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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:13:58 -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/2007/Nov/24/t1195913142cp9fzixuezl3hk3.htm/, Retrieved Fri, 03 May 2024 09:26:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6306, Retrieved Fri, 03 May 2024 09:26:16 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

199

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-11-24 14:13:58] [6b5c00822e2ce0f7cf73539c28d95782] [Current]

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Dataseries X:

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6306&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6306&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6306&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	0.023577	0.1811	0.428456
2	0.06501	0.4994	0.309694
3	-0.269399	-2.0693	0.978546
4	0.062642	0.4812	0.316091
5	-0.008933	-0.0686	0.527237
6	0.094532	0.7261	0.235321
7	-0.191436	-1.4704	0.926623
8	-0.059964	-0.4606	0.676607
9	-0.036192	-0.278	0.609008
10	0.042372	0.3255	0.372989
11	0.041088	0.3156	0.37671
12	0.038834	0.2983	0.383265
13	0.132077	1.0145	0.157242
14	-0.018081	-0.1389	0.554994
15	-0.144768	-1.112	0.864671
16	-0.040418	-0.3105	0.621346

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.023577 & 0.1811 & 0.428456 \tabularnewline
2 & 0.06501 & 0.4994 & 0.309694 \tabularnewline
3 & -0.269399 & -2.0693 & 0.978546 \tabularnewline
4 & 0.062642 & 0.4812 & 0.316091 \tabularnewline
5 & -0.008933 & -0.0686 & 0.527237 \tabularnewline
6 & 0.094532 & 0.7261 & 0.235321 \tabularnewline
7 & -0.191436 & -1.4704 & 0.926623 \tabularnewline
8 & -0.059964 & -0.4606 & 0.676607 \tabularnewline
9 & -0.036192 & -0.278 & 0.609008 \tabularnewline
10 & 0.042372 & 0.3255 & 0.372989 \tabularnewline
11 & 0.041088 & 0.3156 & 0.37671 \tabularnewline
12 & 0.038834 & 0.2983 & 0.383265 \tabularnewline
13 & 0.132077 & 1.0145 & 0.157242 \tabularnewline
14 & -0.018081 & -0.1389 & 0.554994 \tabularnewline
15 & -0.144768 & -1.112 & 0.864671 \tabularnewline
16 & -0.040418 & -0.3105 & 0.621346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6306&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]0[/C][C]1[/C][C]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.023577[/C][C]0.1811[/C][C]0.428456[/C][/ROW]
[ROW][C]2[/C][C]0.06501[/C][C]0.4994[/C][C]0.309694[/C][/ROW]
[ROW][C]3[/C][C]-0.269399[/C][C]-2.0693[/C][C]0.978546[/C][/ROW]
[ROW][C]4[/C][C]0.062642[/C][C]0.4812[/C][C]0.316091[/C][/ROW]
[ROW][C]5[/C][C]-0.008933[/C][C]-0.0686[/C][C]0.527237[/C][/ROW]
[ROW][C]6[/C][C]0.094532[/C][C]0.7261[/C][C]0.235321[/C][/ROW]
[ROW][C]7[/C][C]-0.191436[/C][C]-1.4704[/C][C]0.926623[/C][/ROW]
[ROW][C]8[/C][C]-0.059964[/C][C]-0.4606[/C][C]0.676607[/C][/ROW]
[ROW][C]9[/C][C]-0.036192[/C][C]-0.278[/C][C]0.609008[/C][/ROW]
[ROW][C]10[/C][C]0.042372[/C][C]0.3255[/C][C]0.372989[/C][/ROW]
[ROW][C]11[/C][C]0.041088[/C][C]0.3156[/C][C]0.37671[/C][/ROW]
[ROW][C]12[/C][C]0.038834[/C][C]0.2983[/C][C]0.383265[/C][/ROW]
[ROW][C]13[/C][C]0.132077[/C][C]1.0145[/C][C]0.157242[/C][/ROW]
[ROW][C]14[/C][C]-0.018081[/C][C]-0.1389[/C][C]0.554994[/C][/ROW]
[ROW][C]15[/C][C]-0.144768[/C][C]-1.112[/C][C]0.864671[/C][/ROW]
[ROW][C]16[/C][C]-0.040418[/C][C]-0.3105[/C][C]0.621346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6306&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6306&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
0	1	7.6811	0
1	0.023577	0.1811	0.428456
2	0.06501	0.4994	0.309694
3	-0.269399	-2.0693	0.978546
4	0.062642	0.4812	0.316091
5	-0.008933	-0.0686	0.527237
6	0.094532	0.7261	0.235321
7	-0.191436	-1.4704	0.926623
8	-0.059964	-0.4606	0.676607
9	-0.036192	-0.278	0.609008
10	0.042372	0.3255	0.372989
11	0.041088	0.3156	0.37671
12	0.038834	0.2983	0.383265
13	0.132077	1.0145	0.157242
14	-0.018081	-0.1389	0.554994
15	-0.144768	-1.112	0.864671
16	-0.040418	-0.3105	0.621346

