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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2009 07:04:19 -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/Nov/28/t1259417155wam7rjrdzn203z0.htm/, Retrieved Fri, 03 May 2024 13:49:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61467, Retrieved Fri, 03 May 2024 13:49:34 +0000

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No (this computation is public)

User-defined keywords

WS8 ACF originele reeks

Estimated Impact

136

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

-     [Univariate Data Series] [Populatieaangroei...] [2009-10-19 21:35:49] [9319fa3e1cb204243a6af248e59767c6]
- RMPD    [(Partial) Autocorrelation Function] [WS8 ACF originele...] [2009-11-28 14:04:19] [85defb7a20869746625978e6577e6e44] [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=61467&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=61467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61467&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	0.67738	6.2083	0
2	0.329861	3.0232	0.001658
3	-0.120316	-1.1027	0.13665
4	-0.449231	-4.1173	4.5e-05
5	-0.589608	-5.4038	0
6	-0.573575	-5.2569	1e-06
7	-0.544022	-4.986	2e-06
8	-0.36516	-3.3467	0.000612
9	-0.090119	-0.826	0.205584
10	0.264034	2.4199	0.008841
11	0.580169	5.3173	0
12	0.783687	7.1826	0
13	0.586548	5.3758	0
14	0.294838	2.7022	0.004166
15	-0.101209	-0.9276	0.178137
16	-0.374022	-3.428	0.000472
17	-0.492805	-4.5166	1e-05
18	-0.476958	-4.3714	1.8e-05
19	-0.447082	-4.0976	4.8e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.67738 & 6.2083 & 0 \tabularnewline
2 & 0.329861 & 3.0232 & 0.001658 \tabularnewline
3 & -0.120316 & -1.1027 & 0.13665 \tabularnewline
4 & -0.449231 & -4.1173 & 4.5e-05 \tabularnewline
5 & -0.589608 & -5.4038 & 0 \tabularnewline
6 & -0.573575 & -5.2569 & 1e-06 \tabularnewline
7 & -0.544022 & -4.986 & 2e-06 \tabularnewline
8 & -0.36516 & -3.3467 & 0.000612 \tabularnewline
9 & -0.090119 & -0.826 & 0.205584 \tabularnewline
10 & 0.264034 & 2.4199 & 0.008841 \tabularnewline
11 & 0.580169 & 5.3173 & 0 \tabularnewline
12 & 0.783687 & 7.1826 & 0 \tabularnewline
13 & 0.586548 & 5.3758 & 0 \tabularnewline
14 & 0.294838 & 2.7022 & 0.004166 \tabularnewline
15 & -0.101209 & -0.9276 & 0.178137 \tabularnewline
16 & -0.374022 & -3.428 & 0.000472 \tabularnewline
17 & -0.492805 & -4.5166 & 1e-05 \tabularnewline
18 & -0.476958 & -4.3714 & 1.8e-05 \tabularnewline
19 & -0.447082 & -4.0976 & 4.8e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61467&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]0.67738[/C][C]6.2083[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.329861[/C][C]3.0232[/C][C]0.001658[/C][/ROW]
[ROW][C]3[/C][C]-0.120316[/C][C]-1.1027[/C][C]0.13665[/C][/ROW]
[ROW][C]4[/C][C]-0.449231[/C][C]-4.1173[/C][C]4.5e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.589608[/C][C]-5.4038[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.573575[/C][C]-5.2569[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.544022[/C][C]-4.986[/C][C]2e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.36516[/C][C]-3.3467[/C][C]0.000612[/C][/ROW]
[ROW][C]9[/C][C]-0.090119[/C][C]-0.826[/C][C]0.205584[/C][/ROW]
[ROW][C]10[/C][C]0.264034[/C][C]2.4199[/C][C]0.008841[/C][/ROW]
[ROW][C]11[/C][C]0.580169[/C][C]5.3173[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.783687[/C][C]7.1826[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.586548[/C][C]5.3758[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.294838[/C][C]2.7022[/C][C]0.004166[/C][/ROW]
[ROW][C]15[/C][C]-0.101209[/C][C]-0.9276[/C][C]0.178137[/C][/ROW]
[ROW][C]16[/C][C]-0.374022[/C][C]-3.428[/C][C]0.000472[/C][/ROW]
[ROW][C]17[/C][C]-0.492805[/C][C]-4.5166[/C][C]1e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.476958[/C][C]-4.3714[/C][C]1.8e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.447082[/C][C]-4.0976[/C][C]4.8e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61467&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	0.67738	6.2083	0
2	0.329861	3.0232	0.001658
3	-0.120316	-1.1027	0.13665
4	-0.449231	-4.1173	4.5e-05
5	-0.589608	-5.4038	0
6	-0.573575	-5.2569	1e-06
7	-0.544022	-4.986	2e-06
8	-0.36516	-3.3467	0.000612
9	-0.090119	-0.826	0.205584
10	0.264034	2.4199	0.008841
11	0.580169	5.3173	0
12	0.783687	7.1826	0
13	0.586548	5.3758	0
14	0.294838	2.7022	0.004166
15	-0.101209	-0.9276	0.178137
16	-0.374022	-3.428	0.000472
17	-0.492805	-4.5166	1e-05
18	-0.476958	-4.3714	1.8e-05
19	-0.447082	-4.0976	4.8e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.67738	6.2083	0
2	-0.238346	-2.1845	0.015857
3	-0.461512	-4.2298	3e-05
4	-0.243963	-2.236	0.014003
5	-0.083825	-0.7683	0.222242
6	-0.164962	-1.5119	0.067156
7	-0.512815	-4.7	5e-06
8	-0.311035	-2.8507	0.002744
9	-0.017504	-0.1604	0.436466
10	0.110879	1.0162	0.156221
11	0.050205	0.4601	0.323304
12	0.27048	2.479	0.007588
13	-0.237594	-2.1776	0.016121
14	-0.070962	-0.6504	0.25861
15	0.035329	0.3238	0.373449
16	0.134202	1.23	0.111068
17	0.033684	0.3087	0.37915
18	-0.006347	-0.0582	0.476876
19	-0.063995	-0.5865	0.279547

