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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 06 Dec 2017 17:57:57 +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/2017/Dec/06/t1512579522fog8rcc440ybj8y.htm/, Retrieved Mon, 13 May 2024 23:16:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308626, Retrieved Mon, 13 May 2024 23:16:29 +0000

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No (this computation is public)

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [autocorrelation (...] [2017-12-06 16:57:57] [33956d13de8d8b5d5d1b78ead3554acb] [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=308626&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=308626&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308626&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	-0.54211	-7.6474	0
2	0.02631	0.3711	0.355463
3	0.232249	3.2763	0.00062
4	-0.209399	-2.9539	0.001758
5	0.046739	0.6593	0.255221
6	0.091488	1.2906	0.09917
7	-0.089561	-1.2634	0.103959
8	0.063786	0.8998	0.184653
9	-0.027059	-0.3817	0.351541
10	-0.018393	-0.2595	0.39777
11	0.1895	2.6732	0.004068
12	-0.371624	-5.2424	0
13	0.254066	3.584	0.000213
14	-0.136073	-1.9195	0.028173
15	0.03699	0.5218	0.301194
16	0.035142	0.4957	0.310314
17	-0.077233	-1.0895	0.138625
18	0.02715	0.383	0.351065
19	-0.010473	-0.1477	0.441347
20	-0.040734	-0.5746	0.283097
21	0.087258	1.2309	0.109901
22	-0.149497	-2.1089	0.018101
23	0.159599	2.2514	0.012726

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.54211 & -7.6474 & 0 \tabularnewline
2 & 0.02631 & 0.3711 & 0.355463 \tabularnewline
3 & 0.232249 & 3.2763 & 0.00062 \tabularnewline
4 & -0.209399 & -2.9539 & 0.001758 \tabularnewline
5 & 0.046739 & 0.6593 & 0.255221 \tabularnewline
6 & 0.091488 & 1.2906 & 0.09917 \tabularnewline
7 & -0.089561 & -1.2634 & 0.103959 \tabularnewline
8 & 0.063786 & 0.8998 & 0.184653 \tabularnewline
9 & -0.027059 & -0.3817 & 0.351541 \tabularnewline
10 & -0.018393 & -0.2595 & 0.39777 \tabularnewline
11 & 0.1895 & 2.6732 & 0.004068 \tabularnewline
12 & -0.371624 & -5.2424 & 0 \tabularnewline
13 & 0.254066 & 3.584 & 0.000213 \tabularnewline
14 & -0.136073 & -1.9195 & 0.028173 \tabularnewline
15 & 0.03699 & 0.5218 & 0.301194 \tabularnewline
16 & 0.035142 & 0.4957 & 0.310314 \tabularnewline
17 & -0.077233 & -1.0895 & 0.138625 \tabularnewline
18 & 0.02715 & 0.383 & 0.351065 \tabularnewline
19 & -0.010473 & -0.1477 & 0.441347 \tabularnewline
20 & -0.040734 & -0.5746 & 0.283097 \tabularnewline
