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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 04:14:50 -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/25/t1195988864l0o9akwcsj9o5pt.htm/, Retrieved Sat, 04 May 2024 10:10:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6404, Retrieved Sat, 04 May 2024 10:10:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

213

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

-       [(Partial) Autocorrelation Function] [ws 7] [2007-11-25 11:14:50] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]

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Dataseries X:

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8,1
8,2
8
8,1
8,3
8,2
8,1
7,7
7,6
7,7
8,2
8,4
8,4
8,6
8,4
8,5
8,7
8,7
8,6
7,4
7,3
7,4
9
9,2
9,2
8,5
8,3
8,3
8,6
8,6
8,5
8,1
8,1
8
8,6
8,7
8,7
8,6
8,4
8,4
8,7
8,7
8,5
8,3
8,3
8,3
8,1
8,2
8,1
8,1
7,9
7,7
8,1
8
7,7
7,8
7,6
7,4
7,7
7,9
7,6

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=6404&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=6404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6404&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	7.746	0
1	0.124543	0.9647	0.169282
2	-0.156044	-1.2087	0.884242
3	-0.520611	-4.0326	0.999921
4	-0.180435	-1.3976	0.916317
5	0.05421	0.4199	0.338026
6	0.311856	2.4156	0.009385
7	0.107558	0.8331	0.204034
8	-0.159736	-1.2373	0.889604
9	-0.30066	-2.3289	0.988375
10	-0.070182	-0.5436	0.705645
11	0.115374	0.8937	0.187531
12	0.465633	3.6068	0.000316
13	0.118587	0.9186	0.180999
14	-0.057846	-0.4481	0.672144
15	-0.334909	-2.5942	0.994051
16	-0.17713	-1.372	0.912421

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.124543 & 0.9647 & 0.169282 \tabularnewline
2 & -0.156044 & -1.2087 & 0.884242 \tabularnewline
3 & -0.520611 & -4.0326 & 0.999921 \tabularnewline
4 & -0.180435 & -1.3976 & 0.916317 \tabularnewline
5 & 0.05421 & 0.4199 & 0.338026 \tabularnewline
6 & 0.311856 & 2.4156 & 0.009385 \tabularnewline
7 & 0.107558 & 0.8331 & 0.204034 \tabularnewline
8 & -0.159736 & -1.2373 & 0.889604 \tabularnewline
9 & -0.30066 & -2.3289 & 0.988375 \tabularnewline
10 & -0.070182 & -0.5436 & 0.705645 \tabularnewline
11 & 0.115374 & 0.8937 & 0.187531 \tabularnewline
12 & 0.465633 & 3.6068 & 0.000316 \tabularnewline
13 & 0.118587 & 0.9186 & 0.180999 \tabularnewline
14 & -0.057846 & -0.4481 & 0.672144 \tabularnewline
15 & -0.334909 & -2.5942 & 0.994051 \tabularnewline
16 & -0.17713 & -1.372 & 0.912421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6404&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.124543[/C][C]0.9647[/C][C]0.169282[/C][/ROW]
[ROW][C]2[/C][C]-0.156044[/C][C]-1.2087[/C][C]0.884242[/C][/ROW]
[ROW][C]3[/C][C]-0.520611[/C][C]-4.0326[/C][C]0.999921[/C][/ROW]
[ROW][C]4[/C][C]-0.180435[/C][C]-1.3976[/C][C]0.916317[/C][/ROW]
[ROW][C]5[/C][C]0.05421[/C][C]0.4199[/C][C]0.338026[/C][/ROW]
[ROW][C]6[/C][C]0.311856[/C][C]2.4156[/C][C]0.009385[/C][/ROW]
[ROW][C]7[/C][C]0.107558[/C][C]0.8331[/C][C]0.204034[/C][/ROW]
[ROW][C]8[/C][C]-0.159736[/C][C]-1.2373[/C][C]0.889604[/C][/ROW]
[ROW][C]9[/C][C]-0.30066[/C][C]-2.3289[/C][C]0.988375[/C][/ROW]
[ROW][C]10[/C][C]-0.070182[/C][C]-0.5436[/C][C]0.705645[/C][/ROW]
[ROW][C]11[/C][C]0.115374[/C][C]0.8937[/C][C]0.187531[/C][/ROW]
[ROW][C]12[/C][C]0.465633[/C][C]3.6068[/C][C]0.000316[/C][/ROW]
[ROW][C]13[/C][C]0.118587[/C][C]0.9186[/C][C]0.180999[/C][/ROW]
[ROW][C]14[/C][C]-0.057846[/C][C]-0.4481[/C][C]0.672144[/C][/ROW]
[ROW][C]15[/C][C]-0.334909[/C][C]-2.5942[/C][C]0.994051[/C][/ROW]
[ROW][C]16[/C][C]-0.17713[/C][C]-1.372[/C][C]0.912421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6404&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	7.746	0
1	0.124543	0.9647	0.169282
2	-0.156044	-1.2087	0.884242
3	-0.520611	-4.0326	0.999921
4	-0.180435	-1.3976	0.916317
5	0.05421	0.4199	0.338026
6	0.311856	2.4156	0.009385
7	0.107558	0.8331	0.204034
8	-0.159736	-1.2373	0.889604
9	-0.30066	-2.3289	0.988375
10	-0.070182	-0.5436	0.705645
11	0.115374	0.8937	0.187531
12	0.465633	3.6068	0.000316
13	0.118587	0.9186	0.180999
14	-0.057846	-0.4481	0.672144
15	-0.334909	-2.5942	0.994051
16	-0.17713	-1.372	0.912421

