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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, 24 Nov 2013 10:21:06 -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/2013/Nov/24/t13853065644mg13byxedv2rtv.htm/, Retrieved Thu, 02 May 2024 08:35:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=228061, Retrieved Thu, 02 May 2024 08:35:58 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2013-11-24 15:21:06] [267d6dd6d9f18d2f1c3bf0912f69c4a3] [Current]
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Dataseries X:
5,53
5,53
5,53
5,53
5,53
5,53
5,53
5,53
5,53
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,67
5,89
5,89
5,89
5,89
5,89
5,89
5,89
5,89
5,89
5,89
5,89
5,89
6,08
6,08
6,08
6,08
6,08
6,08
6,08
6,08
6,08
6,08
6,08
6,08
6,28
6,28
6,28
6,28
6,28
6,28
6,28
6,28
6,28
6,28
6,28
6,28
6,31
6,31
6,31
6,31
6,31
6,31
6,31
6,31
6,31
6,31
6,31
6,31
6,48
6,48
6,48
6,48
6,48
6,48
6,48
6,48
6,48
6,48
6,48
6,48
6,5
6,5
6,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228061&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228061&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9627258.82350
20.925458.48190
30.8881758.14030
40.8518887.80770
50.8156017.47510
60.7793147.14250
70.7430276.810
80.7067416.47740
90.6704546.14480
100.6428135.89150
110.6151725.63810
120.5875315.38480
130.5455545.00012e-06
140.5035784.61547e-06
150.4616014.23063e-05
160.4280223.92298.9e-05
170.3944433.61510.000255
180.3608653.30740.000694
190.3272862.99960.001778

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.962725 & 8.8235 & 0 \tabularnewline
2 & 0.92545 & 8.4819 & 0 \tabularnewline
3 & 0.888175 & 8.1403 & 0 \tabularnewline
4 & 0.851888 & 7.8077 & 0 \tabularnewline
5 & 0.815601 & 7.4751 & 0 \tabularnewline
6 & 0.779314 & 7.1425 & 0 \tabularnewline
7 & 0.743027 & 6.81 & 0 \tabularnewline
8 & 0.706741 & 6.4774 & 0 \tabularnewline
9 & 0.670454 & 6.1448 & 0 \tabularnewline
10 & 0.642813 & 5.8915 & 0 \tabularnewline
11 & 0.615172 & 5.6381 & 0 \tabularnewline
12 & 0.587531 & 5.3848 & 0 \tabularnewline
13 & 0.545554 & 5.0001 & 2e-06 \tabularnewline
14 & 0.503578 & 4.6154 & 7e-06 \tabularnewline
15 & 0.461601 & 4.2306 & 3e-05 \tabularnewline
16 & 0.428022 & 3.9229 & 8.9e-05 \tabularnewline
17 & 0.394443 & 3.6151 & 0.000255 \tabularnewline
18 & 0.360865 & 3.3074 & 0.000694 \tabularnewline
19 & 0.327286 & 2.9996 & 0.001778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228061&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]0.962725[/C][C]8.8235[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.92545[/C][C]8.4819[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.888175[/C][C]8.1403[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.851888[/C][C]7.8077[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.815601[/C][C]7.4751[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.779314[/C][C]7.1425[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.743027[/C][C]6.81[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.706741[/C][C]6.4774[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.670454[/C][C]6.1448[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.642813[/C][C]5.8915[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.615172[/C][C]5.6381[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.587531[/C][C]5.3848[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.545554[/C][C]5.0001[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.503578[/C][C]4.6154[/C][C]7e-06[/C][/ROW]
[ROW][C]15[/C][C]0.461601[/C][C]4.2306[/C][C]3e-05[/C][/ROW]
[ROW][C]16[/C][C]0.428022[/C][C]3.9229[/C][C]8.9e-05[/C][/ROW]
[ROW][C]17[/C][C]0.394443[/C][C]3.6151[/C][C]0.000255[/C][/ROW]
[ROW][C]18[/C][C]0.360865[/C][C]3.3074[/C][C]0.000694[/C][/ROW]
[ROW][C]19[/C][C]0.327286[/C][C]2.9996[/C][C]0.001778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228061&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
10.9627258.82350
20.925458.48190
30.8881758.14030
40.8518887.80770
50.8156017.47510
60.7793147.14250
70.7430276.810
80.7067416.47740
90.6704546.14480
100.6428135.89150
110.6151725.63810
120.5875315.38480
130.5455545.00012e-06
140.5035784.61547e-06
150.4616014.23063e-05
160.4280223.92298.9e-05
170.3944433.61510.000255
180.3608653.30740.000694
190.3272862.99960.001778