21 & 0.087258 & 1.2309 & 0.109901 \tabularnewline
22 & -0.149497 & -2.1089 & 0.018101 \tabularnewline
23 & 0.159599 & 2.2514 & 0.012726 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308626&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]-0.54211[/C][C]-7.6474[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.02631[/C][C]0.3711[/C][C]0.355463[/C][/ROW]
[ROW][C]3[/C][C]0.232249[/C][C]3.2763[/C][C]0.00062[/C][/ROW]
[ROW][C]4[/C][C]-0.209399[/C][C]-2.9539[/C][C]0.001758[/C][/ROW]
[ROW][C]5[/C][C]0.046739[/C][C]0.6593[/C][C]0.255221[/C][/ROW]
[ROW][C]6[/C][C]0.091488[/C][C]1.2906[/C][C]0.09917[/C][/ROW]
[ROW][C]7[/C][C]-0.089561[/C][C]-1.2634[/C][C]0.103959[/C][/ROW]
[ROW][C]8[/C][C]0.063786[/C][C]0.8998[/C][C]0.184653[/C][/ROW]
[ROW][C]9[/C][C]-0.027059[/C][C]-0.3817[/C][C]0.351541[/C][/ROW]
[ROW][C]10[/C][C]-0.018393[/C][C]-0.2595[/C][C]0.39777[/C][/ROW]
[ROW][C]11[/C][C]0.1895[/C][C]2.6732[/C][C]0.004068[/C][/ROW]
[ROW][C]12[/C][C]-0.371624[/C][C]-5.2424[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.254066[/C][C]3.584[/C][C]0.000213[/C][/ROW]
[ROW][C]14[/C][C]-0.136073[/C][C]-1.9195[/C][C]0.028173[/C][/ROW]
[ROW][C]15[/C][C]0.03699[/C][C]0.5218[/C][C]0.301194[/C][/ROW]
[ROW][C]16[/C][C]0.035142[/C][C]0.4957[/C][C]0.310314[/C][/ROW]
[ROW][C]17[/C][C]-0.077233[/C][C]-1.0895[/C][C]0.138625[/C][/ROW]
[ROW][C]18[/C][C]0.02715[/C][C]0.383[/C][C]0.351065[/C][/ROW]
[ROW][C]19[/C][C]-0.010473[/C][C]-0.1477[/C][C]0.441347[/C][/ROW]
[ROW][C]20[/C][C]-0.040734[/C][C]-0.5746[/C][C]0.283097[/C][/ROW]
[ROW][C]21[/C][C]0.087258[/C][C]1.2309[/C][C]0.109901[/C][/ROW]
[ROW][C]22[/C][C]-0.149497[/C][C]-2.1089[/C][C]0.018101[/C][/ROW]
[ROW][C]23[/C][C]0.159599[/C][C]2.2514[/C][C]0.012726[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308626&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308626&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	-0.54211	-7.6474	0
2	0.02631	0.3711	0.355463
3	0.232249	3.2763	0.00062
4	-0.209399	-2.9539	0.001758
5	0.046739	0.6593	0.255221
6	0.091488	1.2906	0.09917
7	-0.089561	-1.2634	0.103959
8	0.063786	0.8998	0.184653
9	-0.027059	-0.3817	0.351541
10	-0.018393	-0.2595	0.39777
11	0.1895	2.6732	0.004068
12	-0.371624	-5.2424	0
13	0.254066	3.584	0.000213
14	-0.136073	-1.9195	0.028173
15	0.03699	0.5218	0.301194
16	0.035142	0.4957	0.310314
17	-0.077233	-1.0895	0.138625
18	0.02715	0.383	0.351065
19	-0.010473	-0.1477	0.441347
20	-0.040734	-0.5746	0.283097
21	0.087258	1.2309	0.109901
22	-0.149497	-2.1089	0.018101
23	0.159599	2.2514	0.012726

