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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSat, 17 Dec 2011 16:02:09 -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/17/t1324155852vm0upb3fm2bu95r.htm/, Retrieved Fri, 29 Mar 2024 06:11:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156584, Retrieved Fri, 29 Mar 2024 06:11:31 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:13:00] [b98453cac15ba1066b407e146608df68]
- RMPD    [Spectral Analysis] [wS9: spectral ana...] [2011-12-05 13:26:10] [17977ad44e8eb3a4dcd5a9173c81cab3]
- RMP         [(Partial) Autocorrelation Function] [Paper: ACF] [2011-12-17 21:02:09] [dfccbb29b87008a80f95a64515f2b3fe] [Current]
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Dataseries X:
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156584&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156584&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'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.0118710.0920.46352
20.0388380.30080.382289
3-0.109458-0.84790.199943
4-0.051329-0.39760.34617
5-0.100997-0.78230.218551
6-0.053604-0.41520.339734
70.0281010.21770.414214
80.033530.25970.397983
9-0.006097-0.04720.481245
100.0649770.50330.308294
110.1569071.21540.114488
12-0.377489-2.9240.002435
13-0.09635-0.74630.229193
14-0.016226-0.12570.450201
150.0168480.13050.448301
16-0.034247-0.26530.395853
17-0.041658-0.32270.37403
180.0465180.36030.359933

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.011871 & 0.092 & 0.46352 \tabularnewline
2 & 0.038838 & 0.3008 & 0.382289 \tabularnewline
3 & -0.109458 & -0.8479 & 0.199943 \tabularnewline
4 & -0.051329 & -0.3976 & 0.34617 \tabularnewline
5 & -0.100997 & -0.7823 & 0.218551 \tabularnewline
6 & -0.053604 & -0.4152 & 0.339734 \tabularnewline
7 & 0.028101 & 0.2177 & 0.414214 \tabularnewline
8 & 0.03353 & 0.2597 & 0.397983 \tabularnewline
9 & -0.006097 & -0.0472 & 0.481245 \tabularnewline
10 & 0.064977 & 0.5033 & 0.308294 \tabularnewline
11 & 0.156907 & 1.2154 & 0.114488 \tabularnewline
12 & -0.377489 & -2.924 & 0.002435 \tabularnewline
13 & -0.09635 & -0.7463 & 0.229193 \tabularnewline
14 & -0.016226 & -0.1257 & 0.450201 \tabularnewline
15 & 0.016848 & 0.1305 & 0.448301 \tabularnewline
16 & -0.034247 & -0.2653 & 0.395853 \tabularnewline
17 & -0.041658 & -0.3227 & 0.37403 \tabularnewline
18 & 0.046518 & 0.3603 & 0.359933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156584&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]0.011871[/C][C]0.092[/C][C]0.46352[/C][/ROW]
[ROW][C]2[/C][C]0.038838[/C][C]0.3008[/C][C]0.382289[/C][/ROW]
[ROW][C]3[/C][C]-0.109458[/C][C]-0.8479[/C][C]0.199943[/C][/ROW]
[ROW][C]4[/C][C]-0.051329[/C][C]-0.3976[/C][C]0.34617[/C][/ROW]
[ROW][C]5[/C][C]-0.100997[/C][C]-0.7823[/C][C]0.218551[/C][/ROW]
[ROW][C]6[/C][C]-0.053604[/C][C]-0.4152[/C][C]0.339734[/C][/ROW]
[ROW][C]7[/C][C]0.028101[/C][C]0.2177[/C][C]0.414214[/C][/ROW]
[ROW][C]8[/C][C]0.03353[/C][C]0.2597[/C][C]0.397983[/C][/ROW]
[ROW][C]9[/C][C]-0.006097[/C][C]-0.0472[/C][C]0.481245[/C][/ROW]
[ROW][C]10[/C][C]0.064977[/C][C]0.5033[/C][C]0.308294[/C][/ROW]
[ROW][C]11[/C][C]0.156907[/C][C]1.2154[/C][C]0.114488[/C][/ROW]
[ROW][C]12[/C][C]-0.377489[/C][C]-2.924[/C][C]0.002435[/C][/ROW]
[ROW][C]13[/C][C]-0.09635[/C][C]-0.7463[/C][C]0.229193[/C][/ROW]
[ROW][C]14[/C][C]-0.016226[/C][C]-0.1257[/C][C]0.450201[/C][/ROW]
[ROW][C]15[/C][C]0.016848[/C][C]0.1305[/C][C]0.448301[/C][/ROW]
[ROW][C]16[/C][C]-0.034247[/C][C]-0.2653[/C][C]0.395853[/C][/ROW]
[ROW][C]17[/C][C]-0.041658[/C][C]-0.3227[/C][C]0.37403[/C][/ROW]
[ROW][C]18[/C][C]0.046518[/C][C]0.3603[/C][C]0.359933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156584&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
10.0118710.0920.46352
20.0388380.30080.382289
3-0.109458-0.84790.199943
4-0.051329-0.39760.34617
5-0.100997-0.78230.218551
6-0.053604-0.41520.339734
70.0281010.21770.414214
80.033530.25970.397983
9-0.006097-0.04720.481245
100.0649770.50330.308294
110.1569071.21540.114488
12-0.377489-2.9240.002435
13-0.09635-0.74630.229193
14-0.016226-0.12570.450201
150.0168480.13050.448301
16-0.034247-0.26530.395853
17-0.041658-0.32270.37403
180.0465180.36030.359933







