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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 10:05:34 +0100

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/2016/Dec/23/t1482484053np55w7w503fr7ut.htm/, Retrieved Tue, 07 May 2024 14:44:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302790, Retrieved Tue, 07 May 2024 14:44:50 +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] [Partial correlati...] [2016-12-23 09:05:34] [bb262dce3bb40077245e847c94886178] [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	2 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302790&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302790&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302790&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.596696	-6.343	0
2	0.05816	0.6183	0.268826
3	0.150375	1.5985	0.056362
4	-0.169095	-1.7975	0.037463
5	0.056856	0.6044	0.2734
6	0.08457	0.899	0.185285
7	-0.105923	-1.126	0.13128
8	-0.126377	-1.3434	0.090915
9	0.383472	4.0764	4.3e-05
10	-0.421158	-4.477	9e-06
11	0.371241	3.9464	6.9e-05
12	-0.186621	-1.9838	0.024851
13	-0.16634	-1.7682	0.039862
14	0.295555	3.1418	0.001072
15	-0.1393	-1.4808	0.070723
16	-0.070644	-0.751	0.227119
17	0.131587	1.3988	0.082308
18	-0.029601	-0.3147	0.376798
19	-0.114768	-1.22	0.112502
20	0.244338	2.5974	0.005322
21	-0.165776	-1.7622	0.040368

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.596696 & -6.343 & 0 \tabularnewline
2 & 0.05816 & 0.6183 & 0.268826 \tabularnewline
3 & 0.150375 & 1.5985 & 0.056362 \tabularnewline
4 & -0.169095 & -1.7975 & 0.037463 \tabularnewline
5 & 0.056856 & 0.6044 & 0.2734 \tabularnewline
6 & 0.08457 & 0.899 & 0.185285 \tabularnewline
7 & -0.105923 & -1.126 & 0.13128 \tabularnewline
8 & -0.126377 & -1.3434 & 0.090915 \tabularnewline
9 & 0.383472 & 4.0764 & 4.3e-05 \tabularnewline
10 & -0.421158 & -4.477 & 9e-06 \tabularnewline
11 & 0.371241 & 3.9464 & 6.9e-05 \tabularnewline
12 & -0.186621 & -1.9838 & 0.024851 \tabularnewline
13 & -0.16634 & -1.7682 & 0.039862 \tabularnewline
14 & 0.295555 & 3.1418 & 0.001072 \tabularnewline
15 & -0.1393 & -1.4808 & 0.070723 \tabularnewline
16 & -0.070644 & -0.751 & 0.227119 \tabularnewline
17 & 0.131587 & 1.3988 & 0.082308 \tabularnewline
18 & -0.029601 & -0.3147 & 0.376798 \tabularnewline
19 & -0.114768 & -1.22 & 0.112502 \tabularnewline
