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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 03:08:32 -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/26/t1259230216g77utwcd598x1c3.htm/, Retrieved Sun, 28 Apr 2024 21:57:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59766, Retrieved Sun, 28 Apr 2024 21:57:08 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

124

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:26:39] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [] [2009-11-26 10:08:32] [faa1ded5041cd5a0e2be04844f08502a] [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=59766&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=59766&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59766&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	-0.453276	-3.1404	0.001443
2	0.031128	0.2157	0.415084
3	0.006192	0.0429	0.482978
4	-0.01479	-0.1025	0.459405
5	0.103529	0.7173	0.238341
6	-0.019381	-0.1343	0.446873
7	-0.048778	-0.3379	0.368439
8	-0.044518	-0.3084	0.379544
9	0.081429	0.5642	0.287636
10	-0.065661	-0.4549	0.325611
11	0.222601	1.5422	0.064793
12	-0.324443	-2.2478	0.01461
13	0.082618	0.5724	0.284864
14	0.181963	1.2607	0.10676
15	-0.209885	-1.4541	0.07621
16	0.132496	0.918	0.181615
17	-0.06134	-0.425	0.336376

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.453276 & -3.1404 & 0.001443 \tabularnewline
2 & 0.031128 & 0.2157 & 0.415084 \tabularnewline
3 & 0.006192 & 0.0429 & 0.482978 \tabularnewline
4 & -0.01479 & -0.1025 & 0.459405 \tabularnewline
5 & 0.103529 & 0.7173 & 0.238341 \tabularnewline
6 & -0.019381 & -0.1343 & 0.446873 \tabularnewline
7 & -0.048778 & -0.3379 & 0.368439 \tabularnewline
8 & -0.044518 & -0.3084 & 0.379544 \tabularnewline
9 & 0.081429 & 0.5642 & 0.287636 \tabularnewline
10 & -0.065661 & -0.4549 & 0.325611 \tabularnewline
11 & 0.222601 & 1.5422 & 0.064793 \tabularnewline
12 & -0.324443 & -2.2478 & 0.01461 \tabularnewline
13 & 0.082618 & 0.5724 & 0.284864 \tabularnewline
14 & 0.181963 & 1.2607 & 0.10676 \tabularnewline
15 & -0.209885 & -1.4541 & 0.07621 \tabularnewline
16 & 0.132496 & 0.918 & 0.181615 \tabularnewline
17 & -0.06134 & -0.425 & 0.336376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59766&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]-0.453276[/C][C]-3.1404[/C][C]0.001443[/C][/ROW]
[ROW][C]2[/C][C]0.031128[/C][C]0.2157[/C][C]0.415084[/C][/ROW]
[ROW][C]3[/C][C]0.006192[/C][C]0.0429[/C][C]0.482978[/C][/ROW]
[ROW][C]4[/C][C]-0.01479[/C][C]-0.1025[/C][C]0.459405[/C][/ROW]
[ROW][C]5[/C][C]0.103529[/C][C]0.7173[/C][C]0.238341[/C][/ROW]
[ROW][C]6[/C][C]-0.019381[/C][C]-0.1343[/C][C]0.446873[/C][/ROW]
[ROW][C]7[/C][C]-0.048778[/C][C]-0.3379[/C][C]0.368439[/C][/ROW]
[ROW][C]8[/C][C]-0.044518[/C][C]-0.3084[/C][C]0.379544[/C][/ROW]
[ROW][C]9[/C][C]0.081429[/C][C]0.5642[/C][C]0.287636[/C][/ROW]
[ROW][C]10[/C][C]-0.065661[/C][C]-0.4549[/C][C]0.325611[/C][/ROW]
[ROW][C]11[/C][C]0.222601[/C][C]1.5422[/C][C]0.064793[/C][/ROW]
[ROW][C]12[/C][C]-0.324443[/C][C]-2.2478[/C][C]0.01461[/C][/ROW]
[ROW][C]13[/C][C]0.082618[/C][C]0.5724[/C][C]0.284864[/C][/ROW]
[ROW][C]14[/C][C]0.181963[/C][C]1.2607[/C][C]0.10676[/C][/ROW]
[ROW][C]15[/C][C]-0.209885[/C][C]-1.4541[/C][C]0.07621[/C][/ROW]
[ROW][C]16[/C][C]0.132496[/C][C]0.918[/C][C]0.181615[/C][/ROW]
[ROW][C]17[/C][C]-0.06134[/C][C]-0.425[/C][C]0.336376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59766&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59766&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	-0.453276	-3.1404	0.001443
2	0.031128	0.2157	0.415084
3	0.006192	0.0429	0.482978
4	-0.01479	-0.1025	0.459405
5	0.103529	0.7173	0.238341
6	-0.019381	-0.1343	0.446873
7	-0.048778	-0.3379	0.368439
8	-0.044518	-0.3084	0.379544
9	0.081429	0.5642	0.287636
10	-0.065661	-0.4549	0.325611
11	0.222601	1.5422	0.064793
12	-0.324443	-2.2478	0.01461
13	0.082618	0.5724	0.284864
14	0.181963	1.2607	0.10676
15	-0.209885	-1.4541	0.07621
16	0.132496	0.918	0.181615
17	-0.06134	-0.425	0.336376