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.0118710.0920.46352
20.0387030.29980.382687
3-0.110542-0.85630.197632
4-0.050551-0.39160.348382
5-0.092534-0.71680.238149
6-0.061508-0.47640.317745
70.0250320.19390.423457
80.0139560.10810.457137
9-0.030892-0.23930.405848
100.0561540.4350.332573
110.1597281.23720.110408
12-0.404385-3.13240.00134
13-0.085833-0.66490.254343
140.0852240.66010.255844
15-0.058001-0.44930.327428
16-0.078982-0.61180.271493
17-0.101249-0.78430.217984
18-0.014741-0.11420.454737

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.011871 & 0.092 & 0.46352 \tabularnewline
2 & 0.038703 & 0.2998 & 0.382687 \tabularnewline
3 & -0.110542 & -0.8563 & 0.197632 \tabularnewline
4 & -0.050551 & -0.3916 & 0.348382 \tabularnewline
5 & -0.092534 & -0.7168 & 0.238149 \tabularnewline
6 & -0.061508 & -0.4764 & 0.317745 \tabularnewline
7 & 0.025032 & 0.1939 & 0.423457 \tabularnewline
8 & 0.013956 & 0.1081 & 0.457137 \tabularnewline
9 & -0.030892 & -0.2393 & 0.405848 \tabularnewline
10 & 0.056154 & 0.435 & 0.332573 \tabularnewline
11 & 0.159728 & 1.2372 & 0.110408 \tabularnewline
12 & -0.404385 & -3.1324 & 0.00134 \tabularnewline
13 & -0.085833 & -0.6649 & 0.254343 \tabularnewline
14 & 0.085224 & 0.6601 & 0.255844 \tabularnewline
15 & -0.058001 & -0.4493 & 0.327428 \tabularnewline
16 & -0.078982 & -0.6118 & 0.271493 \tabularnewline
17 & -0.101249 & -0.7843 & 0.217984 \tabularnewline
18 & -0.014741 & -0.1142 & 0.454737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156584&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]0.011871[/C][C]0.092[/C][C]0.46352[/C][/ROW]
[ROW][C]2[/C][C]0.038703[/C][C]0.2998[/C][C]0.382687[/C][/ROW]
[ROW][C]3[/C][C]-0.110542[/C][C]-0.8563[/C][C]0.197632[/C][/ROW]
[ROW][C]4[/C][C]-0.050551[/C][C]-0.3916[/C][C]0.348382[/C][/ROW]
[ROW][C]5[/C][C]-0.092534[/C][C]-0.7168[/C][C]0.238149[/C][/ROW]
[ROW][C]6[/C][C]-0.061508[/C][C]-0.4764[/C][C]0.317745[/C][/ROW]
[ROW][C]7[/C][C]0.025032[/C][C]0.1939[/C][C]0.423457[/C][/ROW]
[ROW][C]8[/C][C]0.013956[/C][C]0.1081[/C][C]0.457137[/C][/ROW]
[ROW][C]9[/C][C]-0.030892[/C][C]-0.2393[/C][C]0.405848[/C][/ROW]
[ROW][C]10[/C][C]0.056154[/C][C]0.435[/C][C]0.332573[/C][/ROW]
[ROW][C]11[/C][C]0.159728[/C][C]1.2372[/C][C]0.110408[/C][/ROW]
[ROW][C]12[/C][C]-0.404385[/C][C]-3.1324[/C][C]0.00134[/C][/ROW]
[ROW][C]13[/C][C]-0.085833[/C][C]-0.6649[/C][C]0.254343[/C][/ROW]
[ROW][C]14[/C][C]0.085224[/C][C]0.6601[/C][C]0.255844[/C][/ROW]
[ROW][C]15[/C][C]-0.058001[/C][C]-0.4493[/C][C]0.327428[/C][/ROW]
[ROW][C]16[/C][C]-0.078982[/C][C]-0.6118[/C][C]0.271493[/C][/ROW]
[ROW][C]17[/C][C]-0.101249[/C][C]-0.7843[/C][C]0.217984[/C][/ROW]
[ROW][C]18[/C][C]-0.014741[/C][C]-0.1142[/C][C]0.454737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156584&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156584&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
10.0118710.0920.46352
20.0387030.29980.382687
3-0.110542-0.85630.197632
4-0.050551-0.39160.348382
5-0.092534-0.71680.238149
6-0.061508-0.47640.317745
70.0250320.19390.423457
80.0139560.10810.457137
9-0.030892-0.23930.405848
100.0561540.4350.332573
110.1597281.23720.110408
12-0.404385-3.13240.00134
13-0.085833-0.66490.254343
140.0852240.66010.255844
15-0.058001-0.44930.327428
16-0.078982-0.61180.271493
17-0.101249-0.78430.217984
18-0.014741-0.11420.454737



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)
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')