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.023577	0.1811	0.428456
1	0.06449	0.4954	0.311094
2	-0.273643	-2.1019	0.980079
3	0.081676	0.6274	0.266419
4	0.022635	0.1739	0.431285
5	0.010808	0.083	0.46706
6	-0.174494	-1.3403	0.907359
7	-0.053569	-0.4115	0.658892
8	0.027276	0.2095	0.417385
9	-0.055937	-0.4297	0.665496
10	0.031563	0.2424	0.40464
11	0.043174	0.3316	0.370674
12	0.163106	1.2528	0.107603
13	-0.054152	-0.416	0.660522
14	-0.197332	-1.5157	0.932537
15	0.060678	0.4661	0.321438
16	-0.14311	-1.0992	0.861937

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.023577 & 0.1811 & 0.428456 \tabularnewline
1 & 0.06449 & 0.4954 & 0.311094 \tabularnewline
2 & -0.273643 & -2.1019 & 0.980079 \tabularnewline
3 & 0.081676 & 0.6274 & 0.266419 \tabularnewline
4 & 0.022635 & 0.1739 & 0.431285 \tabularnewline
5 & 0.010808 & 0.083 & 0.46706 \tabularnewline
6 & -0.174494 & -1.3403 & 0.907359 \tabularnewline
7 & -0.053569 & -0.4115 & 0.658892 \tabularnewline
8 & 0.027276 & 0.2095 & 0.417385 \tabularnewline
9 & -0.055937 & -0.4297 & 0.665496 \tabularnewline
10 & 0.031563 & 0.2424 & 0.40464 \tabularnewline
11 & 0.043174 & 0.3316 & 0.370674 \tabularnewline
12 & 0.163106 & 1.2528 & 0.107603 \tabularnewline
13 & -0.054152 & -0.416 & 0.660522 \tabularnewline
14 & -0.197332 & -1.5157 & 0.932537 \tabularnewline
15 & 0.060678 & 0.4661 & 0.321438 \tabularnewline
16 & -0.14311 & -1.0992 & 0.861937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6306&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]0[/C][C]0.023577[/C][C]0.1811[/C][C]0.428456[/C][/ROW]
[ROW][C]1[/C][C]0.06449[/C][C]0.4954[/C][C]0.311094[/C][/ROW]
[ROW][C]2[/C][C]-0.273643[/C][C]-2.1019[/C][C]0.980079[/C][/ROW]
[ROW][C]3[/C][C]0.081676[/C][C]0.6274[/C][C]0.266419[/C][/ROW]
[ROW][C]4[/C][C]0.022635[/C][C]0.1739[/C][C]0.431285[/C][/ROW]
[ROW][C]5[/C][C]0.010808[/C][C]0.083[/C][C]0.46706[/C][/ROW]
[ROW][C]6[/C][C]-0.174494[/C][C]-1.3403[/C][C]0.907359[/C][/ROW]
[ROW][C]7[/C][C]-0.053569[/C][C]-0.4115[/C][C]0.658892[/C][/ROW]
[ROW][C]8[/C][C]0.027276[/C][C]0.2095[/C][C]0.417385[/C][/ROW]
[ROW][C]9[/C][C]-0.055937[/C][C]-0.4297[/C][C]0.665496[/C][/ROW]
[ROW][C]10[/C][C]0.031563[/C][C]0.2424[/C][C]0.40464[/C][/ROW]
[ROW][C]11[/C][C]0.043174[/C][C]0.3316[/C][C]0.370674[/C][/ROW]
[ROW][C]12[/C][C]0.163106[/C][C]1.2528[/C][C]0.107603[/C][/ROW]
[ROW][C]13[/C][C]-0.054152[/C][C]-0.416[/C][C]0.660522[/C][/ROW]
[ROW][C]14[/C][C]-0.197332[/C][C]-1.5157[/C][C]0.932537[/C][/ROW]
[ROW][C]15[/C][C]0.060678[/C][C]0.4661[/C][C]0.321438[/C][/ROW]
[ROW][C]16[/C][C]-0.14311[/C][C]-1.0992[/C][C]0.861937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6306&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6306&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
0	0.023577	0.1811	0.428456
1	0.06449	0.4954	0.311094
2	-0.273643	-2.1019	0.980079
3	0.081676	0.6274	0.266419
4	0.022635	0.1739	0.431285
5	0.010808	0.083	0.46706
6	-0.174494	-1.3403	0.907359
7	-0.053569	-0.4115	0.658892
8	0.027276	0.2095	0.417385
9	-0.055937	-0.4297	0.665496
10	0.031563	0.2424	0.40464
11	0.043174	0.3316	0.370674
12	0.163106	1.2528	0.107603
13	-0.054152	-0.416	0.660522
14	-0.197332	-1.5157	0.932537
15	0.060678	0.4661	0.321438
16	-0.14311	-1.0992	0.861937

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 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(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