.110457[/C][/ROW]
[ROW][C]14[/C][C]-0.008856[/C][C]-0.1052[/C][C]0.458198[/C][/ROW]
[ROW][C]15[/C][C]0.112797[/C][C]1.3394[/C][C]0.0913[/C][/ROW]
[ROW][C]16[/C][C]-0.032303[/C][C]-0.3836[/C][C]0.350935[/C][/ROW]
[ROW][C]17[/C][C]0.116194[/C][C]1.3797[/C][C]0.084927[/C][/ROW]
[ROW][C]18[/C][C]-0.034941[/C][C]-0.4149[/C][C]0.339422[/C][/ROW]
[ROW][C]19[/C][C]0.110653[/C][C]1.3139[/C][C]0.095501[/C][/ROW]
[ROW][C]20[/C][C]-0.027756[/C][C]-0.3296[/C][C]0.371101[/C][/ROW]
[ROW][C]21[/C][C]0.093198[/C][C]1.1067[/C][C]0.135162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233098&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233098&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
10.5379166.38740
2-0.28667-3.4040.000432
30.252612.99960.001599
4-0.14634-1.73770.042225
50.145591.72880.043018
6-0.088697-1.05320.147022
70.0864571.02660.153178
8-0.059905-0.71130.239027
90.0487080.57840.281965
100.0438570.52080.30167
110.0632030.75050.227104
120.0140660.1670.433795
130.1035471.22950.110457
14-0.008856-0.10520.458198
150.1127971.33940.0913
16-0.032303-0.38360.350935
170.1161941.37970.084927
18-0.034941-0.41490.339422
190.1106531.31390.095501
20-0.027756-0.32960.371101
210.0931981.10670.135162


Figures (Output of Computation)

Input Parameters & R Code

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