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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 20 Dec 2010 17:36:06 +0000

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/2010/Dec/20/t1292866604oyuyrexxitegs1i.htm/, Retrieved Fri, 03 May 2024 23:18:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113027, Retrieved Fri, 03 May 2024 23:18:52 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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

-     [] [correlation betwe...] [1970-01-01 00:00:00] [1df589bc3feb749f1946d8c1ee38b85f]
- RM D  [Pearson Correlation] [correlation betwe...] [2010-12-20 15:44:31] [1df589bc3feb749f1946d8c1ee38b85f]
- RMPD    [Variance Reduction Matrix] [Paper: VRM] [2010-12-20 16:52:21] [1df589bc3feb749f1946d8c1ee38b85f]
- RMP         [(Partial) Autocorrelation Function] [paper: autocorrel...] [2010-12-20 17:36:06] [36a5183bc8f6439b2481209b0fbe6bda] [Current]
- RMPD          [] [paper] [-0001-11-30 00:00:00] [83d13bd1a1b3e64dad996f4022b3c29f] 

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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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113027&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113027&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.821266	8.3349	0
2	0.786684	7.984	0
3	0.734426	7.4536	0
4	0.802977	8.1493	0
5	0.574073	5.8262	0
6	0.494535	5.019	1e-06
7	0.41194	4.1807	3.1e-05
8	0.448532	4.5521	7e-06
9	0.20743	2.1052	0.018854
10	0.12487	1.2673	0.103954
11	0.0436	0.4425	0.329531
12	0.080259	0.8145	0.208609
13	-0.144859	-1.4702	0.072284
14	-0.206267	-2.0934	0.019386
15	-0.263845	-2.6777	0.004314
16	-0.20555	-2.0861	0.01972
17	-0.394953	-4.0083	5.8e-05
18	-0.421865	-4.2815	2.1e-05
19	-0.440438	-4.47	1e-05
20	-0.350253	-3.5547	0.000287

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.821266 & 8.3349 & 0 \tabularnewline
2 & 0.786684 & 7.984 & 0 \tabularnewline
3 & 0.734426 & 7.4536 & 0 \tabularnewline
4 & 0.802977 & 8.1493 & 0 \tabularnewline
5 & 0.574073 & 5.8262 & 0 \tabularnewline
6 & 0.494535 & 5.019 & 1e-06 \tabularnewline
7 & 0.41194 & 4.1807 & 3.1e-05 \tabularnewline
8 & 0.448532 & 4.5521 & 7e-06 \tabularnewline
9 & 0.20743 & 2.1052 & 0.018854 \tabularnewline
10 & 0.12487 & 1.2673 & 0.103954 \tabularnewline
11 & 0.0436 & 0.4425 & 0.329531 \tabularnewline
12 & 0.080259 & 0.8145 & 0.208609 \tabularnewline
13 & -0.144859 & -1.4702 & 0.072284 \tabularnewline
14 & -0.206267 & -2.0934 & 0.019386 \tabularnewline
15 & -0.263845 & -2.6777 & 0.004314 \tabularnewline
16 & -0.20555 & -2.0861 & 0.01972 \tabularnewline
17 & -0.394953 & -4.0083 & 5.8e-05 \tabularnewline
18 & -0.421865 & -4.2815 & 2.1e-05 \tabularnewline
19 & -0.440438 & -4.47 & 1e-05 \tabularnewline
20 & -0.350253 & -3.5547 & 0.000287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113027&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]0.821266[/C][C]8.3349[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.786684[/C][C]7.984[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.734426[/C][C]7.4536[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.802977[/C][C]8.1493[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.574073[/C][C]5.8262[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.494535[/C][C]5.019[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.41194[/C][C]4.1807[/C][C]3.1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.448532[/C][C]4.5521[/C][C]7e-06[/C][/ROW]
[ROW][C]9[/C][C]0.20743[/C][C]2.1052[/C][C]0.018854[/C][/ROW]
[ROW][C]10[/C][C]0.12487[/C][C]1.2673[/C][C]0.103954[/C][/ROW]
[ROW][C]11[/C][C]0.0436[/C][C]0.4425[/C][C]0.329531[/C][/ROW]
[ROW][C]12[/C][C]0.080259[/C][C]0.8145[/C][C]0.208609[/C][/ROW]
[ROW][C]13[/C][C]-0.144859[/C][C]-1.4702[/C][C]0.072284[/C][/ROW]
[ROW][C]14[/C][C]-0.206267[/C][C]-2.0934[/C][C]0.019386[/C][/ROW]
[ROW][C]15[/C][C]-0.263845[/C][C]-2.6777[/C][C]0.004314[/C][/ROW]
[ROW][C]16[/C][C]-0.20555[/C][C]-2.0861[/C][C]0.01972[/C][/ROW]
[ROW][C]17[/C][C]-0.394953[/C][C]-4.0083[/C][C]5.8e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.421865[/C][C]-4.2815[/C][C]2.1e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.440438[/C][C]-4.47[/C][C]1e-05[/C][/ROW]
[ROW][C]20[/C][C]-0.350253[/C][C]-3.5547[/C][C]0.000287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113027&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	0.821266	8.3349	0
2	0.786684	7.984	0
3	0.734426	7.4536	0
4	0.802977	8.1493	0
5	0.574073	5.8262	0
6	0.494535	5.019	1e-06
7	0.41194	4.1807	3.1e-05
8	0.448532	4.5521	7e-06
9	0.20743	2.1052	0.018854
10	0.12487	1.2673	0.103954
11	0.0436	0.4425	0.329531
12	0.080259	0.8145	0.208609
13	-0.144859	-1.4702	0.072284
14	-0.206267	-2.0934	0.019386
15	-0.263845	-2.6777	0.004314
16	-0.20555	-2.0861	0.01972
17	-0.394953	-4.0083	5.8e-05
18	-0.421865	-4.2815	2.1e-05
19	-0.440438	-4.47	1e-05
20	-0.350253	-3.5547	0.000287

