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Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSun, 19 Oct 2014 16:48:38 +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/2014/Oct/19/t1413733793m6ux4y2v3xszn7i.htm/, Retrieved Sat, 11 May 2024 05:28:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243690, Retrieved Sat, 11 May 2024 05:28:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [Trendgezuiverde a...] [2014-10-19 15:48:38] [8bdab0fd537d5455eaa21dec7dfb1324] [Current]
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Dataseries X:
15071
14236
14771
14804
15597
15418
16903
16350
16393
15685
14556
14850
15391
13704
15409
15098
15254
15522
16669
16238
16246
15424
14952
15008
14929
13905
14994
14753
15031
15386
16160
16116
16219
16064
15436
15404
15112
14119
14775
14289
15121
15371
15782
16104
15674
15105
14223
14385
14558
13804
14672
14244
15089
14580
15218
15696
15129
15110
14204
13655
14534
12746
14074
13699
14184
14110
15820
15362
14993
14437
13694
13688




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243690&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243690&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243690&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'George Udny Yule' @ yule.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.358111-3.01750.001768
20.2610842.19990.015534
3-0.073672-0.62080.26837
4-0.069783-0.5880.279198
5-0.259634-2.18770.015992
6-0.012799-0.10780.457211
7-0.253689-2.13760.017996
80.0416880.35130.363214
9-0.070832-0.59680.276256
100.1698021.43080.07844
11-0.157074-1.32350.094953
120.5948045.01192e-06
13-0.227181-1.91430.029809
140.2123981.78970.038884
15-0.047838-0.40310.344048
16-0.03689-0.31080.378415
17-0.143018-1.20510.116085
18-0.080196-0.67570.250699
19-0.143205-1.20670.115783
20-0.026039-0.21940.413481
21-0.074488-0.62760.266125
220.1508211.27080.103967
23-0.107556-0.90630.183925
240.4117373.46940.000445