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9627258.82350
2-0.018991-0.17410.431119
3-0.019359-0.17740.429799
4-0.006227-0.05710.47731
5-0.019602-0.17970.428929
6-0.019994-0.18320.427524
7-0.020222-0.18530.426705
8-0.020819-0.19080.424568
9-0.021262-0.19490.422984
100.0967950.88710.188768
11-0.017509-0.16050.436448
12-0.017821-0.16330.435325
13-0.213456-1.95640.026873
14-0.027493-0.2520.400836
15-0.028271-0.25910.398094
160.0922090.84510.200224
17-0.023497-0.21540.415006
18-0.024063-0.22050.412994
19-0.015532-0.14230.443573

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.962725 & 8.8235 & 0 \tabularnewline
2 & -0.018991 & -0.1741 & 0.431119 \tabularnewline
3 & -0.019359 & -0.1774 & 0.429799 \tabularnewline
4 & -0.006227 & -0.0571 & 0.47731 \tabularnewline
5 & -0.019602 & -0.1797 & 0.428929 \tabularnewline
6 & -0.019994 & -0.1832 & 0.427524 \tabularnewline
7 & -0.020222 & -0.1853 & 0.426705 \tabularnewline
8 & -0.020819 & -0.1908 & 0.424568 \tabularnewline
9 & -0.021262 & -0.1949 & 0.422984 \tabularnewline
10 & 0.096795 & 0.8871 & 0.188768 \tabularnewline
11 & -0.017509 & -0.1605 & 0.436448 \tabularnewline
12 & -0.017821 & -0.1633 & 0.435325 \tabularnewline
13 & -0.213456 & -1.9564 & 0.026873 \tabularnewline
14 & -0.027493 & -0.252 & 0.400836 \tabularnewline
15 & -0.028271 & -0.2591 & 0.398094 \tabularnewline
16 & 0.092209 & 0.8451 & 0.200224 \tabularnewline
17 & -0.023497 & -0.2154 & 0.415006 \tabularnewline
18 & -0.024063 & -0.2205 & 0.412994 \tabularnewline
19 & -0.015532 & -0.1423 & 0.443573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=228061&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]0.962725[/C][C]8.8235[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.018991[/C][C]-0.1741[/C][C]0.431119[/C][/ROW]
[ROW][C]3[/C][C]-0.019359[/C][C]-0.1774[/C][C]0.429799[/C][/ROW]
[ROW][C]4[/C][C]-0.006227[/C][C]-0.0571[/C][C]0.47731[/C][/ROW]
[ROW][C]5[/C][C]-0.019602[/C][C]-0.1797[/C][C]0.428929[/C][/ROW]
[ROW][C]6[/C][C]-0.019994[/C][C]-0.1832[/C][C]0.427524[/C][/ROW]
[ROW][C]7[/C][C]-0.020222[/C][C]-0.1853[/C][C]0.426705[/C][/ROW]
[ROW][C]8[/C][C]-0.020819[/C][C]-0.1908[/C][C]0.424568[/C][/ROW]
[ROW][C]9[/C][C]-0.021262[/C][C]-0.1949[/C][C]0.422984[/C][/ROW]
[ROW][C]10[/C][C]0.096795[/C][C]0.8871[/C][C]0.188768[/C][/ROW]
[ROW][C]11[/C][C]-0.017509[/C][C]-0.1605[/C][C]0.436448[/C][/ROW]
[ROW][C]12[/C][C]-0.017821[/C][C]-0.1633[/C][C]0.435325[/C][/ROW]
[ROW][C]13[/C][C]-0.213456[/C][C]-1.9564[/C][C]0.026873[/C][/ROW]
[ROW][C]14[/C][C]-0.027493[/C][C]-0.252[/C][C]0.400836[/C][/ROW]
[ROW][C]15[/C][C]-0.028271[/C][C]-0.2591[/C][C]0.398094[/C][/ROW]
[ROW][C]16[/C][C]0.092209[/C][C]0.8451[/C][C]0.200224[/C][/ROW]
[ROW][C]17[/C][C]-0.023497[/C][C]-0.2154[/C][C]0.415006[/C][/ROW]
[ROW][C]18[/C][C]-0.024063[/C][C]-0.2205[/C][C]0.412994[/C][/ROW]
[ROW][C]19[/C][C]-0.015532[/C][C]-0.1423[/C][C]0.443573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=228061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=228061&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
10.9627258.82350
2-0.018991-0.17410.431119
3-0.019359-0.17740.429799
4-0.006227-0.05710.47731
5-0.019602-0.17970.428929
6-0.019994-0.18320.427524
7-0.020222-0.18530.426705
8-0.020819-0.19080.424568
9-0.021262-0.19490.422984
100.0967950.88710.188768
11-0.017509-0.16050.436448
12-0.017821-0.16330.435325
13-0.213456-1.95640.026873
14-0.027493-0.2520.400836
15-0.028271-0.25910.398094
160.0922090.84510.200224
17-0.023497-0.21540.415006
18-0.024063-0.22050.412994
19-0.015532-0.14230.443573



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')