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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 26 Jul 2013 05:29:50 -0400

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/2013/Jul/26/t13748310075jcfxsdxr4jadvt.htm/, Retrieved Mon, 29 Apr 2024 03:42:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210826, Retrieved Mon, 29 Apr 2024 03:42:19 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Alexandra De Schutter

Estimated Impact

149

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

-       [(Partial) Autocorrelation Function] [omzet Oregon Scie...] [2013-07-26 09:29:50] [a5e81fc5b84eaf53b9dc73271fe36a59] [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	4 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210826&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210826&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	4 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.911314	9.4706	0
2	0.829571	8.6212	0
3	0.740332	7.6938	0
4	0.639703	6.648	0
5	0.540622	5.6183	0
6	0.445492	4.6297	5e-06
7	0.348306	3.6197	0.000225
8	0.272642	2.8334	0.002749
9	0.198892	2.0669	0.020565
10	0.150397	1.563	0.060492
11	0.110611	1.1495	0.126444
12	0.070708	0.7348	0.23202
13	0.051561	0.5358	0.296588
14	0.033652	0.3497	0.363615
15	0.025983	0.27	0.393829
16	0.010109	0.1051	0.458265
17	-0.003245	-0.0337	0.486579
18	-0.031128	-0.3235	0.373476
19	-0.030046	-0.3122	0.377727
20	-0.035636	-0.3703	0.355925

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.911314 & 9.4706 & 0 \tabularnewline
2 & 0.829571 & 8.6212 & 0 \tabularnewline
3 & 0.740332 & 7.6938 & 0 \tabularnewline
4 & 0.639703 & 6.648 & 0 \tabularnewline
5 & 0.540622 & 5.6183 & 0 \tabularnewline
6 & 0.445492 & 4.6297 & 5e-06 \tabularnewline
7 & 0.348306 & 3.6197 & 0.000225 \tabularnewline
8 & 0.272642 & 2.8334 & 0.002749 \tabularnewline
9 & 0.198892 & 2.0669 & 0.020565 \tabularnewline
10 & 0.150397 & 1.563 & 0.060492 \tabularnewline
11 & 0.110611 & 1.1495 & 0.126444 \tabularnewline
12 & 0.070708 & 0.7348 & 0.23202 \tabularnewline
13 & 0.051561 & 0.5358 & 0.296588 \tabularnewline
14 & 0.033652 & 0.3497 & 0.363615 \tabularnewline
15 & 0.025983 & 0.27 & 0.393829 \tabularnewline
16 & 0.010109 & 0.1051 & 0.458265 \tabularnewline
17 & -0.003245 & -0.0337 & 0.486579 \tabularnewline
18 & -0.031128 & -0.3235 & 0.373476 \tabularnewline
19 & -0.030046 & -0.3122 & 0.377727 \tabularnewline
20 & -0.035636 & -0.3703 & 0.355925 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210826&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]0.911314[/C][C]9.4706[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.829571[/C][C]8.6212[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.740332[/C][C]7.6938[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.639703[/C][C]6.648[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.540622[/C][C]5.6183[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.445492[/C][C]4.6297[/C][C]5e-06[/C][/ROW]
[ROW][C]7[/C][C]0.348306[/C][C]3.6197[/C][C]0.000225[/C][/ROW]
[ROW][C]8[/C][C]0.272642[/C][C]2.8334[/C][C]0.002749[/C][/ROW]
[ROW][C]9[/C][C]0.198892[/C][C]2.0669[/C][C]0.020565[/C][/ROW]
[ROW][C]10[/C][C]0.150397[/C][C]1.563[/C][C]0.060492[/C][/ROW]
[ROW][C]11[/C][C]0.110611[/C][C]1.1495[/C][C]0.126444[/C][/ROW]
[ROW][C]12[/C][C]0.070708[/C][C]0.7348[/C][C]0.23202[/C][/ROW]
[ROW][C]13[/C][C]0.051561[/C][C]0.5358[/C][C]0.296588[/C][/ROW]
[ROW][C]14[/C][C]0.033652[/C][C]0.3497[/C][C]0.363615[/C][/ROW]
[ROW][C]15[/C][C]0.025983[/C][C]0.27[/C][C]0.393829[/C][/ROW]
[ROW][C]16[/C][C]0.010109[/C][C]0.1051[/C][C]0.458265[/C][/ROW]
[ROW][C]17[/C][C]-0.003245[/C][C]-0.0337[/C][C]0.486579[/C][/ROW]
[ROW][C]18[/C][C]-0.031128[/C][C]-0.3235[/C][C]0.373476[/C][/ROW]
[ROW][C]19[/C][C]-0.030046[/C][C]-0.3122[/C][C]0.377727[/C][/ROW]
[ROW][C]20[/C][C]-0.035636[/C][C]-0.3703[/C][C]0.355925[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210826&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	0.911314	9.4706	0
2	0.829571	8.6212	0
3	0.740332	7.6938	0
4	0.639703	6.648	0
5	0.540622	5.6183	0
6	0.445492	4.6297	5e-06
7	0.348306	3.6197	0.000225
8	0.272642	2.8334	0.002749
9	0.198892	2.0669	0.020565
10	0.150397	1.563	0.060492
11	0.110611	1.1495	0.126444
12	0.070708	0.7348	0.23202
13	0.051561	0.5358	0.296588
14	0.033652	0.3497	0.363615
15	0.025983	0.27	0.393829
16	0.010109	0.1051	0.458265
17	-0.003245	-0.0337	0.486579
18	-0.031128	-0.3235	0.373476
19	-0.030046	-0.3122	0.377727
20	-0.035636	-0.3703	0.355925

