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Author's title

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, 29 Dec 2010 01:15:48 +0000

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/2010/Dec/29/t1293586066reiusuauocy6257.htm/, Retrieved Fri, 03 May 2024 05:21:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116588, Retrieved Fri, 03 May 2024 05:21:33 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

157

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

-     [(Partial) Autocorrelation Function] [] [2010-12-22 14:59:16] [30ad580cd6d52fd70fb475df3c05f95d]
-   PD    [(Partial) Autocorrelation Function] [paper - ACF 00] [2010-12-29 01:15:48] [54d0a09f418287eaabab8ba43e4b06f8] [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	9 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 9 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116588&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116588&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116588&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	9 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.448259	6.014	0
2	0.247015	3.3141	0.000556
3	0.011347	0.1522	0.439585
4	-0.2212	-2.9677	0.001704
5	-0.288158	-3.866	7.7e-05
6	-0.420248	-5.6382	0
7	-0.28007	-3.7575	0.000116
8	-0.226617	-3.0404	0.001358
9	0.049525	0.6644	0.253628
10	0.211163	2.833	0.002568
11	0.304622	4.0869	3.3e-05
12	0.63999	8.5864	0
13	0.321436	4.3125	1.3e-05
14	0.224033	3.0057	0.001514
15	0.024448	0.328	0.371643
16	-0.174092	-2.3357	0.010305
17	-0.228747	-3.069	0.00124
18	-0.359715	-4.8261	1e-06
19	-0.253925	-3.4068	0.000405
20	-0.206148	-2.7658	0.003136
21	0.027434	0.3681	0.35663
22	0.204504	2.7437	0.003345

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.448259 & 6.014 & 0 \tabularnewline
2 & 0.247015 & 3.3141 & 0.000556 \tabularnewline
3 & 0.011347 & 0.1522 & 0.439585 \tabularnewline
4 & -0.2212 & -2.9677 & 0.001704 \tabularnewline
5 & -0.288158 & -3.866 & 7.7e-05 \tabularnewline
6 & -0.420248 & -5.6382 & 0 \tabularnewline
7 & -0.28007 & -3.7575 & 0.000116 \tabularnewline
8 & -0.226617 & -3.0404 & 0.001358 \tabularnewline
9 & 0.049525 & 0.6644 & 0.253628 \tabularnewline
10 & 0.211163 & 2.833 & 0.002568 \tabularnewline
11 & 0.304622 & 4.0869 & 3.3e-05 \tabularnewline
12 & 0.63999 & 8.5864 & 0 \tabularnewline
13 & 0.321436 & 4.3125 & 1.3e-05 \tabularnewline
14 & 0.224033 & 3.0057 & 0.001514 \tabularnewline
15 & 0.024448 & 0.328 & 0.371643 \tabularnewline
16 & -0.174092 & -2.3357 & 0.010305 \tabularnewline
17 & -0.228747 & -3.069 & 0.00124 \tabularnewline