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.821266	8.3349	0
2	0.344693	3.4983	0.000346
3	0.097482	0.9893	0.162409
4	0.430977	4.3739	1.5e-05
5	-0.773918	-7.8544	0
6	-0.1393	-1.4137	0.080226
7	0.08106	0.8227	0.206298
8	0.202024	2.0503	0.021436
9	-0.275287	-2.7939	0.003106
10	-0.110712	-1.1236	0.131896
11	-0.038524	-0.391	0.34831
12	0.119847	1.2163	0.113323
13	-0.100788	-1.0229	0.154379
14	-0.085299	-0.8657	0.194337
15	-0.060046	-0.6094	0.271801
16	0.082292	0.8352	0.202777
17	-0.006061	-0.0615	0.475533
18	-0.086375	-0.8766	0.191369
19	-0.021076	-0.2139	0.415525
20	0.044088	0.4474	0.327747

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.821266 & 8.3349 & 0 \tabularnewline
2 & 0.344693 & 3.4983 & 0.000346 \tabularnewline
3 & 0.097482 & 0.9893 & 0.162409 \tabularnewline
4 & 0.430977 & 4.3739 & 1.5e-05 \tabularnewline
5 & -0.773918 & -7.8544 & 0 \tabularnewline
6 & -0.1393 & -1.4137 & 0.080226 \tabularnewline
7 & 0.08106 & 0.8227 & 0.206298 \tabularnewline
8 & 0.202024 & 2.0503 & 0.021436 \tabularnewline
9 & -0.275287 & -2.7939 & 0.003106 \tabularnewline
10 & -0.110712 & -1.1236 & 0.131896 \tabularnewline
11 & -0.038524 & -0.391 & 0.34831 \tabularnewline
12 & 0.119847 & 1.2163 & 0.113323 \tabularnewline
13 & -0.100788 & -1.0229 & 0.154379 \tabularnewline
14 & -0.085299 & -0.8657 & 0.194337 \tabularnewline
15 & -0.060046 & -0.6094 & 0.271801 \tabularnewline
16 & 0.082292 & 0.8352 & 0.202777 \tabularnewline
17 & -0.006061 & -0.0615 & 0.475533 \tabularnewline
18 & -0.086375 & -0.8766 & 0.191369 \tabularnewline
19 & -0.021076 & -0.2139 & 0.415525 \tabularnewline
20 & 0.044088 & 0.4474 & 0.327747 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113027&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]0.821266[/C][C]8.3349[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.344693[/C][C]3.4983[/C][C]0.000346[/C][/ROW]
[ROW][C]3[/C][C]0.097482[/C][C]0.9893[/C][C]0.162409[/C][/ROW]
[ROW][C]4[/C][C]0.430977[/C][C]4.3739[/C][C]1.5e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.773918[/C][C]-7.8544[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.1393[/C][C]-1.4137[/C][C]0.080226[/C][/ROW]
[ROW][C]7[/C][C]0.08106[/C][C]0.8227[/C][C]0.206298[/C][/ROW]
[ROW][C]8[/C][C]0.202024[/C][C]2.0503[/C][C]0.021436[/C][/ROW]
[ROW][C]9[/C][C]-0.275287[/C][C]-2.7939[/C][C]0.003106[/C][/ROW]
[ROW][C]10[/C][C]-0.110712[/C][C]-1.1236[/C][C]0.131896[/C][/ROW]
[ROW][C]11[/C][C]-0.038524[/C][C]-0.391[/C][C]0.34831[/C][/ROW]
[ROW][C]12[/C][C]0.119847[/C][C]1.2163[/C][C]0.113323[/C][/ROW]
[ROW][C]13[/C][C]-0.100788[/C][C]-1.0229[/C][C]0.154379[/C][/ROW]
[ROW][C]14[/C][C]-0.085299[/C][C]-0.8657[/C][C]0.194337[/C][/ROW]
[ROW][C]15[/C][C]-0.060046[/C][C]-0.6094[/C][C]0.271801[/C][/ROW]
[ROW][C]16[/C][C]0.082292[/C][C]0.8352[/C][C]0.202777[/C][/ROW]
[ROW][C]17[/C][C]-0.006061[/C][C]-0.0615[/C][C]0.475533[/C][/ROW]
[ROW][C]18[/C][C]-0.086375[/C][C]-0.8766[/C][C]0.191369[/C][/ROW]
[ROW][C]19[/C][C]-0.021076[/C][C]-0.2139[/C][C]0.415525[/C][/ROW]
[ROW][C]20[/C][C]0.044088[/C][C]0.4474[/C][C]0.327747[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113027&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113027&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	0.821266	8.3349	0
2	0.344693	3.4983	0.000346
3	0.097482	0.9893	0.162409
4	0.430977	4.3739	1.5e-05
5	-0.773918	-7.8544	0
6	-0.1393	-1.4137	0.080226
7	0.08106	0.8227	0.206298
8	0.202024	2.0503	0.021436
9	-0.275287	-2.7939	0.003106
10	-0.110712	-1.1236	0.131896
11	-0.038524	-0.391	0.34831
12	0.119847	1.2163	0.113323
13	-0.100788	-1.0229	0.154379
14	-0.085299	-0.8657	0.194337
15	-0.060046	-0.6094	0.271801
16	0.082292	0.8352	0.202777
17	-0.006061	-0.0615	0.475533
18	-0.086375	-0.8766	0.191369
19	-0.021076	-0.2139	0.415525
20	0.044088	0.4474	0.327747

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code