20 & 0.244338 & 2.5974 & 0.005322 \tabularnewline
21 & -0.165776 & -1.7622 & 0.040368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302790&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]-0.596696[/C][C]-6.343[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.05816[/C][C]0.6183[/C][C]0.268826[/C][/ROW]
[ROW][C]3[/C][C]0.150375[/C][C]1.5985[/C][C]0.056362[/C][/ROW]
[ROW][C]4[/C][C]-0.169095[/C][C]-1.7975[/C][C]0.037463[/C][/ROW]
[ROW][C]5[/C][C]0.056856[/C][C]0.6044[/C][C]0.2734[/C][/ROW]
[ROW][C]6[/C][C]0.08457[/C][C]0.899[/C][C]0.185285[/C][/ROW]
[ROW][C]7[/C][C]-0.105923[/C][C]-1.126[/C][C]0.13128[/C][/ROW]
[ROW][C]8[/C][C]-0.126377[/C][C]-1.3434[/C][C]0.090915[/C][/ROW]
[ROW][C]9[/C][C]0.383472[/C][C]4.0764[/C][C]4.3e-05[/C][/ROW]
[ROW][C]10[/C][C]-0.421158[/C][C]-4.477[/C][C]9e-06[/C][/ROW]
[ROW][C]11[/C][C]0.371241[/C][C]3.9464[/C][C]6.9e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.186621[/C][C]-1.9838[/C][C]0.024851[/C][/ROW]
[ROW][C]13[/C][C]-0.16634[/C][C]-1.7682[/C][C]0.039862[/C][/ROW]
[ROW][C]14[/C][C]0.295555[/C][C]3.1418[/C][C]0.001072[/C][/ROW]
[ROW][C]15[/C][C]-0.1393[/C][C]-1.4808[/C][C]0.070723[/C][/ROW]
[ROW][C]16[/C][C]-0.070644[/C][C]-0.751[/C][C]0.227119[/C][/ROW]
[ROW][C]17[/C][C]0.131587[/C][C]1.3988[/C][C]0.082308[/C][/ROW]
[ROW][C]18[/C][C]-0.029601[/C][C]-0.3147[/C][C]0.376798[/C][/ROW]
[ROW][C]19[/C][C]-0.114768[/C][C]-1.22[/C][C]0.112502[/C][/ROW]
[ROW][C]20[/C][C]0.244338[/C][C]2.5974[/C][C]0.005322[/C][/ROW]
[ROW][C]21[/C][C]-0.165776[/C][C]-1.7622[/C][C]0.040368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302790&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302790&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	-0.596696	-6.343	0
2	0.05816	0.6183	0.268826
3	0.150375	1.5985	0.056362
4	-0.169095	-1.7975	0.037463
5	0.056856	0.6044	0.2734
6	0.08457	0.899	0.185285
7	-0.105923	-1.126	0.13128
8	-0.126377	-1.3434	0.090915
9	0.383472	4.0764	4.3e-05
10	-0.421158	-4.477	9e-06
11	0.371241	3.9464	6.9e-05
12	-0.186621	-1.9838	0.024851
13	-0.16634	-1.7682	0.039862
14	0.295555	3.1418	0.001072
15	-0.1393	-1.4808	0.070723
16	-0.070644	-0.751	0.227119
17	0.131587	1.3988	0.082308
18	-0.029601	-0.3147	0.376798
19	-0.114768	-1.22	0.112502
20	0.244338	2.5974	0.005322
21	-0.165776	-1.7622	0.040368