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.54211	-7.6474	0
2	-0.378937	-5.3456	0
3	0.076879	1.0845	0.139725
4	0.012616	0.178	0.429462
5	-0.042592	-0.6008	0.274317
6	0.033254	0.4691	0.319754
7	0.042805	0.6038	0.273318
8	0.075605	1.0665	0.143736
9	0.000753	0.0106	0.495767
10	-0.026672	-0.3763	0.353563
11	0.252978	3.5687	0.000225
12	-0.224665	-3.1693	0.000885
13	-0.12597	-1.777	0.038546
14	-0.258031	-3.64	0.000174
15	0.045847	0.6467	0.25927
16	0.005677	0.0801	0.468127
17	-0.075091	-1.0593	0.145376
18	-0.06211	-0.8762	0.190997
19	-0.042449	-0.5988	0.27499
20	-0.031293	-0.4414	0.329684
21	0.058828	0.8299	0.203805
22	-0.14822	-2.0909	0.018904
23	0.242686	3.4235	0.000375

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.54211 & -7.6474 & 0 \tabularnewline
2 & -0.378937 & -5.3456 & 0 \tabularnewline
3 & 0.076879 & 1.0845 & 0.139725 \tabularnewline
4 & 0.012616 & 0.178 & 0.429462 \tabularnewline
5 & -0.042592 & -0.6008 & 0.274317 \tabularnewline
6 & 0.033254 & 0.4691 & 0.319754 \tabularnewline
7 & 0.042805 & 0.6038 & 0.273318 \tabularnewline
8 & 0.075605 & 1.0665 & 0.143736 \tabularnewline
9 & 0.000753 & 0.0106 & 0.495767 \tabularnewline
10 & -0.026672 & -0.3763 & 0.353563 \tabularnewline
11 & 0.252978 & 3.5687 & 0.000225 \tabularnewline
12 & -0.224665 & -3.1693 & 0.000885 \tabularnewline
13 & -0.12597 & -1.777 & 0.038546 \tabularnewline
14 & -0.258031 & -3.64 & 0.000174 \tabularnewline
15 & 0.045847 & 0.6467 & 0.25927 \tabularnewline
16 & 0.005677 & 0.0801 & 0.468127 \tabularnewline
17 & -0.075091 & -1.0593 & 0.145376 \tabularnewline
18 & -0.06211 & -0.8762 & 0.190997 \tabularnewline
19 & -0.042449 & -0.5988 & 0.27499 \tabularnewline
20 & -0.031293 & -0.4414 & 0.329684 \tabularnewline
21 & 0.058828 & 0.8299 & 0.203805 \tabularnewline
22 & -0.14822 & -2.0909 & 0.018904 \tabularnewline
23 & 0.242686 & 3.4235 & 0.000375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308626&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]-0.54211[/C][C]-7.6474[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.378937[/C][C]-5.3456[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.076879[/C][C]1.0845[/C][C]0.139725[/C][/ROW]
[ROW][C]4[/C][C]0.012616[/C][C]0.178[/C][C]0.429462[/C][/ROW]
[ROW][C]5[/C][C]-0.042592[/C][C]-0.6008[/C][C]0.274317[/C][/ROW]
[ROW][C]6[/C][C]0.033254[/C][C]0.4691[/C][C]0.319754[/C][/ROW]
[ROW][C]7[/C][C]0.042805[/C][C]0.6038[/C][C]0.273318[/C][/ROW]
[ROW][C]8[/C][C]0.075605[/C][C]1.0665[/C][C]0.143736[/C][/ROW]
[ROW][C]9[/C][C]0.000753[/C][C]0.0106[/C][C]0.495767[/C][/ROW]
[ROW][C]10[/C][C]-0.026672[/C][C]-0.3763[/C][C]0.353563[/C][/ROW]
[ROW][C]11[/C][C]0.252978[/C][C]3.5687[/C][C]0.000225[/C][/ROW]
[ROW][C]12[/C][C]-0.224665[/C][C]-3.1693[/C][C]0.000885[/C][/ROW]
[ROW][C]13[/C][C]-0.12597[/C][C]-1.777[/C][C]0.038546[/C][/ROW]
[ROW][C]14[/C][C]-0.258031[/C][C]-3.64[/C][C]0.000174[/C][/ROW]
[ROW][C]15[/C][C]0.045847[/C][C]0.6467[/C][C]0.25927[/C][/ROW]
[ROW][C]16[/C][C]0.005677[/C][C]0.0801[/C][C]0.468127[/C][/ROW]
[ROW][C]17[/C][C]-0.075091[/C][C]-1.0593[/C][C]0.145376[/C][/ROW]
[ROW][C]18[/C][C]-0.06211[/C][C]-0.8762[/C][C]0.190997[/C][/ROW]
[ROW][C]19[/C][C]-0.042449[/C][C]-0.5988[/C][C]0.27499[/C][/ROW]
[ROW][C]20[/C][C]-0.031293[/C][C]-0.4414[/C][C]0.329684[/C][/ROW]
[ROW][C]21[/C][C]0.058828[/C][C]0.8299[/C][C]0.203805[/C][/ROW]
[ROW][C]22[/C][C]-0.14822[/C][C]-2.0909[/C][C]0.018904[/C][/ROW]
[ROW][C]23[/C][C]0.242686[/C][C]3.4235[/C][C]0.000375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308626&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308626&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	-0.54211	-7.6474	0
2	-0.378937	-5.3456	0
3	0.076879	1.0845	0.139725
4	0.012616	0.178	0.429462
5	-0.042592	-0.6008	0.274317
6	0.033254	0.4691	0.319754
7	0.042805	0.6038	0.273318
8	0.075605	1.0665	0.143736
9	0.000753	0.0106	0.495767
10	-0.026672	-0.3763	0.353563
11	0.252978	3.5687	0.000225
12	-0.224665	-3.1693	0.000885
13	-0.12597	-1.777	0.038546
14	-0.258031	-3.64	0.000174
15	0.045847	0.6467	0.25927
16	0.005677	0.0801	0.468127
17	-0.075091	-1.0593	0.145376
18	-0.06211	-0.8762	0.190997
19	-0.042449	-0.5988	0.27499
20	-0.031293	-0.4414	0.329684
21	0.058828	0.8299	0.203805
22	-0.14822	-2.0909	0.018904
23	0.242686	3.4235	0.000375

Figure 1

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Postscript link

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Figure 2

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Figure 3

PNG link

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Parameters (Session):

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