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.67738 & 6.2083 & 0 \tabularnewline
2 & -0.238346 & -2.1845 & 0.015857 \tabularnewline
3 & -0.461512 & -4.2298 & 3e-05 \tabularnewline
4 & -0.243963 & -2.236 & 0.014003 \tabularnewline
5 & -0.083825 & -0.7683 & 0.222242 \tabularnewline
6 & -0.164962 & -1.5119 & 0.067156 \tabularnewline
7 & -0.512815 & -4.7 & 5e-06 \tabularnewline
8 & -0.311035 & -2.8507 & 0.002744 \tabularnewline
9 & -0.017504 & -0.1604 & 0.436466 \tabularnewline
10 & 0.110879 & 1.0162 & 0.156221 \tabularnewline
11 & 0.050205 & 0.4601 & 0.323304 \tabularnewline
12 & 0.27048 & 2.479 & 0.007588 \tabularnewline
13 & -0.237594 & -2.1776 & 0.016121 \tabularnewline
14 & -0.070962 & -0.6504 & 0.25861 \tabularnewline
15 & 0.035329 & 0.3238 & 0.373449 \tabularnewline
16 & 0.134202 & 1.23 & 0.111068 \tabularnewline
17 & 0.033684 & 0.3087 & 0.37915 \tabularnewline
18 & -0.006347 & -0.0582 & 0.476876 \tabularnewline
19 & -0.063995 & -0.5865 & 0.279547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61467&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]0.67738[/C][C]6.2083[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.238346[/C][C]-2.1845[/C][C]0.015857[/C][/ROW]
[ROW][C]3[/C][C]-0.461512[/C][C]-4.2298[/C][C]3e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.243963[/C][C]-2.236[/C][C]0.014003[/C][/ROW]
[ROW][C]5[/C][C]-0.083825[/C][C]-0.7683[/C][C]0.222242[/C][/ROW]
[ROW][C]6[/C][C]-0.164962[/C][C]-1.5119[/C][C]0.067156[/C][/ROW]
[ROW][C]7[/C][C]-0.512815[/C][C]-4.7[/C][C]5e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.311035[/C][C]-2.8507[/C][C]0.002744[/C][/ROW]
[ROW][C]9[/C][C]-0.017504[/C][C]-0.1604[/C][C]0.436466[/C][/ROW]
[ROW][C]10[/C][C]0.110879[/C][C]1.0162[/C][C]0.156221[/C][/ROW]
[ROW][C]11[/C][C]0.050205[/C][C]0.4601[/C][C]0.323304[/C][/ROW]
[ROW][C]12[/C][C]0.27048[/C][C]2.479[/C][C]0.007588[/C][/ROW]
[ROW][C]13[/C][C]-0.237594[/C][C]-2.1776[/C][C]0.016121[/C][/ROW]
[ROW][C]14[/C][C]-0.070962[/C][C]-0.6504[/C][C]0.25861[/C][/ROW]
[ROW][C]15[/C][C]0.035329[/C][C]0.3238[/C][C]0.373449[/C][/ROW]
[ROW][C]16[/C][C]0.134202[/C][C]1.23[/C][C]0.111068[/C][/ROW]
[ROW][C]17[/C][C]0.033684[/C][C]0.3087[/C][C]0.37915[/C][/ROW]
[ROW][C]18[/C][C]-0.006347[/C][C]-0.0582[/C][C]0.476876[/C][/ROW]
[ROW][C]19[/C][C]-0.063995[/C][C]-0.5865[/C][C]0.279547[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61467&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61467&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	0.67738	6.2083	0
2	-0.238346	-2.1845	0.015857
3	-0.461512	-4.2298	3e-05
4	-0.243963	-2.236	0.014003
5	-0.083825	-0.7683	0.222242
6	-0.164962	-1.5119	0.067156
7	-0.512815	-4.7	5e-06
8	-0.311035	-2.8507	0.002744
9	-0.017504	-0.1604	0.436466
10	0.110879	1.0162	0.156221
11	0.050205	0.4601	0.323304
12	0.27048	2.479	0.007588
13	-0.237594	-2.1776	0.016121
14	-0.070962	-0.6504	0.25861
15	0.035329	0.3238	0.373449
16	0.134202	1.23	0.111068
17	0.033684	0.3087	0.37915
18	-0.006347	-0.0582	0.476876
19	-0.063995	-0.5865	0.279547

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