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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 computationTue, 08 Dec 2009 14:09:44 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/08/t1260306661l640n19mqyc4yse.htm/, Retrieved Sat, 27 Apr 2024 14:35:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64867, Retrieved Sat, 27 Apr 2024 14:35:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W21
Estimated Impact110

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] [time series analy...] [2009-12-08 21:09:44] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
35,75
36,25
35,32
33,80
31,54
30,74
30,55
30,06
30,30
32,24
33,42
33,31
33,76
33,61
33,68
34,17
34,17
34,07
32,36
31,57
31,34
30,81
29,95
29,74
29,56
29,91
29,82
31,46
32,55
32,82
32,74
33,05
32,63
31,85
31,99
31,39
30,16
30,04
29,55
29,12
29,31
29,36
29,67
30,69
31,08
31,08
31,10
30,96
31,94
31,59
32,01
32,13
32,20
32,05
32,12
31,66
32,99
36,02
37,10
37,96
38,96
41,66
47,29
49,42
48,17
46,25
45,43
43,83
41,51
38,25
35,23
34,18

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64867&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64867&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' @ 72.249.127.135






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9608968.15350
20.8715327.39520
30.7611426.45850
40.6408865.43810
50.5138734.36042.1e-05
60.3834593.25380.000868
70.2638392.23870.014132
80.1723311.46230.074009
90.1103340.93620.176147
100.0675330.5730.284201
110.0384370.32620.372628
120.0204970.17390.431209
130.0123020.10440.458576
140.0100970.08570.465982
150.002250.01910.49241
16-0.012949-0.10990.456406
17-0.033646-0.28550.388043
18-0.059232-0.50260.308389

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.960896 & 8.1535 & 0 \tabularnewline
2 & 0.871532 & 7.3952 & 0 \tabularnewline
3 & 0.761142 & 6.4585 & 0 \tabularnewline
4 & 0.640886 & 5.4381 & 0 \tabularnewline
5 & 0.513873 & 4.3604 & 2.1e-05 \tabularnewline
6 & 0.383459 & 3.2538 & 0.000868 \tabularnewline
7 & 0.263839 & 2.2387 & 0.014132 \tabularnewline
8 & 0.172331 & 1.4623 & 0.074009 \tabularnewline
9 & 0.110334 & 0.9362 & 0.176147 \tabularnewline
10 & 0.067533 & 0.573 & 0.284201 \tabularnewline
11 & 0.038437 & 0.3262 & 0.372628 \tabularnewline
12 & 0.020497 & 0.1739 & 0.431209 \tabularnewline
13 & 0.012302 & 0.1044 & 0.458576 \tabularnewline
14 & 0.010097 & 0.0857 & 0.465982 \tabularnewline
15 & 0.00225 & 0.0191 & 0.49241 \tabularnewline
16 & -0.012949 & -0.1099 & 0.456406 \tabularnewline
17 & -0.033646 & -0.2855 & 0.388043 \tabularnewline
18 & -0.059232 & -0.5026 & 0.308389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64867&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]0.960896[/C][C]8.1535[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.871532[/C][C]7.3952[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.761142[/C][C]6.4585[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.640886[/C][C]5.4381[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.513873[/C][C]4.3604[/C][C]2.1e-05[/C][/ROW]
[ROW][C]6[/C][C]0.383459[/C][C]3.2538[/C][C]0.000868[/C][/ROW]
[ROW][C]7[/C][C]0.263839[/C][C]2.2387[/C][C]0.014132[/C][/ROW]
[ROW][C]8[/C][C]0.172331[/C][C]1.4623[/C][C]0.074009[/C][/ROW]
[ROW][C]9[/C][C]0.110334[/C][C]0.9362[/C][C]0.176147[/C][/ROW]
[ROW][C]10[/C][C]0.067533[/C][C]0.573[/C][C]0.284201[/C][/ROW]
[ROW][C]11[/C][C]0.038437[/C][C]0.3262[/C][C]0.372628[/C][/ROW]
[ROW][C]12[/C][C]0.020497[/C][C]0.1739[/C][C]0.431209[/C][/ROW]
[ROW][C]13[/C][C]0.012302[/C][C]0.1044[/C][C]0.458576[/C][/ROW]
[ROW][C]14[/C][C]0.010097[/C][C]0.0857[/C][C]0.465982[/C][/ROW]
[ROW][C]15[/C][C]0.00225[/C][C]0.0191[/C][C]0.49241[/C][/ROW]
[ROW][C]16[/C][C]-0.012949[/C][C]-0.1099[/C][C]0.456406[/C][/ROW]
[ROW][C]17[/C][C]-0.033646[/C][C]-0.2855[/C][C]0.388043[/C][/ROW]
[ROW][C]18[/C][C]-0.059232[/C][C]-0.5026[/C][C]0.308389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64867&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64867&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
10.9608968.15350
20.8715327.39520
30.7611426.45850
40.6408865.43810
50.5138734.36042.1e-05
60.3834593.25380.000868
70.2638392.23870.014132
80.1723311.46230.074009
90.1103340.93620.176147
100.0675330.5730.284201
110.0384370.32620.372628
120.0204970.17390.431209
130.0123020.10440.458576
140.0100970.08570.465982
150.002250.01910.49241
16-0.012949-0.10990.456406
17-0.033646-0.28550.388043
18-0.059232-0.50260.308389