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.596696	-6.343	0
2	-0.46259	-4.9174	1e-06
3	-0.147965	-1.5729	0.05927
4	-0.164506	-1.7487	0.041528
5	-0.173019	-1.8392	0.034255
6	-0.010249	-0.109	0.456717
7	0.008742	0.0929	0.463063
8	-0.36337	-3.8627	9.4e-05
9	0.086707	0.9217	0.179323
10	-0.16566	-1.761	0.040473
11	0.251308	2.6714	0.004334
12	0.096331	1.024	0.154007
13	-0.227762	-2.4211	0.008532
14	-0.119812	-1.2736	0.102706
15	-0.06301	-0.6698	0.252175
16	-0.159984	-1.7007	0.045879
17	-0.015699	-0.1669	0.43388
18	-0.052889	-0.5622	0.287541
19	0.022441	0.2386	0.405942
20	-0.079699	-0.8472	0.199335
21	0.126145	1.3409	0.091314

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.596696 & -6.343 & 0 \tabularnewline
2 & -0.46259 & -4.9174 & 1e-06 \tabularnewline
3 & -0.147965 & -1.5729 & 0.05927 \tabularnewline
4 & -0.164506 & -1.7487 & 0.041528 \tabularnewline
5 & -0.173019 & -1.8392 & 0.034255 \tabularnewline
6 & -0.010249 & -0.109 & 0.456717 \tabularnewline
7 & 0.008742 & 0.0929 & 0.463063 \tabularnewline
8 & -0.36337 & -3.8627 & 9.4e-05 \tabularnewline
9 & 0.086707 & 0.9217 & 0.179323 \tabularnewline
10 & -0.16566 & -1.761 & 0.040473 \tabularnewline
11 & 0.251308 & 2.6714 & 0.004334 \tabularnewline
12 & 0.096331 & 1.024 & 0.154007 \tabularnewline
13 & -0.227762 & -2.4211 & 0.008532 \tabularnewline
14 & -0.119812 & -1.2736 & 0.102706 \tabularnewline
15 & -0.06301 & -0.6698 & 0.252175 \tabularnewline
16 & -0.159984 & -1.7007 & 0.045879 \tabularnewline
17 & -0.015699 & -0.1669 & 0.43388 \tabularnewline
18 & -0.052889 & -0.5622 & 0.287541 \tabularnewline
19 & 0.022441 & 0.2386 & 0.405942 \tabularnewline
20 & -0.079699 & -0.8472 & 0.199335 \tabularnewline
21 & 0.126145 & 1.3409 & 0.091314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302790&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]-0.596696[/C][C]-6.343[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.46259[/C][C]-4.9174[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.147965[/C][C]-1.5729[/C][C]0.05927[/C][/ROW]
[ROW][C]4[/C][C]-0.164506[/C][C]-1.7487[/C][C]0.041528[/C][/ROW]
[ROW][C]5[/C][C]-0.173019[/C][C]-1.8392[/C][C]0.034255[/C][/ROW]
[ROW][C]6[/C][C]-0.010249[/C][C]-0.109[/C][C]0.456717[/C][/ROW]
[ROW][C]7[/C][C]0.008742[/C][C]0.0929[/C][C]0.463063[/C][/ROW]
[ROW][C]8[/C][C]-0.36337[/C][C]-3.8627[/C][C]9.4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.086707[/C][C]0.9217[/C][C]0.179323[/C][/ROW]
[ROW][C]10[/C][C]-0.16566[/C][C]-1.761[/C][C]0.040473[/C][/ROW]
[ROW][C]11[/C][C]0.251308[/C][C]2.6714[/C][C]0.004334[/C][/ROW]
[ROW][C]12[/C][C]0.096331[/C][C]1.024[/C][C]0.154007[/C][/ROW]
[ROW][C]13[/C][C]-0.227762[/C][C]-2.4211[/C][C]0.008532[/C][/ROW]
[ROW][C]14[/C][C]-0.119812[/C][C]-1.2736[/C][C]0.102706[/C][/ROW]
[ROW][C]15[/C][C]-0.06301[/C][C]-0.6698[/C][C]0.252175[/C][/ROW]
[ROW][C]16[/C][C]-0.159984[/C][C]-1.7007[/C][C]0.045879[/C][/ROW]
[ROW][C]17[/C][C]-0.015699[/C][C]-0.1669[/C][C]0.43388[/C][/ROW]
[ROW][C]18[/C][C]-0.052889[/C][C]-0.5622[/C][C]0.287541[/C][/ROW]
[ROW][C]19[/C][C]0.022441[/C][C]0.2386[/C][C]0.405942[/C][/ROW]
[ROW][C]20[/C][C]-0.079699[/C][C]-0.8472[/C][C]0.199335[/C][/ROW]
[ROW][C]21[/C][C]0.126145[/C][C]1.3409[/C][C]0.091314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302790&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302790&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	-0.596696	-6.343	0
2	-0.46259	-4.9174	1e-06
3	-0.147965	-1.5729	0.05927
4	-0.164506	-1.7487	0.041528
5	-0.173019	-1.8392	0.034255
6	-0.010249	-0.109	0.456717
7	0.008742	0.0929	0.463063
8	-0.36337	-3.8627	9.4e-05
9	0.086707	0.9217	0.179323
10	-0.16566	-1.761	0.040473
11	0.251308	2.6714	0.004334
12	0.096331	1.024	0.154007
13	-0.227762	-2.4211	0.008532
14	-0.119812	-1.2736	0.102706
15	-0.06301	-0.6698	0.252175
16	-0.159984	-1.7007	0.045879
17	-0.015699	-0.1669	0.43388
18	-0.052889	-0.5622	0.287541
19	0.022441	0.2386	0.405942
20	-0.079699	-0.8472	0.199335
21	0.126145	1.3409	0.091314

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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)
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,'ACF(k)',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,'PACF(k)',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