18 & -0.359715 & -4.8261 & 1e-06 \tabularnewline
19 & -0.253925 & -3.4068 & 0.000405 \tabularnewline
20 & -0.206148 & -2.7658 & 0.003136 \tabularnewline
21 & 0.027434 & 0.3681 & 0.35663 \tabularnewline
22 & 0.204504 & 2.7437 & 0.003345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116588&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]0.448259[/C][C]6.014[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.247015[/C][C]3.3141[/C][C]0.000556[/C][/ROW]
[ROW][C]3[/C][C]0.011347[/C][C]0.1522[/C][C]0.439585[/C][/ROW]
[ROW][C]4[/C][C]-0.2212[/C][C]-2.9677[/C][C]0.001704[/C][/ROW]
[ROW][C]5[/C][C]-0.288158[/C][C]-3.866[/C][C]7.7e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.420248[/C][C]-5.6382[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.28007[/C][C]-3.7575[/C][C]0.000116[/C][/ROW]
[ROW][C]8[/C][C]-0.226617[/C][C]-3.0404[/C][C]0.001358[/C][/ROW]
[ROW][C]9[/C][C]0.049525[/C][C]0.6644[/C][C]0.253628[/C][/ROW]
[ROW][C]10[/C][C]0.211163[/C][C]2.833[/C][C]0.002568[/C][/ROW]
[ROW][C]11[/C][C]0.304622[/C][C]4.0869[/C][C]3.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.63999[/C][C]8.5864[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.321436[/C][C]4.3125[/C][C]1.3e-05[/C][/ROW]
[ROW][C]14[/C][C]0.224033[/C][C]3.0057[/C][C]0.001514[/C][/ROW]
[ROW][C]15[/C][C]0.024448[/C][C]0.328[/C][C]0.371643[/C][/ROW]
[ROW][C]16[/C][C]-0.174092[/C][C]-2.3357[/C][C]0.010305[/C][/ROW]
[ROW][C]17[/C][C]-0.228747[/C][C]-3.069[/C][C]0.00124[/C][/ROW]
[ROW][C]18[/C][C]-0.359715[/C][C]-4.8261[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.253925[/C][C]-3.4068[/C][C]0.000405[/C][/ROW]
[ROW][C]20[/C][C]-0.206148[/C][C]-2.7658[/C][C]0.003136[/C][/ROW]
[ROW][C]21[/C][C]0.027434[/C][C]0.3681[/C][C]0.35663[/C][/ROW]
[ROW][C]22[/C][C]0.204504[/C][C]2.7437[/C][C]0.003345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116588&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116588&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	0.448259	6.014	0
2	0.247015	3.3141	0.000556
3	0.011347	0.1522	0.439585
4	-0.2212	-2.9677	0.001704
5	-0.288158	-3.866	7.7e-05
6	-0.420248	-5.6382	0
7	-0.28007	-3.7575	0.000116
8	-0.226617	-3.0404	0.001358
9	0.049525	0.6644	0.253628
10	0.211163	2.833	0.002568
11	0.304622	4.0869	3.3e-05
12	0.63999	8.5864	0
13	0.321436	4.3125	1.3e-05
14	0.224033	3.0057	0.001514
15	0.024448	0.328	0.371643
16	-0.174092	-2.3357	0.010305
17	-0.228747	-3.069	0.00124
18	-0.359715	-4.8261	1e-06
19	-0.253925	-3.4068	0.000405
20	-0.206148	-2.7658	0.003136
21	0.027434	0.3681	0.35663
22	0.204504	2.7437	0.003345