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9608968.15350
2-0.675416-5.73110
30.1694381.43770.077422
4-0.197853-1.67880.048759
5-0.079841-0.67750.250138
6-0.070852-0.60120.274797
70.1955151.6590.050733
80.177481.5060.068225
9-0.055977-0.4750.318118
10-0.072597-0.6160.269918
110.0340080.28860.386869
12-0.084042-0.71310.239039
13-0.01884-0.15990.43672
14-0.010042-0.08520.466166
15-0.131506-1.11590.134095
160.1114570.94570.173721
17-0.112672-0.95610.171121
18-0.012285-0.10420.458635

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.960896 & 8.1535 & 0 \tabularnewline
2 & -0.675416 & -5.7311 & 0 \tabularnewline
3 & 0.169438 & 1.4377 & 0.077422 \tabularnewline
4 & -0.197853 & -1.6788 & 0.048759 \tabularnewline
5 & -0.079841 & -0.6775 & 0.250138 \tabularnewline
6 & -0.070852 & -0.6012 & 0.274797 \tabularnewline
7 & 0.195515 & 1.659 & 0.050733 \tabularnewline
8 & 0.17748 & 1.506 & 0.068225 \tabularnewline
9 & -0.055977 & -0.475 & 0.318118 \tabularnewline
10 & -0.072597 & -0.616 & 0.269918 \tabularnewline
11 & 0.034008 & 0.2886 & 0.386869 \tabularnewline
12 & -0.084042 & -0.7131 & 0.239039 \tabularnewline
13 & -0.01884 & -0.1599 & 0.43672 \tabularnewline
14 & -0.010042 & -0.0852 & 0.466166 \tabularnewline
15 & -0.131506 & -1.1159 & 0.134095 \tabularnewline
16 & 0.111457 & 0.9457 & 0.173721 \tabularnewline
17 & -0.112672 & -0.9561 & 0.171121 \tabularnewline
18 & -0.012285 & -0.1042 & 0.458635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64867&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]0.960896[/C][C]8.1535[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.675416[/C][C]-5.7311[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.169438[/C][C]1.4377[/C][C]0.077422[/C][/ROW]
[ROW][C]4[/C][C]-0.197853[/C][C]-1.6788[/C][C]0.048759[/C][/ROW]
[ROW][C]5[/C][C]-0.079841[/C][C]-0.6775[/C][C]0.250138[/C][/ROW]
[ROW][C]6[/C][C]-0.070852[/C][C]-0.6012[/C][C]0.274797[/C][/ROW]
[ROW][C]7[/C][C]0.195515[/C][C]1.659[/C][C]0.050733[/C][/ROW]
[ROW][C]8[/C][C]0.17748[/C][C]1.506[/C][C]0.068225[/C][/ROW]
[ROW][C]9[/C][C]-0.055977[/C][C]-0.475[/C][C]0.318118[/C][/ROW]
[ROW][C]10[/C][C]-0.072597[/C][C]-0.616[/C][C]0.269918[/C][/ROW]
[ROW][C]11[/C][C]0.034008[/C][C]0.2886[/C][C]0.386869[/C][/ROW]
[ROW][C]12[/C][C]-0.084042[/C][C]-0.7131[/C][C]0.239039[/C][/ROW]
[ROW][C]13[/C][C]-0.01884[/C][C]-0.1599[/C][C]0.43672[/C][/ROW]
[ROW][C]14[/C][C]-0.010042[/C][C]-0.0852[/C][C]0.466166[/C][/ROW]
[ROW][C]15[/C][C]-0.131506[/C][C]-1.1159[/C][C]0.134095[/C][/ROW]
[ROW][C]16[/C][C]0.111457[/C][C]0.9457[/C][C]0.173721[/C][/ROW]
[ROW][C]17[/C][C]-0.112672[/C][C]-0.9561[/C][C]0.171121[/C][/ROW]
[ROW][C]18[/C][C]-0.012285[/C][C]-0.1042[/C][C]0.458635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64867&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64867&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
10.9608968.15350
2-0.675416-5.73110
30.1694381.43770.077422
4-0.197853-1.67880.048759
5-0.079841-0.67750.250138
6-0.070852-0.60120.274797
70.1955151.6590.050733
80.177481.5060.068225
9-0.055977-0.4750.318118
10-0.072597-0.6160.269918
110.0340080.28860.386869
12-0.084042-0.71310.239039
13-0.01884-0.15990.43672
14-0.010042-0.08520.466166
15-0.131506-1.11590.134095
160.1114570.94570.173721
17-0.112672-0.95610.171121
18-0.012285-0.10420.458635


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 ;
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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')