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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 12 Dec 2009 08:50:40 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/12/t1260633290kkv2eejgvy7lefx.htm/, Retrieved Mon, 29 Apr 2024 08:59:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67025, Retrieved Mon, 29 Apr 2024 08:59:41 +0000

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No (this computation is public)

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Estimated Impact

114

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [ACF] [2009-12-12 15:50:40] [5d37783481a916b2505b66314b556267] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67025&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67025&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67025&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.694937	5.4276	1e-06
2	0.612527	4.784	6e-06
3	0.657186	5.1328	2e-06
4	0.509555	3.9798	9.3e-05
5	0.454088	3.5465	0.000378
6	0.460958	3.6002	0.00032
7	0.315243	2.4621	0.008326
8	0.296733	2.3176	0.011922
9	0.28147	2.1983	0.015864
10	0.162079	1.2659	0.105185
11	0.184458	1.4407	0.077396
12	0.281253	2.1967	0.015927
13	0.106223	0.8296	0.204991
14	0.068182	0.5325	0.29815
15	0.100641	0.786	0.217447
16	0.061395	0.4795	0.316646
17	0.030127	0.2353	0.407381

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.694937 & 5.4276 & 1e-06 \tabularnewline
2 & 0.612527 & 4.784 & 6e-06 \tabularnewline
3 & 0.657186 & 5.1328 & 2e-06 \tabularnewline
4 & 0.509555 & 3.9798 & 9.3e-05 \tabularnewline
5 & 0.454088 & 3.5465 & 0.000378 \tabularnewline
6 & 0.460958 & 3.6002 & 0.00032 \tabularnewline
7 & 0.315243 & 2.4621 & 0.008326 \tabularnewline
8 & 0.296733 & 2.3176 & 0.011922 \tabularnewline
9 & 0.28147 & 2.1983 & 0.015864 \tabularnewline
10 & 0.162079 & 1.2659 & 0.105185 \tabularnewline
11 & 0.184458 & 1.4407 & 0.077396 \tabularnewline
12 & 0.281253 & 2.1967 & 0.015927 \tabularnewline
13 & 0.106223 & 0.8296 & 0.204991 \tabularnewline
14 & 0.068182 & 0.5325 & 0.29815 \tabularnewline
15 & 0.100641 & 0.786 & 0.217447 \tabularnewline
16 & 0.061395 & 0.4795 & 0.316646 \tabularnewline
17 & 0.030127 & 0.2353 & 0.407381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67025&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]0.694937[/C][C]5.4276[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.612527[/C][C]4.784[/C][C]6e-06[/C][/ROW]
[ROW][C]3[/C][C]0.657186[/C][C]5.1328[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.509555[/C][C]3.9798[/C][C]9.3e-05[/C][/ROW]
[ROW][C]5[/C][C]0.454088[/C][C]3.5465[/C][C]0.000378[/C][/ROW]
[ROW][C]6[/C][C]0.460958[/C][C]3.6002[/C][C]0.00032[/C][/ROW]
[ROW][C]7[/C][C]0.315243[/C][C]2.4621[/C][C]0.008326[/C][/ROW]
[ROW][C]8[/C][C]0.296733[/C][C]2.3176[/C][C]0.011922[/C][/ROW]
[ROW][C]9[/C][C]0.28147[/C][C]2.1983[/C][C]0.015864[/C][/ROW]
[ROW][C]10[/C][C]0.162079[/C][C]1.2659[/C][C]0.105185[/C][/ROW]
[ROW][C]11[/C][C]0.184458[/C][C]1.4407[/C][C]0.077396[/C][/ROW]
[ROW][C]12[/C][C]0.281253[/C][C]2.1967[/C][C]0.015927[/C][/ROW]
[ROW][C]13[/C][C]0.106223[/C][C]0.8296[/C][C]0.204991[/C][/ROW]
[ROW][C]14[/C][C]0.068182[/C][C]0.5325[/C][C]0.29815[/C][/ROW]
[ROW][C]15[/C][C]0.100641[/C][C]0.786[/C][C]0.217447[/C][/ROW]
[ROW][C]16[/C][C]0.061395[/C][C]0.4795[/C][C]0.316646[/C][/ROW]
[ROW][C]17[/C][C]0.030127[/C][C]0.2353[/C][C]0.407381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67025&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67025&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	0.694937	5.4276	1e-06
2	0.612527	4.784	6e-06
3	0.657186	5.1328	2e-06
4	0.509555	3.9798	9.3e-05
5	0.454088	3.5465	0.000378
6	0.460958	3.6002	0.00032
7	0.315243	2.4621	0.008326
8	0.296733	2.3176	0.011922
9	0.28147	2.1983	0.015864
10	0.162079	1.2659	0.105185
11	0.184458	1.4407	0.077396
12	0.281253	2.1967	0.015927
13	0.106223	0.8296	0.204991
14	0.068182	0.5325	0.29815
15	0.100641	0.786	0.217447
16	0.061395	0.4795	0.316646
17	0.030127	0.2353	0.407381

