## Free Statistics

of Irreproducible Research!

Author's title
Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 30 Dec 2011 14:21:27 -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/2011/Dec/30/t1325272947fu0pg1r4dqlnix3.htm/, Retrieved Wed, 11 Sep 2024 07:36:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160897, Retrieved Wed, 11 Sep 2024 07:36:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W11
Estimated Impact217
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2011-12-30 19:21:27] [ded1bbd321fb25f4a0a8bacc8426c40e] [Current]
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Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698

 Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160897&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160897&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160897&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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ jenkins.wessa.net

 Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.581191 4.5019 1.6e-05 2 0.366467 2.8386 0.003087 3 0.143157 1.1089 0.135952 4 0.022204 0.172 0.432011 5 0.032109 0.2487 0.402214 6 0.016271 0.126 0.450064 7 -0.03923 -0.3039 0.381138 8 -0.043867 -0.3398 0.367601 9 -0.060991 -0.4724 0.319166 10 -0.278502 -2.1573 0.0175 11 -0.435643 -3.3745 0.000651 12 -0.550778 -4.2663 3.6e-05 13 -0.417675 -3.2353 0.000989 14 -0.213554 -1.6542 0.051656 15 -0.01961 -0.1519 0.439889 16 -0.098895 -0.766 0.223328 17 -0.011575 -0.0897 0.464429 18 -0.009765 -0.0756 0.469979

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.581191 & 4.5019 & 1.6e-05 \tabularnewline
2 & 0.366467 & 2.8386 & 0.003087 \tabularnewline
3 & 0.143157 & 1.1089 & 0.135952 \tabularnewline
4 & 0.022204 & 0.172 & 0.432011 \tabularnewline
5 & 0.032109 & 0.2487 & 0.402214 \tabularnewline
6 & 0.016271 & 0.126 & 0.450064 \tabularnewline
7 & -0.03923 & -0.3039 & 0.381138 \tabularnewline
8 & -0.043867 & -0.3398 & 0.367601 \tabularnewline
9 & -0.060991 & -0.4724 & 0.319166 \tabularnewline
10 & -0.278502 & -2.1573 & 0.0175 \tabularnewline
11 & -0.435643 & -3.3745 & 0.000651 \tabularnewline
12 & -0.550778 & -4.2663 & 3.6e-05 \tabularnewline
13 & -0.417675 & -3.2353 & 0.000989 \tabularnewline
14 & -0.213554 & -1.6542 & 0.051656 \tabularnewline
15 & -0.01961 & -0.1519 & 0.439889 \tabularnewline
16 & -0.098895 & -0.766 & 0.223328 \tabularnewline
17 & -0.011575 & -0.0897 & 0.464429 \tabularnewline
18 & -0.009765 & -0.0756 & 0.469979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160897&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]0.581191[/C][C]4.5019[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.366467[/C][C]2.8386[/C][C]0.003087[/C][/ROW]
[ROW][C]3[/C][C]0.143157[/C][C]1.1089[/C][C]0.135952[/C][/ROW]
[ROW][C]4[/C][C]0.022204[/C][C]0.172[/C][C]0.432011[/C][/ROW]
[ROW][C]5[/C][C]0.032109[/C][C]0.2487[/C][C]0.402214[/C][/ROW]
[ROW][C]6[/C][C]0.016271[/C][C]0.126[/C][C]0.450064[/C][/ROW]
[ROW][C]7[/C][C]-0.03923[/C][C]-0.3039[/C][C]0.381138[/C][/ROW]
[ROW][C]8[/C][C]-0.043867[/C][C]-0.3398[/C][C]0.367601[/C][/ROW]
[ROW][C]9[/C][C]-0.060991[/C][C]-0.4724[/C][C]0.319166[/C][/ROW]
[ROW][C]10[/C][C]-0.278502[/C][C]-2.1573[/C][C]0.0175[/C][/ROW]
[ROW][C]11[/C][C]-0.435643[/C][C]-3.3745[/C][C]0.000651[/C][/ROW]
[ROW][C]12[/C][C]-0.550778[/C][C]-4.2663[/C][C]3.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.417675[/C][C]-3.2353[/C][C]0.000989[/C][/ROW]
[ROW][C]14[/C][C]-0.213554[/C][C]-1.6542[/C][C]0.051656[/C][/ROW]
[ROW][C]15[/C][C]-0.01961[/C][C]-0.1519[/C][C]0.439889[/C][/ROW]
[ROW][C]16[/C][C]-0.098895[/C][C]-0.766[/C][C]0.223328[/C][/ROW]
[ROW][C]17[/C][C]-0.011575[/C][C]-0.0897[/C][C]0.464429[/C][/ROW]
[ROW][C]18[/C][C]-0.009765[/C][C]-0.0756[/C][C]0.469979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160897&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160897&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 k ACF(k) T-STAT P-value 1 0.581191 4.5019 1.6e-05 2 0.366467 2.8386 0.003087 3 0.143157 1.1089 0.135952 4 0.022204 0.172 0.432011 5 0.032109 0.2487 0.402214 6 0.016271 0.126 0.450064 7 -0.03923 -0.3039 0.381138 8 -0.043867 -0.3398 0.367601 9 -0.060991 -0.4724 0.319166 10 -0.278502 -2.1573 0.0175 11 -0.435643 -3.3745 0.000651 12 -0.550778 -4.2663 3.6e-05 13 -0.417675 -3.2353 0.000989 14 -0.213554 -1.6542 0.051656 15 -0.01961 -0.1519 0.439889 16 -0.098895 -0.766 0.223328 17 -0.011575 -0.0897 0.464429 18 -0.009765 -0.0756 0.469979

