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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 16 Dec 2014 13:59:28 +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/2014/Dec/16/t14187383820hvu5ab9u2ph81s.htm/, Retrieved Fri, 01 Nov 2024 00:58:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=269574, Retrieved Fri, 01 Nov 2024 00:58:06 +0000

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

-       [(Partial) Autocorrelation Function] [ACF ex] [2014-12-16 13:59:28] [9636d26fd774798d33054b538c301d75] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269574&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269574&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269574&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.729554	8.3819	0
2	0.385873	4.4333	1e-05
3	0.000633	0.0073	0.497103
4	-0.433131	-4.9763	1e-06
5	-0.728574	-8.3707	0
6	-0.813002	-9.3407	0
7	-0.72075	-8.2808	0
8	-0.388618	-4.4649	9e-06
9	0.03083	0.3542	0.361875
10	0.366343	4.209	2.4e-05
11	0.687473	7.8985	0
12	0.856625	9.8419	0
13	0.665179	7.6423	0
14	0.359634	4.1319	3.2e-05
15	-0.012164	-0.1397	0.444536
16	-0.389613	-4.4763	8e-06
17	-0.642634	-7.3833	0
18	-0.738432	-8.4839	0
19	-0.653104	-7.5036	0
20	-0.345582	-3.9704	5.9e-05
21	0.007144	0.0821	0.467353

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.729554 & 8.3819 & 0 \tabularnewline
2 & 0.385873 & 4.4333 & 1e-05 \tabularnewline
3 & 0.000633 & 0.0073 & 0.497103 \tabularnewline
4 & -0.433131 & -4.9763 & 1e-06 \tabularnewline
5 & -0.728574 & -8.3707 & 0 \tabularnewline
6 & -0.813002 & -9.3407 & 0 \tabularnewline
7 & -0.72075 & -8.2808 & 0 \tabularnewline
8 & -0.388618 & -4.4649 & 9e-06 \tabularnewline
9 & 0.03083 & 0.3542 & 0.361875 \tabularnewline
10 & 0.366343 & 4.209 & 2.4e-05 \tabularnewline
11 & 0.687473 & 7.8985 & 0 \tabularnewline
12 & 0.856625 & 9.8419 & 0 \tabularnewline
13 & 0.665179 & 7.6423 & 0 \tabularnewline
14 & 0.359634 & 4.1319 & 3.2e-05 \tabularnewline
15 & -0.012164 & -0.1397 & 0.444536 \tabularnewline
16 & -0.389613 & -4.4763 & 8e-06 \tabularnewline
17 & -0.642634 & -7.3833 & 0 \tabularnewline
18 & -0.738432 & -8.4839 & 0 \tabularnewline
19 & -0.653104 & -7.5036 & 0 \tabularnewline
20 & -0.345582 & -3.9704 & 5.9e-05 \tabularnewline
21 & 0.007144 & 0.0821 & 0.467353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269574&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]0.729554[/C][C]8.3819[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.385873[/C][C]4.4333[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.000633[/C][C]0.0073[/C][C]0.497103[/C][/ROW]
[ROW][C]4[/C][C]-0.433131[/C][C]-4.9763[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]-0.728574[/C][C]-8.3707[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.813002[/C][C]-9.3407[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.72075[/C][C]-8.2808[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.388618[/C][C]-4.4649[/C][C]9e-06[/C][/ROW]
[ROW][C]9[/C][C]0.03083[/C][C]0.3542[/C][C]0.361875[/C][/ROW]
[ROW][C]10[/C][C]0.366343[/C][C]4.209[/C][C]2.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.687473[/C][C]7.8985[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.856625[/C][C]9.8419[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.665179[/C][C]7.6423[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.359634[/C][C]4.1319[/C][C]3.2e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.012164[/C][C]-0.1397[/C][C]0.444536[/C][/ROW]
[ROW][C]16[/C][C]-0.389613[/C][C]-4.4763[/C][C]8e-06[/C][/ROW]
[ROW][C]17[/C][C]-0.642634[/C][C]-7.3833[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.738432[/C][C]-8.4839[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.653104[/C][C]-7.5036[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.345582[/C][C]-3.9704[/C][C]5.9e-05[/C][/ROW]
[ROW][C]21[/C][C]0.007144[/C][C]0.0821[/C][C]0.467353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269574&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269574&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	0.729554	8.3819	0
2	0.385873	4.4333	1e-05
3	0.000633	0.0073	0.497103
4	-0.433131	-4.9763	1e-06
5	-0.728574	-8.3707	0
6	-0.813002	-9.3407	0
7	-0.72075	-8.2808	0
8	-0.388618	-4.4649	9e-06
9	0.03083	0.3542	0.361875
10	0.366343	4.209	2.4e-05
11	0.687473	7.8985	0
12	0.856625	9.8419	0
13	0.665179	7.6423	0
14	0.359634	4.1319	3.2e-05
15	-0.012164	-0.1397	0.444536
16	-0.389613	-4.4763	8e-06
17	-0.642634	-7.3833	0
18	-0.738432	-8.4839	0
19	-0.653104	-7.5036	0
20	-0.345582	-3.9704	5.9e-05
21	0.007144	0.0821	0.467353