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.694937	5.4276	1e-06
2	0.250627	1.9575	0.027436
3	0.338501	2.6438	0.005204
4	-0.134498	-1.0505	0.148825
5	0.008404	0.0656	0.473942
6	0.045198	0.353	0.362649
7	-0.164779	-1.287	0.101485
8	0.049209	0.3843	0.351034
9	-0.023451	-0.1832	0.427642
10	-0.082183	-0.6419	0.261682
11	0.09071	0.7085	0.240677
12	0.266998	2.0853	0.020616
13	-0.255223	-1.9934	0.02535
14	-0.126947	-0.9915	0.162682
15	-0.034946	-0.2729	0.392912
16	0.16211	1.2661	0.105142
17	-0.072238	-0.5642	0.287346

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.694937 & 5.4276 & 1e-06 \tabularnewline
2 & 0.250627 & 1.9575 & 0.027436 \tabularnewline
3 & 0.338501 & 2.6438 & 0.005204 \tabularnewline
4 & -0.134498 & -1.0505 & 0.148825 \tabularnewline
5 & 0.008404 & 0.0656 & 0.473942 \tabularnewline
6 & 0.045198 & 0.353 & 0.362649 \tabularnewline
7 & -0.164779 & -1.287 & 0.101485 \tabularnewline
8 & 0.049209 & 0.3843 & 0.351034 \tabularnewline
9 & -0.023451 & -0.1832 & 0.427642 \tabularnewline
10 & -0.082183 & -0.6419 & 0.261682 \tabularnewline
11 & 0.09071 & 0.7085 & 0.240677 \tabularnewline
12 & 0.266998 & 2.0853 & 0.020616 \tabularnewline
13 & -0.255223 & -1.9934 & 0.02535 \tabularnewline
14 & -0.126947 & -0.9915 & 0.162682 \tabularnewline
15 & -0.034946 & -0.2729 & 0.392912 \tabularnewline
16 & 0.16211 & 1.2661 & 0.105142 \tabularnewline
17 & -0.072238 & -0.5642 & 0.287346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67025&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]0.694937[/C][C]5.4276[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.250627[/C][C]1.9575[/C][C]0.027436[/C][/ROW]
[ROW][C]3[/C][C]0.338501[/C][C]2.6438[/C][C]0.005204[/C][/ROW]
[ROW][C]4[/C][C]-0.134498[/C][C]-1.0505[/C][C]0.148825[/C][/ROW]
[ROW][C]5[/C][C]0.008404[/C][C]0.0656[/C][C]0.473942[/C][/ROW]
[ROW][C]6[/C][C]0.045198[/C][C]0.353[/C][C]0.362649[/C][/ROW]
[ROW][C]7[/C][C]-0.164779[/C][C]-1.287[/C][C]0.101485[/C][/ROW]
[ROW][C]8[/C][C]0.049209[/C][C]0.3843[/C][C]0.351034[/C][/ROW]
[ROW][C]9[/C][C]-0.023451[/C][C]-0.1832[/C][C]0.427642[/C][/ROW]
[ROW][C]10[/C][C]-0.082183[/C][C]-0.6419[/C][C]0.261682[/C][/ROW]
[ROW][C]11[/C][C]0.09071[/C][C]0.7085[/C][C]0.240677[/C][/ROW]
[ROW][C]12[/C][C]0.266998[/C][C]2.0853[/C][C]0.020616[/C][/ROW]
[ROW][C]13[/C][C]-0.255223[/C][C]-1.9934[/C][C]0.02535[/C][/ROW]
[ROW][C]14[/C][C]-0.126947[/C][C]-0.9915[/C][C]0.162682[/C][/ROW]
[ROW][C]15[/C][C]-0.034946[/C][C]-0.2729[/C][C]0.392912[/C][/ROW]
[ROW][C]16[/C][C]0.16211[/C][C]1.2661[/C][C]0.105142[/C][/ROW]
[ROW][C]17[/C][C]-0.072238[/C][C]-0.5642[/C][C]0.287346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67025&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67025&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	0.694937	5.4276	1e-06
2	0.250627	1.9575	0.027436
3	0.338501	2.6438	0.005204
4	-0.134498	-1.0505	0.148825
5	0.008404	0.0656	0.473942
6	0.045198	0.353	0.362649
7	-0.164779	-1.287	0.101485
8	0.049209	0.3843	0.351034
9	-0.023451	-0.1832	0.427642
10	-0.082183	-0.6419	0.261682
11	0.09071	0.7085	0.240677
12	0.266998	2.0853	0.020616
13	-0.255223	-1.9934	0.02535
14	-0.126947	-0.9915	0.162682
15	-0.034946	-0.2729	0.392912
16	0.16211	1.2661	0.105142
17	-0.072238	-0.5642	0.287346

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code