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.453276	-3.1404	0.001443
2	-0.219411	-1.5201	0.06752
3	-0.100565	-0.6967	0.244665
4	-0.064456	-0.4466	0.328598
5	0.096323	0.6673	0.253874
6	0.109156	0.7563	0.226597
7	0.015973	0.1107	0.456173
8	-0.089908	-0.6229	0.268149
9	-1.8e-05	-1e-04	0.49995
10	-0.062414	-0.4324	0.333689
11	0.236645	1.6395	0.053821
12	-0.134535	-0.9321	0.177979
13	-0.135018	-0.9354	0.177125
14	0.148921	1.0318	0.153679
15	-0.0881	-0.6104	0.272247
16	-0.002684	-0.0186	0.492619
17	0.0454	0.3145	0.377238

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.453276 & -3.1404 & 0.001443 \tabularnewline
2 & -0.219411 & -1.5201 & 0.06752 \tabularnewline
3 & -0.100565 & -0.6967 & 0.244665 \tabularnewline
4 & -0.064456 & -0.4466 & 0.328598 \tabularnewline
5 & 0.096323 & 0.6673 & 0.253874 \tabularnewline
6 & 0.109156 & 0.7563 & 0.226597 \tabularnewline
7 & 0.015973 & 0.1107 & 0.456173 \tabularnewline
8 & -0.089908 & -0.6229 & 0.268149 \tabularnewline
9 & -1.8e-05 & -1e-04 & 0.49995 \tabularnewline
10 & -0.062414 & -0.4324 & 0.333689 \tabularnewline
11 & 0.236645 & 1.6395 & 0.053821 \tabularnewline
12 & -0.134535 & -0.9321 & 0.177979 \tabularnewline
13 & -0.135018 & -0.9354 & 0.177125 \tabularnewline
14 & 0.148921 & 1.0318 & 0.153679 \tabularnewline
15 & -0.0881 & -0.6104 & 0.272247 \tabularnewline
16 & -0.002684 & -0.0186 & 0.492619 \tabularnewline
17 & 0.0454 & 0.3145 & 0.377238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59766&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]-0.453276[/C][C]-3.1404[/C][C]0.001443[/C][/ROW]
[ROW][C]2[/C][C]-0.219411[/C][C]-1.5201[/C][C]0.06752[/C][/ROW]
[ROW][C]3[/C][C]-0.100565[/C][C]-0.6967[/C][C]0.244665[/C][/ROW]
[ROW][C]4[/C][C]-0.064456[/C][C]-0.4466[/C][C]0.328598[/C][/ROW]
[ROW][C]5[/C][C]0.096323[/C][C]0.6673[/C][C]0.253874[/C][/ROW]
[ROW][C]6[/C][C]0.109156[/C][C]0.7563[/C][C]0.226597[/C][/ROW]
[ROW][C]7[/C][C]0.015973[/C][C]0.1107[/C][C]0.456173[/C][/ROW]
[ROW][C]8[/C][C]-0.089908[/C][C]-0.6229[/C][C]0.268149[/C][/ROW]
[ROW][C]9[/C][C]-1.8e-05[/C][C]-1e-04[/C][C]0.49995[/C][/ROW]
[ROW][C]10[/C][C]-0.062414[/C][C]-0.4324[/C][C]0.333689[/C][/ROW]
[ROW][C]11[/C][C]0.236645[/C][C]1.6395[/C][C]0.053821[/C][/ROW]
[ROW][C]12[/C][C]-0.134535[/C][C]-0.9321[/C][C]0.177979[/C][/ROW]
[ROW][C]13[/C][C]-0.135018[/C][C]-0.9354[/C][C]0.177125[/C][/ROW]
[ROW][C]14[/C][C]0.148921[/C][C]1.0318[/C][C]0.153679[/C][/ROW]
[ROW][C]15[/C][C]-0.0881[/C][C]-0.6104[/C][C]0.272247[/C][/ROW]
[ROW][C]16[/C][C]-0.002684[/C][C]-0.0186[/C][C]0.492619[/C][/ROW]
[ROW][C]17[/C][C]0.0454[/C][C]0.3145[/C][C]0.377238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59766&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59766&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	-0.453276	-3.1404	0.001443
2	-0.219411	-1.5201	0.06752
3	-0.100565	-0.6967	0.244665
4	-0.064456	-0.4466	0.328598
5	0.096323	0.6673	0.253874
6	0.109156	0.7563	0.226597
7	0.015973	0.1107	0.456173
8	-0.089908	-0.6229	0.268149
9	-1.8e-05	-1e-04	0.49995
10	-0.062414	-0.4324	0.333689
11	0.236645	1.6395	0.053821
12	-0.134535	-0.9321	0.177979
13	-0.135018	-0.9354	0.177125
14	0.148921	1.0318	0.153679
15	-0.0881	-0.6104	0.272247
16	-0.002684	-0.0186	0.492619
17	0.0454	0.3145	0.377238

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code