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.729554	8.3819	0
2	-0.312935	-3.5953	0.000228
3	-0.333398	-3.8304	9.8e-05
4	-0.514378	-5.9098	0
5	-0.357729	-4.11	3.5e-05
6	-0.26746	-3.0729	0.001288
7	-0.312997	-3.5961	0.000228
8	-0.020074	-0.2306	0.40898
9	-0.008544	-0.0982	0.460977
10	-0.213708	-2.4553	0.007689
11	0.141314	1.6236	0.053426
12	0.351783	4.0417	4.5e-05
13	-0.172154	-1.9779	0.025012
14	-0.066494	-0.764	0.223126
15	0.027936	0.321	0.374374
16	0.157988	1.8151	0.035886
17	0.071028	0.8161	0.20797
18	0.004341	0.0499	0.48015
19	0.027255	0.3131	0.377337
20	0.016092	0.1849	0.4268
21	-0.095615	-1.0985	0.136986

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.729554 & 8.3819 & 0 \tabularnewline
2 & -0.312935 & -3.5953 & 0.000228 \tabularnewline
3 & -0.333398 & -3.8304 & 9.8e-05 \tabularnewline
4 & -0.514378 & -5.9098 & 0 \tabularnewline
5 & -0.357729 & -4.11 & 3.5e-05 \tabularnewline
6 & -0.26746 & -3.0729 & 0.001288 \tabularnewline
7 & -0.312997 & -3.5961 & 0.000228 \tabularnewline
8 & -0.020074 & -0.2306 & 0.40898 \tabularnewline
9 & -0.008544 & -0.0982 & 0.460977 \tabularnewline
10 & -0.213708 & -2.4553 & 0.007689 \tabularnewline
11 & 0.141314 & 1.6236 & 0.053426 \tabularnewline
12 & 0.351783 & 4.0417 & 4.5e-05 \tabularnewline
13 & -0.172154 & -1.9779 & 0.025012 \tabularnewline
14 & -0.066494 & -0.764 & 0.223126 \tabularnewline
15 & 0.027936 & 0.321 & 0.374374 \tabularnewline
16 & 0.157988 & 1.8151 & 0.035886 \tabularnewline
17 & 0.071028 & 0.8161 & 0.20797 \tabularnewline
18 & 0.004341 & 0.0499 & 0.48015 \tabularnewline
19 & 0.027255 & 0.3131 & 0.377337 \tabularnewline
20 & 0.016092 & 0.1849 & 0.4268 \tabularnewline
21 & -0.095615 & -1.0985 & 0.136986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=269574&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]0.729554[/C][C]8.3819[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.312935[/C][C]-3.5953[/C][C]0.000228[/C][/ROW]
[ROW][C]3[/C][C]-0.333398[/C][C]-3.8304[/C][C]9.8e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.514378[/C][C]-5.9098[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.357729[/C][C]-4.11[/C][C]3.5e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.26746[/C][C]-3.0729[/C][C]0.001288[/C][/ROW]
[ROW][C]7[/C][C]-0.312997[/C][C]-3.5961[/C][C]0.000228[/C][/ROW]
[ROW][C]8[/C][C]-0.020074[/C][C]-0.2306[/C][C]0.40898[/C][/ROW]
[ROW][C]9[/C][C]-0.008544[/C][C]-0.0982[/C][C]0.460977[/C][/ROW]
[ROW][C]10[/C][C]-0.213708[/C][C]-2.4553[/C][C]0.007689[/C][/ROW]
[ROW][C]11[/C][C]0.141314[/C][C]1.6236[/C][C]0.053426[/C][/ROW]
[ROW][C]12[/C][C]0.351783[/C][C]4.0417[/C][C]4.5e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.172154[/C][C]-1.9779[/C][C]0.025012[/C][/ROW]
[ROW][C]14[/C][C]-0.066494[/C][C]-0.764[/C][C]0.223126[/C][/ROW]
[ROW][C]15[/C][C]0.027936[/C][C]0.321[/C][C]0.374374[/C][/ROW]
[ROW][C]16[/C][C]0.157988[/C][C]1.8151[/C][C]0.035886[/C][/ROW]
[ROW][C]17[/C][C]0.071028[/C][C]0.8161[/C][C]0.20797[/C][/ROW]
[ROW][C]18[/C][C]0.004341[/C][C]0.0499[/C][C]0.48015[/C][/ROW]
[ROW][C]19[/C][C]0.027255[/C][C]0.3131[/C][C]0.377337[/C][/ROW]
[ROW][C]20[/C][C]0.016092[/C][C]0.1849[/C][C]0.4268[/C][/ROW]
[ROW][C]21[/C][C]-0.095615[/C][C]-1.0985[/C][C]0.136986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=269574&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=269574&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	0.729554	8.3819	0
2	-0.312935	-3.5953	0.000228
3	-0.333398	-3.8304	9.8e-05
4	-0.514378	-5.9098	0
5	-0.357729	-4.11	3.5e-05
6	-0.26746	-3.0729	0.001288
7	-0.312997	-3.5961	0.000228
8	-0.020074	-0.2306	0.40898
9	-0.008544	-0.0982	0.460977
10	-0.213708	-2.4553	0.007689
11	0.141314	1.6236	0.053426
12	0.351783	4.0417	4.5e-05
13	-0.172154	-1.9779	0.025012
14	-0.066494	-0.764	0.223126
15	0.027936	0.321	0.374374
16	0.157988	1.8151	0.035886
17	0.071028	0.8161	0.20797
18	0.004341	0.0499	0.48015
19	0.027255	0.3131	0.377337
20	0.016092	0.1849	0.4268
21	-0.095615	-1.0985	0.136986

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 = 12 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code