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Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSat, 24 Oct 2015 19:23:53 +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/2015/Oct/24/t1445711045rw5usnp308hwhpd.htm/, Retrieved Sat, 18 May 2024 14:23:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283055, Retrieved Sat, 18 May 2024 14:23:32 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2015-10-24 18:23:53] [237b8e3b7b7bc12136ba0893525d9132] [Current]
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Dataseries X:
71,83
71,39
73,71
74,13
74,45
74,95
75,09
75,23
76,11
76,64
76,97
78,23
77,15
76,33
70,19
68,42
66,49
63,41
62,92
65,53
65,26
68,25
74,39
78,71
82,15
86,05
89,46
89,32
88,94
93,35
94,72
96,11
104,06
104,11
103,9
110,75
110,82
107,59
96,03
95,69
90,63
75,87
75,57
78,78
74,93
75,85
75,49
76,87
78,18
79,37
80,59
81,18
81,02
82,75
83,63
85,35
90,52
90,66
90,69
92,56
92,87
93,82
96,32
96,03
96,53
102,96
102,38
102,66
106,83
106,5
106,78
108,49
108,77
110,43
110,84
110,52
110,11
109,42
109,06
108,98
108,36
108,11
108,44
107,76
106,27
101,07
100,79
100,97
99,33
99,35
99,23
98,14
98,17
98,48
99
99,19
99,1
100,13
100,07
95,26
94,72
94,25
89,46
88,38
88,57
93,82
93,94
93,92




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283055&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283055&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.96689610.04830
20.9194869.55560
30.8684199.02490
40.7981088.29420
50.7215877.4990
60.6491096.74570
70.5803836.03150
80.5122845.32380
90.4472284.64775e-06
100.3912874.06644.5e-05
110.3356073.48770.000353
120.2814072.92450.002103
130.2352752.4450.00805
140.1884251.95820.026395
150.1378221.43230.077475
160.0995291.03430.151645
170.067960.70630.240774
180.0391650.4070.342402
190.0202860.21080.416713
200.0112080.11650.453746

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.966896 & 10.0483 & 0 \tabularnewline
2 & 0.919486 & 9.5556 & 0 \tabularnewline
3 & 0.868419 & 9.0249 & 0 \tabularnewline
4 & 0.798108 & 8.2942 & 0 \tabularnewline
5 & 0.721587 & 7.499 & 0 \tabularnewline
6 & 0.649109 & 6.7457 & 0 \tabularnewline
7 & 0.580383 & 6.0315 & 0 \tabularnewline
8 & 0.512284 & 5.3238 & 0 \tabularnewline
9 & 0.447228 & 4.6477 & 5e-06 \tabularnewline
10 & 0.391287 & 4.0664 & 4.5e-05 \tabularnewline
11 & 0.335607 & 3.4877 & 0.000353 \tabularnewline
12 & 0.281407 & 2.9245 & 0.002103 \tabularnewline
13 & 0.235275 & 2.445 & 0.00805 \tabularnewline
14 & 0.188425 & 1.9582 & 0.026395 \tabularnewline
15 & 0.137822 & 1.4323 & 0.077475 \tabularnewline
16 & 0.099529 & 1.0343 & 0.151645 \tabularnewline
17 & 0.06796 & 0.7063 & 0.240774 \tabularnewline
18 & 0.039165 & 0.407 & 0.342402 \tabularnewline
19 & 0.020286 & 0.2108 & 0.416713 \tabularnewline
20 & 0.011208 & 0.1165 & 0.453746 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283055&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]0.966896[/C][C]10.0483[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.919486[/C][C]9.5556[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.868419[/C][C]9.0249[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.798108[/C][C]8.2942[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.721587[/C][C]7.499[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.649109[/C][C]6.7457[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.580383[/C][C]6.0315[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.512284[/C][C]5.3238[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.447228[/C][C]4.6477[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.391287[/C][C]4.0664[/C][C]4.5e-05[/C][/ROW]
[ROW][C]11[/C][C]0.335607[/C][C]3.4877[/C][C]0.000353[/C][/ROW]
[ROW][C]12[/C][C]0.281407[/C][C]2.9245[/C][C]0.002103[/C][/ROW]
[ROW][C]13[/C][C]0.235275[/C][C]2.445[/C][C]0.00805[/C][/ROW]
[ROW][C]14[/C][C]0.188425[/C][C]1.9582[/C][C]0.026395[/C][/ROW]
[ROW][C]15[/C][C]0.137822[/C][C]1.4323[/C][C]0.077475[/C][/ROW]
[ROW][C]16[/C][C]0.099529[/C][C]1.0343[/C][C]0.151645[/C][/ROW]
[ROW][C]17[/C][C]0.06796[/C][C]0.7063[/C][C]0.240774[/C][/ROW]
[ROW][C]18[/C][C]0.039165[/C][C]0.407[/C][C]0.342402[/C][/ROW]
[ROW][C]19[/C][C]0.020286[/C][C]0.2108[/C][C]0.416713[/C][/ROW]
[ROW][C]20[/C][C]0.011208[/C][C]0.1165[/C][C]0.453746[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283055&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
10.96689610.04830
20.9194869.55560
30.8684199.02490
40.7981088.29420
50.7215877.4990
60.6491096.74570
70.5803836.03150
80.5122845.32380
90.4472284.64775e-06
100.3912874.06644.5e-05
110.3356073.48770.000353
120.2814072.92450.002103
130.2352752.4450.00805
140.1884251.95820.026395
150.1378221.43230.077475
160.0995291.03430.151645
170.067960.70630.240774
180.0391650.4070.342402
190.0202860.21080.416713
200.0112080.11650.453746