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.448259	6.014	0
2	0.057666	0.7737	0.22007
3	-0.149225	-2.0021	0.02339
4	-0.242739	-3.2567	0.000674
5	-0.112864	-1.5142	0.065862
6	-0.252197	-3.3836	0.000439
7	0.002873	0.0385	0.48465
8	-0.111665	-1.4981	0.067924
9	0.172732	2.3174	0.010802
10	0.075085	1.0074	0.157553
11	0.095332	1.279	0.10127
12	0.500171	6.7105	0
13	-0.176681	-2.3704	0.009413
14	0.062661	0.8407	0.200821
15	0.046724	0.6269	0.265771
16	-0.025205	-0.3382	0.36782
17	0.056556	0.7588	0.22449
18	-0.036995	-0.4963	0.31013
19	-0.028316	-0.3799	0.352236
20	0.037566	0.504	0.307438
21	-0.03562	-0.4779	0.316655
22	0.110594	1.4838	0.069808

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.448259 & 6.014 & 0 \tabularnewline
2 & 0.057666 & 0.7737 & 0.22007 \tabularnewline
3 & -0.149225 & -2.0021 & 0.02339 \tabularnewline
4 & -0.242739 & -3.2567 & 0.000674 \tabularnewline
5 & -0.112864 & -1.5142 & 0.065862 \tabularnewline
6 & -0.252197 & -3.3836 & 0.000439 \tabularnewline
7 & 0.002873 & 0.0385 & 0.48465 \tabularnewline
8 & -0.111665 & -1.4981 & 0.067924 \tabularnewline
9 & 0.172732 & 2.3174 & 0.010802 \tabularnewline
10 & 0.075085 & 1.0074 & 0.157553 \tabularnewline
11 & 0.095332 & 1.279 & 0.10127 \tabularnewline
12 & 0.500171 & 6.7105 & 0 \tabularnewline
13 & -0.176681 & -2.3704 & 0.009413 \tabularnewline
14 & 0.062661 & 0.8407 & 0.200821 \tabularnewline
15 & 0.046724 & 0.6269 & 0.265771 \tabularnewline
16 & -0.025205 & -0.3382 & 0.36782 \tabularnewline
17 & 0.056556 & 0.7588 & 0.22449 \tabularnewline
18 & -0.036995 & -0.4963 & 0.31013 \tabularnewline
19 & -0.028316 & -0.3799 & 0.352236 \tabularnewline
20 & 0.037566 & 0.504 & 0.307438 \tabularnewline
21 & -0.03562 & -0.4779 & 0.316655 \tabularnewline
22 & 0.110594 & 1.4838 & 0.069808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116588&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]0.448259[/C][C]6.014[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.057666[/C][C]0.7737[/C][C]0.22007[/C][/ROW]
[ROW][C]3[/C][C]-0.149225[/C][C]-2.0021[/C][C]0.02339[/C][/ROW]
[ROW][C]4[/C][C]-0.242739[/C][C]-3.2567[/C][C]0.000674[/C][/ROW]
[ROW][C]5[/C][C]-0.112864[/C][C]-1.5142[/C][C]0.065862[/C][/ROW]
[ROW][C]6[/C][C]-0.252197[/C][C]-3.3836[/C][C]0.000439[/C][/ROW]
[ROW][C]7[/C][C]0.002873[/C][C]0.0385[/C][C]0.48465[/C][/ROW]
[ROW][C]8[/C][C]-0.111665[/C][C]-1.4981[/C][C]0.067924[/C][/ROW]
[ROW][C]9[/C][C]0.172732[/C][C]2.3174[/C][C]0.010802[/C][/ROW]
[ROW][C]10[/C][C]0.075085[/C][C]1.0074[/C][C]0.157553[/C][/ROW]
[ROW][C]11[/C][C]0.095332[/C][C]1.279[/C][C]0.10127[/C][/ROW]
[ROW][C]12[/C][C]0.500171[/C][C]6.7105[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.176681[/C][C]-2.3704[/C][C]0.009413[/C][/ROW]
[ROW][C]14[/C][C]0.062661[/C][C]0.8407[/C][C]0.200821[/C][/ROW]
[ROW][C]15[/C][C]0.046724[/C][C]0.6269[/C][C]0.265771[/C][/ROW]
[ROW][C]16[/C][C]-0.025205[/C][C]-0.3382[/C][C]0.36782[/C][/ROW]
[ROW][C]17[/C][C]0.056556[/C][C]0.7588[/C][C]0.22449[/C][/ROW]
[ROW][C]18[/C][C]-0.036995[/C][C]-0.4963[/C][C]0.31013[/C][/ROW]
[ROW][C]19[/C][C]-0.028316[/C][C]-0.3799[/C][C]0.352236[/C][/ROW]
[ROW][C]20[/C][C]0.037566[/C][C]0.504[/C][C]0.307438[/C][/ROW]
[ROW][C]21[/C][C]-0.03562[/C][C]-0.4779[/C][C]0.316655[/C][/ROW]
[ROW][C]22[/C][C]0.110594[/C][C]1.4838[/C][C]0.069808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116588&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116588&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	0.448259	6.014	0
2	0.057666	0.7737	0.22007
3	-0.149225	-2.0021	0.02339
4	-0.242739	-3.2567	0.000674
5	-0.112864	-1.5142	0.065862
6	-0.252197	-3.3836	0.000439
7	0.002873	0.0385	0.48465
8	-0.111665	-1.4981	0.067924
9	0.172732	2.3174	0.010802
10	0.075085	1.0074	0.157553
11	0.095332	1.279	0.10127
12	0.500171	6.7105	0
13	-0.176681	-2.3704	0.009413
14	0.062661	0.8407	0.200821
15	0.046724	0.6269	0.265771
16	-0.025205	-0.3382	0.36782
17	0.056556	0.7588	0.22449
18	-0.036995	-0.4963	0.31013
19	-0.028316	-0.3799	0.352236
20	0.037566	0.504	0.307438
21	-0.03562	-0.4779	0.316655
22	0.110594	1.4838	0.069808

Figure 1

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

Parameters (R input):

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code