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.124543	0.9647	0.169282
1	-0.174258	-1.3498	0.908924
2	-0.498733	-3.8632	0.999861
3	-0.143957	-1.1151	0.865371
4	-0.09532	-0.7383	0.768409
5	0.017534	0.1358	0.446209
6	-0.080554	-0.624	0.732493
7	-0.22295	-1.727	0.95534
8	-0.227664	-1.7635	0.958544
9	-0.108752	-0.8424	0.798541
10	-0.156888	-1.2152	0.885484
11	0.251009	1.9443	0.028275
12	0.014036	0.1087	0.456894
13	0.099587	0.7714	0.22175
14	0.084996	0.6584	0.256408
15	-0.017091	-0.1324	0.55244
16	0.101911	0.7894	0.216494

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.124543 & 0.9647 & 0.169282 \tabularnewline
1 & -0.174258 & -1.3498 & 0.908924 \tabularnewline
2 & -0.498733 & -3.8632 & 0.999861 \tabularnewline
3 & -0.143957 & -1.1151 & 0.865371 \tabularnewline
4 & -0.09532 & -0.7383 & 0.768409 \tabularnewline
5 & 0.017534 & 0.1358 & 0.446209 \tabularnewline
6 & -0.080554 & -0.624 & 0.732493 \tabularnewline
7 & -0.22295 & -1.727 & 0.95534 \tabularnewline
8 & -0.227664 & -1.7635 & 0.958544 \tabularnewline
9 & -0.108752 & -0.8424 & 0.798541 \tabularnewline
10 & -0.156888 & -1.2152 & 0.885484 \tabularnewline
11 & 0.251009 & 1.9443 & 0.028275 \tabularnewline
12 & 0.014036 & 0.1087 & 0.456894 \tabularnewline
13 & 0.099587 & 0.7714 & 0.22175 \tabularnewline
14 & 0.084996 & 0.6584 & 0.256408 \tabularnewline
15 & -0.017091 & -0.1324 & 0.55244 \tabularnewline
16 & 0.101911 & 0.7894 & 0.216494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6404&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]0.124543[/C][C]0.9647[/C][C]0.169282[/C][/ROW]
[ROW][C]1[/C][C]-0.174258[/C][C]-1.3498[/C][C]0.908924[/C][/ROW]
[ROW][C]2[/C][C]-0.498733[/C][C]-3.8632[/C][C]0.999861[/C][/ROW]
[ROW][C]3[/C][C]-0.143957[/C][C]-1.1151[/C][C]0.865371[/C][/ROW]
[ROW][C]4[/C][C]-0.09532[/C][C]-0.7383[/C][C]0.768409[/C][/ROW]
[ROW][C]5[/C][C]0.017534[/C][C]0.1358[/C][C]0.446209[/C][/ROW]
[ROW][C]6[/C][C]-0.080554[/C][C]-0.624[/C][C]0.732493[/C][/ROW]
[ROW][C]7[/C][C]-0.22295[/C][C]-1.727[/C][C]0.95534[/C][/ROW]
[ROW][C]8[/C][C]-0.227664[/C][C]-1.7635[/C][C]0.958544[/C][/ROW]
[ROW][C]9[/C][C]-0.108752[/C][C]-0.8424[/C][C]0.798541[/C][/ROW]
[ROW][C]10[/C][C]-0.156888[/C][C]-1.2152[/C][C]0.885484[/C][/ROW]
[ROW][C]11[/C][C]0.251009[/C][C]1.9443[/C][C]0.028275[/C][/ROW]
[ROW][C]12[/C][C]0.014036[/C][C]0.1087[/C][C]0.456894[/C][/ROW]
[ROW][C]13[/C][C]0.099587[/C][C]0.7714[/C][C]0.22175[/C][/ROW]
[ROW][C]14[/C][C]0.084996[/C][C]0.6584[/C][C]0.256408[/C][/ROW]
[ROW][C]15[/C][C]-0.017091[/C][C]-0.1324[/C][C]0.55244[/C][/ROW]
[ROW][C]16[/C][C]0.101911[/C][C]0.7894[/C][C]0.216494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6404&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	0.124543	0.9647	0.169282
1	-0.174258	-1.3498	0.908924
2	-0.498733	-3.8632	0.999861
3	-0.143957	-1.1151	0.865371
4	-0.09532	-0.7383	0.768409
5	0.017534	0.1358	0.446209
6	-0.080554	-0.624	0.732493
7	-0.22295	-1.727	0.95534
8	-0.227664	-1.7635	0.958544
9	-0.108752	-0.8424	0.798541
10	-0.156888	-1.2152	0.885484
11	0.251009	1.9443	0.028275
12	0.014036	0.1087	0.456894
13	0.099587	0.7714	0.22175
14	0.084996	0.6584	0.256408
15	-0.017091	-0.1324	0.55244
16	0.101911	0.7894	0.216494

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -2.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -2.0 ; 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

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Input Parameters & R Code