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.96689610.04830
2-0.236549-2.45830.007775
3-0.036021-0.37430.35444
4-0.32667-3.39490.000481
5-0.02058-0.21390.415526
60.0379170.3940.347161
70.0816720.84880.198946
8-0.042919-0.4460.328235
9-0.038774-0.40290.343891
100.0434050.45110.32642
11-0.0933-0.96960.167207
12-0.004307-0.04480.48219
130.0233870.2430.404215
14-0.08195-0.85170.198146
15-0.090015-0.93550.175818
160.1567871.62940.053073
170.0135740.14110.444039
180.0448260.46580.321132
190.0333740.34680.364694
200.0208790.2170.414317

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.966896 & 10.0483 & 0 \tabularnewline
2 & -0.236549 & -2.4583 & 0.007775 \tabularnewline
3 & -0.036021 & -0.3743 & 0.35444 \tabularnewline
4 & -0.32667 & -3.3949 & 0.000481 \tabularnewline
5 & -0.02058 & -0.2139 & 0.415526 \tabularnewline
6 & 0.037917 & 0.394 & 0.347161 \tabularnewline
7 & 0.081672 & 0.8488 & 0.198946 \tabularnewline
8 & -0.042919 & -0.446 & 0.328235 \tabularnewline
9 & -0.038774 & -0.4029 & 0.343891 \tabularnewline
10 & 0.043405 & 0.4511 & 0.32642 \tabularnewline
11 & -0.0933 & -0.9696 & 0.167207 \tabularnewline
12 & -0.004307 & -0.0448 & 0.48219 \tabularnewline
13 & 0.023387 & 0.243 & 0.404215 \tabularnewline
14 & -0.08195 & -0.8517 & 0.198146 \tabularnewline
15 & -0.090015 & -0.9355 & 0.175818 \tabularnewline
16 & 0.156787 & 1.6294 & 0.053073 \tabularnewline
17 & 0.013574 & 0.1411 & 0.444039 \tabularnewline
18 & 0.044826 & 0.4658 & 0.321132 \tabularnewline
19 & 0.033374 & 0.3468 & 0.364694 \tabularnewline
20 & 0.020879 & 0.217 & 0.414317 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283055&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]0.966896[/C][C]10.0483[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.236549[/C][C]-2.4583[/C][C]0.007775[/C][/ROW]
[ROW][C]3[/C][C]-0.036021[/C][C]-0.3743[/C][C]0.35444[/C][/ROW]
[ROW][C]4[/C][C]-0.32667[/C][C]-3.3949[/C][C]0.000481[/C][/ROW]
[ROW][C]5[/C][C]-0.02058[/C][C]-0.2139[/C][C]0.415526[/C][/ROW]
[ROW][C]6[/C][C]0.037917[/C][C]0.394[/C][C]0.347161[/C][/ROW]
[ROW][C]7[/C][C]0.081672[/C][C]0.8488[/C][C]0.198946[/C][/ROW]
[ROW][C]8[/C][C]-0.042919[/C][C]-0.446[/C][C]0.328235[/C][/ROW]
[ROW][C]9[/C][C]-0.038774[/C][C]-0.4029[/C][C]0.343891[/C][/ROW]
[ROW][C]10[/C][C]0.043405[/C][C]0.4511[/C][C]0.32642[/C][/ROW]
[ROW][C]11[/C][C]-0.0933[/C][C]-0.9696[/C][C]0.167207[/C][/ROW]
[ROW][C]12[/C][C]-0.004307[/C][C]-0.0448[/C][C]0.48219[/C][/ROW]
[ROW][C]13[/C][C]0.023387[/C][C]0.243[/C][C]0.404215[/C][/ROW]
[ROW][C]14[/C][C]-0.08195[/C][C]-0.8517[/C][C]0.198146[/C][/ROW]
[ROW][C]15[/C][C]-0.090015[/C][C]-0.9355[/C][C]0.175818[/C][/ROW]
[ROW][C]16[/C][C]0.156787[/C][C]1.6294[/C][C]0.053073[/C][/ROW]
[ROW][C]17[/C][C]0.013574[/C][C]0.1411[/C][C]0.444039[/C][/ROW]
[ROW][C]18[/C][C]0.044826[/C][C]0.4658[/C][C]0.321132[/C][/ROW]
[ROW][C]19[/C][C]0.033374[/C][C]0.3468[/C][C]0.364694[/C][/ROW]
[ROW][C]20[/C][C]0.020879[/C][C]0.217[/C][C]0.414317[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283055&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283055&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
10.96689610.04830
2-0.236549-2.45830.007775
3-0.036021-0.37430.35444
4-0.32667-3.39490.000481
5-0.02058-0.21390.415526
60.0379170.3940.347161
70.0816720.84880.198946
8-0.042919-0.4460.328235
9-0.038774-0.40290.343891
100.0434050.45110.32642
11-0.0933-0.96960.167207
12-0.004307-0.04480.48219
130.0233870.2430.404215
14-0.08195-0.85170.198146
15-0.090015-0.93550.175818
160.1567871.62940.053073
170.0135740.14110.444039
180.0448260.46580.321132
190.0333740.34680.364694
200.0208790.2170.414317



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 ; 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')