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.358111 & -3.0175 & 0.001768 \tabularnewline
2 & 0.261084 & 2.1999 & 0.015534 \tabularnewline
3 & -0.073672 & -0.6208 & 0.26837 \tabularnewline
4 & -0.069783 & -0.588 & 0.279198 \tabularnewline
5 & -0.259634 & -2.1877 & 0.015992 \tabularnewline
6 & -0.012799 & -0.1078 & 0.457211 \tabularnewline
7 & -0.253689 & -2.1376 & 0.017996 \tabularnewline
8 & 0.041688 & 0.3513 & 0.363214 \tabularnewline
9 & -0.070832 & -0.5968 & 0.276256 \tabularnewline
10 & 0.169802 & 1.4308 & 0.07844 \tabularnewline
11 & -0.157074 & -1.3235 & 0.094953 \tabularnewline
12 & 0.594804 & 5.0119 & 2e-06 \tabularnewline
13 & -0.227181 & -1.9143 & 0.029809 \tabularnewline
14 & 0.212398 & 1.7897 & 0.038884 \tabularnewline
15 & -0.047838 & -0.4031 & 0.344048 \tabularnewline
16 & -0.03689 & -0.3108 & 0.378415 \tabularnewline
17 & -0.143018 & -1.2051 & 0.116085 \tabularnewline
18 & -0.080196 & -0.6757 & 0.250699 \tabularnewline
19 & -0.143205 & -1.2067 & 0.115783 \tabularnewline
20 & -0.026039 & -0.2194 & 0.413481 \tabularnewline
21 & -0.074488 & -0.6276 & 0.266125 \tabularnewline
22 & 0.150821 & 1.2708 & 0.103967 \tabularnewline
23 & -0.107556 & -0.9063 & 0.183925 \tabularnewline
24 & 0.411737 & 3.4694 & 0.000445 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243690&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]-0.358111[/C][C]-3.0175[/C][C]0.001768[/C][/ROW]
[ROW][C]2[/C][C]0.261084[/C][C]2.1999[/C][C]0.015534[/C][/ROW]
[ROW][C]3[/C][C]-0.073672[/C][C]-0.6208[/C][C]0.26837[/C][/ROW]
[ROW][C]4[/C][C]-0.069783[/C][C]-0.588[/C][C]0.279198[/C][/ROW]
[ROW][C]5[/C][C]-0.259634[/C][C]-2.1877[/C][C]0.015992[/C][/ROW]
[ROW][C]6[/C][C]-0.012799[/C][C]-0.1078[/C][C]0.457211[/C][/ROW]
[ROW][C]7[/C][C]-0.253689[/C][C]-2.1376[/C][C]0.017996[/C][/ROW]
[ROW][C]8[/C][C]0.041688[/C][C]0.3513[/C][C]0.363214[/C][/ROW]
[ROW][C]9[/C][C]-0.070832[/C][C]-0.5968[/C][C]0.276256[/C][/ROW]
[ROW][C]10[/C][C]0.169802[/C][C]1.4308[/C][C]0.07844[/C][/ROW]
[ROW][C]11[/C][C]-0.157074[/C][C]-1.3235[/C][C]0.094953[/C][/ROW]
[ROW][C]12[/C][C]0.594804[/C][C]5.0119[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.227181[/C][C]-1.9143[/C][C]0.029809[/C][/ROW]
[ROW][C]14[/C][C]0.212398[/C][C]1.7897[/C][C]0.038884[/C][/ROW]
[ROW][C]15[/C][C]-0.047838[/C][C]-0.4031[/C][C]0.344048[/C][/ROW]
[ROW][C]16[/C][C]-0.03689[/C][C]-0.3108[/C][C]0.378415[/C][/ROW]
[ROW][C]17[/C][C]-0.143018[/C][C]-1.2051[/C][C]0.116085[/C][/ROW]
[ROW][C]18[/C][C]-0.080196[/C][C]-0.6757[/C][C]0.250699[/C][/ROW]
[ROW][C]19[/C][C]-0.143205[/C][C]-1.2067[/C][C]0.115783[/C][/ROW]
[ROW][C]20[/C][C]-0.026039[/C][C]-0.2194[/C][C]0.413481[/C][/ROW]
[ROW][C]21[/C][C]-0.074488[/C][C]-0.6276[/C][C]0.266125[/C][/ROW]
[ROW][C]22[/C][C]0.150821[/C][C]1.2708[/C][C]0.103967[/C][/ROW]
[ROW][C]23[/C][C]-0.107556[/C][C]-0.9063[/C][C]0.183925[/C][/ROW]
[ROW][C]24[/C][C]0.411737[/C][C]3.4694[/C][C]0.000445[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243690&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243690&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
1-0.358111-3.01750.001768
20.2610842.19990.015534
3-0.073672-0.62080.26837
4-0.069783-0.5880.279198
5-0.259634-2.18770.015992
6-0.012799-0.10780.457211
7-0.253689-2.13760.017996
80.0416880.35130.363214
9-0.070832-0.59680.276256
100.1698021.43080.07844
11-0.157074-1.32350.094953
120.5948045.01192e-06
13-0.227181-1.91430.029809
140.2123981.78970.038884
15-0.047838-0.40310.344048
16-0.03689-0.31080.378415
17-0.143018-1.20510.116085
18-0.080196-0.67570.250699
19-0.143205-1.20670.115783
20-0.026039-0.21940.413481
21-0.074488-0.62760.266125
220.1508211.27080.103967
23-0.107556-0.90630.183925
240.4117373.46940.000445







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.358111-3.01750.001768
20.1523821.2840.101659
30.0706360.59520.276804
4-0.1334-1.1240.132389
5-0.386526-3.25690.000864
6-0.22027-1.8560.0338
7-0.272226-2.29380.012382
8-0.18955-1.59720.057334
9-0.225539-1.90040.030719
10-0.106281-0.89550.186763
11-0.456285-3.84470.00013
120.2413442.03360.022865
130.0738720.62250.267818
14-0.100184-0.84420.200706
15-0.089674-0.75560.226192
160.0284490.23970.405621
170.1787621.50630.068217
18-0.018465-0.15560.438401
190.0348780.29390.384851
20-0.051478-0.43380.332888
21-0.058286-0.49110.312424
220.0906440.76380.223764
23-0.007905-0.06660.473541
240.0182190.15350.439214

