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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 11 Jan 2016 10:19:56 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/11/t1452507607e19fi19010h7eyw.htm/, Retrieved Tue, 07 May 2024 16:01:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289409, Retrieved Tue, 07 May 2024 16:01:57 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-01-11 10:19:56] [b273fd68f4630bf668d6e366c549a45c] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289409&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289409&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.287146	2.4195	0.009052
2	0.025523	0.2151	0.415168
3	0.003715	0.0313	0.487559
4	-0.227626	-1.918	0.029566
5	-0.367386	-3.0957	0.001405
6	-0.328805	-2.7706	0.003569
7	-0.327001	-2.7554	0.003722
8	-0.299726	-2.5255	0.006893
9	-0.102126	-0.8605	0.196198
10	0.276333	2.3284	0.011371
11	0.409544	3.4509	0.000472
12	0.307306	2.5894	0.005828
13	0.391027	3.2948	0.000769
14	0.205895	1.7349	0.043548
15	-0.098555	-0.8304	0.204538
16	-0.170928	-1.4403	0.077094
17	-0.239472	-2.0178	0.023695
18	-0.311361	-2.6236	0.005322

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.287146 & 2.4195 & 0.009052 \tabularnewline
2 & 0.025523 & 0.2151 & 0.415168 \tabularnewline
3 & 0.003715 & 0.0313 & 0.487559 \tabularnewline
4 & -0.227626 & -1.918 & 0.029566 \tabularnewline
5 & -0.367386 & -3.0957 & 0.001405 \tabularnewline
6 & -0.328805 & -2.7706 & 0.003569 \tabularnewline
7 & -0.327001 & -2.7554 & 0.003722 \tabularnewline
8 & -0.299726 & -2.5255 & 0.006893 \tabularnewline
9 & -0.102126 & -0.8605 & 0.196198 \tabularnewline
10 & 0.276333 & 2.3284 & 0.011371 \tabularnewline
11 & 0.409544 & 3.4509 & 0.000472 \tabularnewline
12 & 0.307306 & 2.5894 & 0.005828 \tabularnewline
13 & 0.391027 & 3.2948 & 0.000769 \tabularnewline
14 & 0.205895 & 1.7349 & 0.043548 \tabularnewline
15 & -0.098555 & -0.8304 & 0.204538 \tabularnewline
16 & -0.170928 & -1.4403 & 0.077094 \tabularnewline
17 & -0.239472 & -2.0178 & 0.023695 \tabularnewline
18 & -0.311361 & -2.6236 & 0.005322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289409&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]0.287146[/C][C]2.4195[/C][C]0.009052[/C][/ROW]
[ROW][C]2[/C][C]0.025523[/C][C]0.2151[/C][C]0.415168[/C][/ROW]
[ROW][C]3[/C][C]0.003715[/C][C]0.0313[/C][C]0.487559[/C][/ROW]
[ROW][C]4[/C][C]-0.227626[/C][C]-1.918[/C][C]0.029566[/C][/ROW]
[ROW][C]5[/C][C]-0.367386[/C][C]-3.0957[/C][C]0.001405[/C][/ROW]
[ROW][C]6[/C][C]-0.328805[/C][C]-2.7706[/C][C]0.003569[/C][/ROW]
[ROW][C]7[/C][C]-0.327001[/C][C]-2.7554[/C][C]0.003722[/C][/ROW]
[ROW][C]8[/C][C]-0.299726[/C][C]-2.5255[/C][C]0.006893[/C][/ROW]
[ROW][C]9[/C][C]-0.102126[/C][C]-0.8605[/C][C]0.196198[/C][/ROW]
[ROW][C]10[/C][C]0.276333[/C][C]2.3284[/C][C]0.011371[/C][/ROW]
[ROW][C]11[/C][C]0.409544[/C][C]3.4509[/C][C]0.000472[/C][/ROW]
[ROW][C]12[/C][C]0.307306[/C][C]2.5894[/C][C]0.005828[/C][/ROW]
[ROW][C]13[/C][C]0.391027[/C][C]3.2948[/C][C]0.000769[/C][/ROW]
[ROW][C]14[/C][C]0.205895[/C][C]1.7349[/C][C]0.043548[/C][/ROW]
[ROW][C]15[/C][C]-0.098555[/C][C]-0.8304[/C][C]0.204538[/C][/ROW]
[ROW][C]16[/C][C]-0.170928[/C][C]-1.4403[/C][C]0.077094[/C][/ROW]
[ROW][C]17[/C][C]-0.239472[/C][C]-2.0178[/C][C]0.023695[/C][/ROW]
[ROW][C]18[/C][C]-0.311361[/C][C]-2.6236[/C][C]0.005322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289409&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	0.287146	2.4195	0.009052
2	0.025523	0.2151	0.415168
3	0.003715	0.0313	0.487559
4	-0.227626	-1.918	0.029566
5	-0.367386	-3.0957	0.001405
6	-0.328805	-2.7706	0.003569
7	-0.327001	-2.7554	0.003722
8	-0.299726	-2.5255	0.006893
9	-0.102126	-0.8605	0.196198
10	0.276333	2.3284	0.011371
11	0.409544	3.4509	0.000472
12	0.307306	2.5894	0.005828
13	0.391027	3.2948	0.000769
14	0.205895	1.7349	0.043548
15	-0.098555	-0.8304	0.204538
16	-0.170928	-1.4403	0.077094
17	-0.239472	-2.0178	0.023695
18	-0.311361	-2.6236	0.005322