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.911314	9.4706	0
2	-0.005435	-0.0565	0.477532
3	-0.087452	-0.9088	0.182733
4	-0.122201	-1.2699	0.103416
5	-0.056489	-0.587	0.279198
6	-0.034963	-0.3633	0.35853
7	-0.072257	-0.7509	0.227166
8	0.055355	0.5753	0.283155
9	-0.040535	-0.4213	0.337205
10	0.084855	0.8818	0.18991
11	-7.6e-05	-8e-04	0.499684
12	-0.054381	-0.5651	0.286574
13	0.06161	0.6403	0.261678
14	-0.028939	-0.3007	0.382094
15	0.038745	0.4027	0.344001
16	-0.091653	-0.9525	0.171489
17	-0.000303	-0.0031	0.498747
18	-0.110987	-1.1534	0.125643
19	0.153301	1.5931	0.057025
20	-0.016859	-0.1752	0.430624

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.911314 & 9.4706 & 0 \tabularnewline
2 & -0.005435 & -0.0565 & 0.477532 \tabularnewline
3 & -0.087452 & -0.9088 & 0.182733 \tabularnewline
4 & -0.122201 & -1.2699 & 0.103416 \tabularnewline
5 & -0.056489 & -0.587 & 0.279198 \tabularnewline
6 & -0.034963 & -0.3633 & 0.35853 \tabularnewline
7 & -0.072257 & -0.7509 & 0.227166 \tabularnewline
8 & 0.055355 & 0.5753 & 0.283155 \tabularnewline
9 & -0.040535 & -0.4213 & 0.337205 \tabularnewline
10 & 0.084855 & 0.8818 & 0.18991 \tabularnewline
11 & -7.6e-05 & -8e-04 & 0.499684 \tabularnewline
12 & -0.054381 & -0.5651 & 0.286574 \tabularnewline
13 & 0.06161 & 0.6403 & 0.261678 \tabularnewline
14 & -0.028939 & -0.3007 & 0.382094 \tabularnewline
15 & 0.038745 & 0.4027 & 0.344001 \tabularnewline
16 & -0.091653 & -0.9525 & 0.171489 \tabularnewline
17 & -0.000303 & -0.0031 & 0.498747 \tabularnewline
18 & -0.110987 & -1.1534 & 0.125643 \tabularnewline
19 & 0.153301 & 1.5931 & 0.057025 \tabularnewline
20 & -0.016859 & -0.1752 & 0.430624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210826&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]0.911314[/C][C]9.4706[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.005435[/C][C]-0.0565[/C][C]0.477532[/C][/ROW]
[ROW][C]3[/C][C]-0.087452[/C][C]-0.9088[/C][C]0.182733[/C][/ROW]
[ROW][C]4[/C][C]-0.122201[/C][C]-1.2699[/C][C]0.103416[/C][/ROW]
[ROW][C]5[/C][C]-0.056489[/C][C]-0.587[/C][C]0.279198[/C][/ROW]
[ROW][C]6[/C][C]-0.034963[/C][C]-0.3633[/C][C]0.35853[/C][/ROW]
[ROW][C]7[/C][C]-0.072257[/C][C]-0.7509[/C][C]0.227166[/C][/ROW]
[ROW][C]8[/C][C]0.055355[/C][C]0.5753[/C][C]0.283155[/C][/ROW]
[ROW][C]9[/C][C]-0.040535[/C][C]-0.4213[/C][C]0.337205[/C][/ROW]
[ROW][C]10[/C][C]0.084855[/C][C]0.8818[/C][C]0.18991[/C][/ROW]
[ROW][C]11[/C][C]-7.6e-05[/C][C]-8e-04[/C][C]0.499684[/C][/ROW]
[ROW][C]12[/C][C]-0.054381[/C][C]-0.5651[/C][C]0.286574[/C][/ROW]
[ROW][C]13[/C][C]0.06161[/C][C]0.6403[/C][C]0.261678[/C][/ROW]
[ROW][C]14[/C][C]-0.028939[/C][C]-0.3007[/C][C]0.382094[/C][/ROW]
[ROW][C]15[/C][C]0.038745[/C][C]0.4027[/C][C]0.344001[/C][/ROW]
[ROW][C]16[/C][C]-0.091653[/C][C]-0.9525[/C][C]0.171489[/C][/ROW]
[ROW][C]17[/C][C]-0.000303[/C][C]-0.0031[/C][C]0.498747[/C][/ROW]
[ROW][C]18[/C][C]-0.110987[/C][C]-1.1534[/C][C]0.125643[/C][/ROW]
[ROW][C]19[/C][C]0.153301[/C][C]1.5931[/C][C]0.057025[/C][/ROW]
[ROW][C]20[/C][C]-0.016859[/C][C]-0.1752[/C][C]0.430624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210826&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	0.911314	9.4706	0
2	-0.005435	-0.0565	0.477532
3	-0.087452	-0.9088	0.182733
4	-0.122201	-1.2699	0.103416
5	-0.056489	-0.587	0.279198
6	-0.034963	-0.3633	0.35853
7	-0.072257	-0.7509	0.227166
8	0.055355	0.5753	0.283155
9	-0.040535	-0.4213	0.337205
10	0.084855	0.8818	0.18991
11	-7.6e-05	-8e-04	0.499684
12	-0.054381	-0.5651	0.286574
13	0.06161	0.6403	0.261678
14	-0.028939	-0.3007	0.382094
15	0.038745	0.4027	0.344001
16	-0.091653	-0.9525	0.171489
17	-0.000303	-0.0031	0.498747
18	-0.110987	-1.1534	0.125643
19	0.153301	1.5931	0.057025
20	-0.016859	-0.1752	0.430624

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 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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