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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Mar 2014 12:49:59 -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/2014/Mar/17/t1395075029dbmc62a1u86d6wc.htm/, Retrieved Tue, 14 May 2024 01:51:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234315, Retrieved Tue, 14 May 2024 01:51:02 +0000

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

-       [(Partial) Autocorrelation Function] [Degree of non-sea...] [2014-03-17 16:49:59] [1195732e18620915cb775ad7ef5494bd] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234315&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]3 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=234315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234315&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.012485	0.1137	0.454858
2	-0.011978	-0.1091	0.456685
3	0.100122	0.9122	0.182164
4	-0.10918	-0.9947	0.161393
5	0.157035	1.4307	0.078142
6	0.160635	1.4635	0.07356
7	-0.038951	-0.3549	0.361796
8	0.089218	0.8128	0.209325
9	-0.131497	-1.198	0.117164
10	-0.034156	-0.3112	0.378223
11	0.057038	0.5196	0.302349
12	-0.06687	-0.6092	0.272022
13	0.057084	0.5201	0.302203
14	-0.006623	-0.0603	0.476015
15	-0.077221	-0.7035	0.241852
16	0.067085	0.6112	0.271378
17	-0.103825	-0.9459	0.173475
18	0.059808	0.5449	0.29365
19	0.114518	1.0433	0.149918

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.012485 & 0.1137 & 0.454858 \tabularnewline
2 & -0.011978 & -0.1091 & 0.456685 \tabularnewline
3 & 0.100122 & 0.9122 & 0.182164 \tabularnewline
4 & -0.10918 & -0.9947 & 0.161393 \tabularnewline
5 & 0.157035 & 1.4307 & 0.078142 \tabularnewline
6 & 0.160635 & 1.4635 & 0.07356 \tabularnewline
7 & -0.038951 & -0.3549 & 0.361796 \tabularnewline
8 & 0.089218 & 0.8128 & 0.209325 \tabularnewline
9 & -0.131497 & -1.198 & 0.117164 \tabularnewline
10 & -0.034156 & -0.3112 & 0.378223 \tabularnewline
11 & 0.057038 & 0.5196 & 0.302349 \tabularnewline
12 & -0.06687 & -0.6092 & 0.272022 \tabularnewline
13 & 0.057084 & 0.5201 & 0.302203 \tabularnewline
14 & -0.006623 & -0.0603 & 0.476015 \tabularnewline
15 & -0.077221 & -0.7035 & 0.241852 \tabularnewline
16 & 0.067085 & 0.6112 & 0.271378 \tabularnewline
17 & -0.103825 & -0.9459 & 0.173475 \tabularnewline
18 & 0.059808 & 0.5449 & 0.29365 \tabularnewline
19 & 0.114518 & 1.0433 & 0.149918 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234315&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]0.012485[/C][C]0.1137[/C][C]0.454858[/C][/ROW]
[ROW][C]2[/C][C]-0.011978[/C][C]-0.1091[/C][C]0.456685[/C][/ROW]
[ROW][C]3[/C][C]0.100122[/C][C]0.9122[/C][C]0.182164[/C][/ROW]
[ROW][C]4[/C][C]-0.10918[/C][C]-0.9947[/C][C]0.161393[/C][/ROW]
[ROW][C]5[/C][C]0.157035[/C][C]1.4307[/C][C]0.078142[/C][/ROW]
[ROW][C]6[/C][C]0.160635[/C][C]1.4635[/C][C]0.07356[/C][/ROW]
[ROW][C]7[/C][C]-0.038951[/C][C]-0.3549[/C][C]0.361796[/C][/ROW]
[ROW][C]8[/C][C]0.089218[/C][C]0.8128[/C][C]0.209325[/C][/ROW]
[ROW][C]9[/C][C]-0.131497[/C][C]-1.198[/C][C]0.117164[/C][/ROW]
[ROW][C]10[/C][C]-0.034156[/C][C]-0.3112[/C][C]0.378223[/C][/ROW]
[ROW][C]11[/C][C]0.057038[/C][C]0.5196[/C][C]0.302349[/C][/ROW]
[ROW][C]12[/C][C]-0.06687[/C][C]-0.6092[/C][C]0.272022[/C][/ROW]
[ROW][C]13[/C][C]0.057084[/C][C]0.5201[/C][C]0.302203[/C][/ROW]
[ROW][C]14[/C][C]-0.006623[/C][C]-0.0603[/C][C]0.476015[/C][/ROW]
[ROW][C]15[/C][C]-0.077221[/C][C]-0.7035[/C][C]0.241852[/C][/ROW]
[ROW][C]16[/C][C]0.067085[/C][C]0.6112[/C][C]0.271378[/C][/ROW]
[ROW][C]17[/C][C]-0.103825[/C][C]-0.9459[/C][C]0.173475[/C][/ROW]
[ROW][C]18[/C][C]0.059808[/C][C]0.5449[/C][C]0.29365[/C][/ROW]
[ROW][C]19[/C][C]0.114518[/C][C]1.0433[/C][C]0.149918[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234315&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	0.012485	0.1137	0.454858
2	-0.011978	-0.1091	0.456685
3	0.100122	0.9122	0.182164
4	-0.10918	-0.9947	0.161393
5	0.157035	1.4307	0.078142
6	0.160635	1.4635	0.07356
7	-0.038951	-0.3549	0.361796
8	0.089218	0.8128	0.209325
9	-0.131497	-1.198	0.117164
10	-0.034156	-0.3112	0.378223
11	0.057038	0.5196	0.302349
12	-0.06687	-0.6092	0.272022
13	0.057084	0.5201	0.302203
14	-0.006623	-0.0603	0.476015
15	-0.077221	-0.7035	0.241852
16	0.067085	0.6112	0.271378
17	-0.103825	-0.9459	0.173475
18	0.059808	0.5449	0.29365
19	0.114518	1.0433	0.149918