 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.581191 4.5019 1.6e-05 2 0.043314 0.3355 0.369206 3 -0.129777 -1.0052 0.159407 4 -0.038609 -0.2991 0.382963 5 0.099607 0.7716 0.221703 6 -0.016915 -0.131 0.448097 7 -0.104024 -0.8058 0.211779 8 0.015847 0.1227 0.451358 9 -0.00253 -0.0196 0.492214 10 -0.370425 -2.8693 0.002836 11 -0.275131 -2.1312 0.018591 12 -0.186274 -1.4429 0.077129 13 0.098999 0.7668 0.223091 14 0.080144 0.6208 0.268543 15 0.106702 0.8265 0.205895 16 -0.274173 -2.1237 0.018912 17 0.122904 0.952 0.172455 18 0.036793 0.285 0.388313

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.581191 & 4.5019 & 1.6e-05 \tabularnewline
2 & 0.043314 & 0.3355 & 0.369206 \tabularnewline
3 & -0.129777 & -1.0052 & 0.159407 \tabularnewline
4 & -0.038609 & -0.2991 & 0.382963 \tabularnewline
5 & 0.099607 & 0.7716 & 0.221703 \tabularnewline
6 & -0.016915 & -0.131 & 0.448097 \tabularnewline
7 & -0.104024 & -0.8058 & 0.211779 \tabularnewline
8 & 0.015847 & 0.1227 & 0.451358 \tabularnewline
9 & -0.00253 & -0.0196 & 0.492214 \tabularnewline
10 & -0.370425 & -2.8693 & 0.002836 \tabularnewline
11 & -0.275131 & -2.1312 & 0.018591 \tabularnewline
12 & -0.186274 & -1.4429 & 0.077129 \tabularnewline
13 & 0.098999 & 0.7668 & 0.223091 \tabularnewline
14 & 0.080144 & 0.6208 & 0.268543 \tabularnewline
15 & 0.106702 & 0.8265 & 0.205895 \tabularnewline
16 & -0.274173 & -2.1237 & 0.018912 \tabularnewline
17 & 0.122904 & 0.952 & 0.172455 \tabularnewline
18 & 0.036793 & 0.285 & 0.388313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160897&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]0.581191[/C][C]4.5019[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.043314[/C][C]0.3355[/C][C]0.369206[/C][/ROW]
[ROW][C]3[/C][C]-0.129777[/C][C]-1.0052[/C][C]0.159407[/C][/ROW]
[ROW][C]4[/C][C]-0.038609[/C][C]-0.2991[/C][C]0.382963[/C][/ROW]
[ROW][C]5[/C][C]0.099607[/C][C]0.7716[/C][C]0.221703[/C][/ROW]
[ROW][C]6[/C][C]-0.016915[/C][C]-0.131[/C][C]0.448097[/C][/ROW]
[ROW][C]7[/C][C]-0.104024[/C][C]-0.8058[/C][C]0.211779[/C][/ROW]
[ROW][C]8[/C][C]0.015847[/C][C]0.1227[/C][C]0.451358[/C][/ROW]
[ROW][C]9[/C][C]-0.00253[/C][C]-0.0196[/C][C]0.492214[/C][/ROW]
[ROW][C]10[/C][C]-0.370425[/C][C]-2.8693[/C][C]0.002836[/C][/ROW]
[ROW][C]11[/C][C]-0.275131[/C][C]-2.1312[/C][C]0.018591[/C][/ROW]
[ROW][C]12[/C][C]-0.186274[/C][C]-1.4429[/C][C]0.077129[/C][/ROW]
[ROW][C]13[/C][C]0.098999[/C][C]0.7668[/C][C]0.223091[/C][/ROW]
[ROW][C]14[/C][C]0.080144[/C][C]0.6208[/C][C]0.268543[/C][/ROW]
[ROW][C]15[/C][C]0.106702[/C][C]0.8265[/C][C]0.205895[/C][/ROW]
[ROW][C]16[/C][C]-0.274173[/C][C]-2.1237[/C][C]0.018912[/C][/ROW]
[ROW][C]17[/C][C]0.122904[/C][C]0.952[/C][C]0.172455[/C][/ROW]
[ROW][C]18[/C][C]0.036793[/C][C]0.285[/C][C]0.388313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160897&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160897&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 k PACF(k) T-STAT P-value 1 0.581191 4.5019 1.6e-05 2 0.043314 0.3355 0.369206 3 -0.129777 -1.0052 0.159407 4 -0.038609 -0.2991 0.382963 5 0.099607 0.7716 0.221703 6 -0.016915 -0.131 0.448097 7 -0.104024 -0.8058 0.211779 8 0.015847 0.1227 0.451358 9 -0.00253 -0.0196 0.492214 10 -0.370425 -2.8693 0.002836 11 -0.275131 -2.1312 0.018591 12 -0.186274 -1.4429 0.077129 13 0.098999 0.7668 0.223091 14 0.080144 0.6208 0.268543 15 0.106702 0.8265 0.205895 16 -0.274173 -2.1237 0.018912 17 0.122904 0.952 0.172455 18 0.036793 0.285 0.388313

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)
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.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
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)