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.287146	2.4195	0.009052
2	-0.062045	-0.5228	0.30137
3	0.01504	0.1267	0.449755
4	-0.253205	-2.1335	0.018168
5	-0.264532	-2.229	0.01449
6	-0.217508	-1.8328	0.035516
7	-0.281665	-2.3734	0.010169
8	-0.356153	-3.001	0.001856
9	-0.335416	-2.8263	0.003056
10	-0.031332	-0.264	0.39627
11	0.044821	0.3777	0.353403
12	-0.079522	-0.6701	0.252494
13	0.13649	1.1501	0.126984
14	0.035622	0.3002	0.382467
15	-0.082173	-0.6924	0.245471
16	-0.064579	-0.5441	0.294022
17	-0.028417	-0.2394	0.405725
18	0.078727	0.6634	0.254621

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.287146 & 2.4195 & 0.009052 \tabularnewline
2 & -0.062045 & -0.5228 & 0.30137 \tabularnewline
3 & 0.01504 & 0.1267 & 0.449755 \tabularnewline
4 & -0.253205 & -2.1335 & 0.018168 \tabularnewline
5 & -0.264532 & -2.229 & 0.01449 \tabularnewline
6 & -0.217508 & -1.8328 & 0.035516 \tabularnewline
7 & -0.281665 & -2.3734 & 0.010169 \tabularnewline
8 & -0.356153 & -3.001 & 0.001856 \tabularnewline
9 & -0.335416 & -2.8263 & 0.003056 \tabularnewline
10 & -0.031332 & -0.264 & 0.39627 \tabularnewline
11 & 0.044821 & 0.3777 & 0.353403 \tabularnewline
12 & -0.079522 & -0.6701 & 0.252494 \tabularnewline
13 & 0.13649 & 1.1501 & 0.126984 \tabularnewline
14 & 0.035622 & 0.3002 & 0.382467 \tabularnewline
15 & -0.082173 & -0.6924 & 0.245471 \tabularnewline
16 & -0.064579 & -0.5441 & 0.294022 \tabularnewline
17 & -0.028417 & -0.2394 & 0.405725 \tabularnewline
18 & 0.078727 & 0.6634 & 0.254621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289409&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]0.287146[/C][C]2.4195[/C][C]0.009052[/C][/ROW]
[ROW][C]2[/C][C]-0.062045[/C][C]-0.5228[/C][C]0.30137[/C][/ROW]
[ROW][C]3[/C][C]0.01504[/C][C]0.1267[/C][C]0.449755[/C][/ROW]
[ROW][C]4[/C][C]-0.253205[/C][C]-2.1335[/C][C]0.018168[/C][/ROW]
[ROW][C]5[/C][C]-0.264532[/C][C]-2.229[/C][C]0.01449[/C][/ROW]
[ROW][C]6[/C][C]-0.217508[/C][C]-1.8328[/C][C]0.035516[/C][/ROW]
[ROW][C]7[/C][C]-0.281665[/C][C]-2.3734[/C][C]0.010169[/C][/ROW]
[ROW][C]8[/C][C]-0.356153[/C][C]-3.001[/C][C]0.001856[/C][/ROW]
[ROW][C]9[/C][C]-0.335416[/C][C]-2.8263[/C][C]0.003056[/C][/ROW]
[ROW][C]10[/C][C]-0.031332[/C][C]-0.264[/C][C]0.39627[/C][/ROW]
[ROW][C]11[/C][C]0.044821[/C][C]0.3777[/C][C]0.353403[/C][/ROW]
[ROW][C]12[/C][C]-0.079522[/C][C]-0.6701[/C][C]0.252494[/C][/ROW]
[ROW][C]13[/C][C]0.13649[/C][C]1.1501[/C][C]0.126984[/C][/ROW]
[ROW][C]14[/C][C]0.035622[/C][C]0.3002[/C][C]0.382467[/C][/ROW]
[ROW][C]15[/C][C]-0.082173[/C][C]-0.6924[/C][C]0.245471[/C][/ROW]
[ROW][C]16[/C][C]-0.064579[/C][C]-0.5441[/C][C]0.294022[/C][/ROW]
[ROW][C]17[/C][C]-0.028417[/C][C]-0.2394[/C][C]0.405725[/C][/ROW]
[ROW][C]18[/C][C]0.078727[/C][C]0.6634[/C][C]0.254621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289409&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	0.287146	2.4195	0.009052
2	-0.062045	-0.5228	0.30137
3	0.01504	0.1267	0.449755
4	-0.253205	-2.1335	0.018168
5	-0.264532	-2.229	0.01449
6	-0.217508	-1.8328	0.035516
7	-0.281665	-2.3734	0.010169
8	-0.356153	-3.001	0.001856
9	-0.335416	-2.8263	0.003056
10	-0.031332	-0.264	0.39627
11	0.044821	0.3777	0.353403
12	-0.079522	-0.6701	0.252494
13	0.13649	1.1501	0.126984
14	0.035622	0.3002	0.382467
15	-0.082173	-0.6924	0.245471
16	-0.064579	-0.5441	0.294022
17	-0.028417	-0.2394	0.405725
18	0.078727	0.6634	0.254621

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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)
x <- na.omit(x)
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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code