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.012485	0.1137	0.454858
2	-0.012135	-0.1106	0.456117
3	0.100456	0.9152	0.18137
4	-0.113158	-1.0309	0.152788
5	0.167787	1.5286	0.065081
6	0.143484	1.3072	0.097377
7	-0.019991	-0.1821	0.427964
8	0.055998	0.5102	0.305643
9	-0.139124	-1.2675	0.104265
10	-0.012278	-0.1119	0.455604
11	-0.015379	-0.1401	0.444456
12	-0.048702	-0.4437	0.329207
13	0.030579	0.2786	0.390629
14	-0.004063	-0.037	0.48528
15	-0.007686	-0.07	0.472171
16	0.044278	0.4034	0.34385
17	-0.081189	-0.7397	0.230796
18	0.075576	0.6885	0.246521
19	0.072476	0.6603	0.25545

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.012485 & 0.1137 & 0.454858 \tabularnewline
2 & -0.012135 & -0.1106 & 0.456117 \tabularnewline
3 & 0.100456 & 0.9152 & 0.18137 \tabularnewline
4 & -0.113158 & -1.0309 & 0.152788 \tabularnewline
5 & 0.167787 & 1.5286 & 0.065081 \tabularnewline
6 & 0.143484 & 1.3072 & 0.097377 \tabularnewline
7 & -0.019991 & -0.1821 & 0.427964 \tabularnewline
8 & 0.055998 & 0.5102 & 0.305643 \tabularnewline
9 & -0.139124 & -1.2675 & 0.104265 \tabularnewline
10 & -0.012278 & -0.1119 & 0.455604 \tabularnewline
11 & -0.015379 & -0.1401 & 0.444456 \tabularnewline
12 & -0.048702 & -0.4437 & 0.329207 \tabularnewline
13 & 0.030579 & 0.2786 & 0.390629 \tabularnewline
14 & -0.004063 & -0.037 & 0.48528 \tabularnewline
15 & -0.007686 & -0.07 & 0.472171 \tabularnewline
16 & 0.044278 & 0.4034 & 0.34385 \tabularnewline
17 & -0.081189 & -0.7397 & 0.230796 \tabularnewline
18 & 0.075576 & 0.6885 & 0.246521 \tabularnewline
19 & 0.072476 & 0.6603 & 0.25545 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234315&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]0.012485[/C][C]0.1137[/C][C]0.454858[/C][/ROW]
[ROW][C]2[/C][C]-0.012135[/C][C]-0.1106[/C][C]0.456117[/C][/ROW]
[ROW][C]3[/C][C]0.100456[/C][C]0.9152[/C][C]0.18137[/C][/ROW]
[ROW][C]4[/C][C]-0.113158[/C][C]-1.0309[/C][C]0.152788[/C][/ROW]
[ROW][C]5[/C][C]0.167787[/C][C]1.5286[/C][C]0.065081[/C][/ROW]
[ROW][C]6[/C][C]0.143484[/C][C]1.3072[/C][C]0.097377[/C][/ROW]
[ROW][C]7[/C][C]-0.019991[/C][C]-0.1821[/C][C]0.427964[/C][/ROW]
[ROW][C]8[/C][C]0.055998[/C][C]0.5102[/C][C]0.305643[/C][/ROW]
[ROW][C]9[/C][C]-0.139124[/C][C]-1.2675[/C][C]0.104265[/C][/ROW]
[ROW][C]10[/C][C]-0.012278[/C][C]-0.1119[/C][C]0.455604[/C][/ROW]
[ROW][C]11[/C][C]-0.015379[/C][C]-0.1401[/C][C]0.444456[/C][/ROW]
[ROW][C]12[/C][C]-0.048702[/C][C]-0.4437[/C][C]0.329207[/C][/ROW]
[ROW][C]13[/C][C]0.030579[/C][C]0.2786[/C][C]0.390629[/C][/ROW]
[ROW][C]14[/C][C]-0.004063[/C][C]-0.037[/C][C]0.48528[/C][/ROW]
[ROW][C]15[/C][C]-0.007686[/C][C]-0.07[/C][C]0.472171[/C][/ROW]
[ROW][C]16[/C][C]0.044278[/C][C]0.4034[/C][C]0.34385[/C][/ROW]
[ROW][C]17[/C][C]-0.081189[/C][C]-0.7397[/C][C]0.230796[/C][/ROW]
[ROW][C]18[/C][C]0.075576[/C][C]0.6885[/C][C]0.246521[/C][/ROW]
[ROW][C]19[/C][C]0.072476[/C][C]0.6603[/C][C]0.25545[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234315&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	0.012485	0.1137	0.454858
2	-0.012135	-0.1106	0.456117
3	0.100456	0.9152	0.18137
4	-0.113158	-1.0309	0.152788
5	0.167787	1.5286	0.065081
6	0.143484	1.3072	0.097377
7	-0.019991	-0.1821	0.427964
8	0.055998	0.5102	0.305643
9	-0.139124	-1.2675	0.104265
10	-0.012278	-0.1119	0.455604
11	-0.015379	-0.1401	0.444456
12	-0.048702	-0.4437	0.329207
13	0.030579	0.2786	0.390629
14	-0.004063	-0.037	0.48528
15	-0.007686	-0.07	0.472171
16	0.044278	0.4034	0.34385
17	-0.081189	-0.7397	0.230796
18	0.075576	0.6885	0.246521
19	0.072476	0.6603	0.25545

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

Parameters (R input):

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code