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.358111 & -3.0175 & 0.001768 \tabularnewline
2 & 0.152382 & 1.284 & 0.101659 \tabularnewline
3 & 0.070636 & 0.5952 & 0.276804 \tabularnewline
4 & -0.1334 & -1.124 & 0.132389 \tabularnewline
5 & -0.386526 & -3.2569 & 0.000864 \tabularnewline
6 & -0.22027 & -1.856 & 0.0338 \tabularnewline
7 & -0.272226 & -2.2938 & 0.012382 \tabularnewline
8 & -0.18955 & -1.5972 & 0.057334 \tabularnewline
9 & -0.225539 & -1.9004 & 0.030719 \tabularnewline
10 & -0.106281 & -0.8955 & 0.186763 \tabularnewline
11 & -0.456285 & -3.8447 & 0.00013 \tabularnewline
12 & 0.241344 & 2.0336 & 0.022865 \tabularnewline
13 & 0.073872 & 0.6225 & 0.267818 \tabularnewline
14 & -0.100184 & -0.8442 & 0.200706 \tabularnewline
15 & -0.089674 & -0.7556 & 0.226192 \tabularnewline
16 & 0.028449 & 0.2397 & 0.405621 \tabularnewline
17 & 0.178762 & 1.5063 & 0.068217 \tabularnewline
18 & -0.018465 & -0.1556 & 0.438401 \tabularnewline
19 & 0.034878 & 0.2939 & 0.384851 \tabularnewline
20 & -0.051478 & -0.4338 & 0.332888 \tabularnewline
21 & -0.058286 & -0.4911 & 0.312424 \tabularnewline
22 & 0.090644 & 0.7638 & 0.223764 \tabularnewline
23 & -0.007905 & -0.0666 & 0.473541 \tabularnewline
24 & 0.018219 & 0.1535 & 0.439214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243690&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]-0.358111[/C][C]-3.0175[/C][C]0.001768[/C][/ROW]
[ROW][C]2[/C][C]0.152382[/C][C]1.284[/C][C]0.101659[/C][/ROW]
[ROW][C]3[/C][C]0.070636[/C][C]0.5952[/C][C]0.276804[/C][/ROW]
[ROW][C]4[/C][C]-0.1334[/C][C]-1.124[/C][C]0.132389[/C][/ROW]
[ROW][C]5[/C][C]-0.386526[/C][C]-3.2569[/C][C]0.000864[/C][/ROW]
[ROW][C]6[/C][C]-0.22027[/C][C]-1.856[/C][C]0.0338[/C][/ROW]
[ROW][C]7[/C][C]-0.272226[/C][C]-2.2938[/C][C]0.012382[/C][/ROW]
[ROW][C]8[/C][C]-0.18955[/C][C]-1.5972[/C][C]0.057334[/C][/ROW]
[ROW][C]9[/C][C]-0.225539[/C][C]-1.9004[/C][C]0.030719[/C][/ROW]
[ROW][C]10[/C][C]-0.106281[/C][C]-0.8955[/C][C]0.186763[/C][/ROW]
[ROW][C]11[/C][C]-0.456285[/C][C]-3.8447[/C][C]0.00013[/C][/ROW]
[ROW][C]12[/C][C]0.241344[/C][C]2.0336[/C][C]0.022865[/C][/ROW]
[ROW][C]13[/C][C]0.073872[/C][C]0.6225[/C][C]0.267818[/C][/ROW]
[ROW][C]14[/C][C]-0.100184[/C][C]-0.8442[/C][C]0.200706[/C][/ROW]
[ROW][C]15[/C][C]-0.089674[/C][C]-0.7556[/C][C]0.226192[/C][/ROW]
[ROW][C]16[/C][C]0.028449[/C][C]0.2397[/C][C]0.405621[/C][/ROW]
[ROW][C]17[/C][C]0.178762[/C][C]1.5063[/C][C]0.068217[/C][/ROW]
[ROW][C]18[/C][C]-0.018465[/C][C]-0.1556[/C][C]0.438401[/C][/ROW]
[ROW][C]19[/C][C]0.034878[/C][C]0.2939[/C][C]0.384851[/C][/ROW]
[ROW][C]20[/C][C]-0.051478[/C][C]-0.4338[/C][C]0.332888[/C][/ROW]
[ROW][C]21[/C][C]-0.058286[/C][C]-0.4911[/C][C]0.312424[/C][/ROW]
[ROW][C]22[/C][C]0.090644[/C][C]0.7638[/C][C]0.223764[/C][/ROW]
[ROW][C]23[/C][C]-0.007905[/C][C]-0.0666[/C][C]0.473541[/C][/ROW]
[ROW][C]24[/C][C]0.018219[/C][C]0.1535[/C][C]0.439214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243690&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243690&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
1-0.358111-3.01750.001768
20.1523821.2840.101659
30.0706360.59520.276804
4-0.1334-1.1240.132389
5-0.386526-3.25690.000864
6-0.22027-1.8560.0338
7-0.272226-2.29380.012382
8-0.18955-1.59720.057334
9-0.225539-1.90040.030719
10-0.106281-0.89550.186763
11-0.456285-3.84470.00013
120.2413442.03360.022865
130.0738720.62250.267818
14-0.100184-0.84420.200706
15-0.089674-0.75560.226192
160.0284490.23970.405621
170.1787621.50630.068217
18-0.018465-0.15560.438401
190.0348780.29390.384851
20-0.051478-0.43380.332888
21-0.058286-0.49110.312424
220.0906440.76380.223764
23-0.007905-0.06660.473541
240.0182190.15350.439214



Parameters (Session):
par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 24 ; 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 <- '24'
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')