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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 25 May 2012 09:24:06 -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/2012/May/25/t13379522798iaq6lxg8gznr3l.htm/, Retrieved Sat, 04 May 2024 01:53:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167489, Retrieved Sat, 04 May 2024 01:53:53 +0000

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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] [autocorelatie ] [2012-05-25 13:24:06] [c6701916d11cfe737d4a1a362ef25325] [Current]

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Dataseries X:

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Histogram

Boxplots

7.72
7.67
7.84
7.79
7.83
7.94
8.02
8.06
8.12
8.13
7.97
8.01
8.00
7.90
7.99
8.02
8.08
8.02
8.07
8.11
8.19
8.16
8.08
8.22
8.15
8.19
8.31
8.30
8.34
8.31
8.38
8.34
8.44
8.64
8.60
8.61
8.54
8.69
8.73
8.91
9.01
9.08
8.94
9.03
9.02
8.96
9.03
8.94
8.95
8.95
8.99
8.93
8.98
8.95
9.02
8.92
9.10
9.06
8.97
8.89

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	'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167489&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167489&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167489&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.95151	7.3704	0
2	0.90284	6.9934	0
3	0.856359	6.6333	0
4	0.804288	6.23	0
5	0.758939	5.8787	0
6	0.718494	5.5654	0
7	0.682174	5.2841	1e-06
8	0.639221	4.9514	3e-06
9	0.605475	4.69	8e-06
10	0.568419	4.403	2.2e-05
11	0.522362	4.0462	7.6e-05
12	0.476355	3.6898	0.000243
13	0.428048	3.3156	0.000778
14	0.365905	2.8343	0.003124
15	0.308747	2.3915	0.009965
16	0.251001	1.9442	0.028279
17	0.198149	1.5349	0.065038

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95151 & 7.3704 & 0 \tabularnewline
2 & 0.90284 & 6.9934 & 0 \tabularnewline
3 & 0.856359 & 6.6333 & 0 \tabularnewline
4 & 0.804288 & 6.23 & 0 \tabularnewline
5 & 0.758939 & 5.8787 & 0 \tabularnewline
6 & 0.718494 & 5.5654 & 0 \tabularnewline
7 & 0.682174 & 5.2841 & 1e-06 \tabularnewline
8 & 0.639221 & 4.9514 & 3e-06 \tabularnewline
9 & 0.605475 & 4.69 & 8e-06 \tabularnewline
10 & 0.568419 & 4.403 & 2.2e-05 \tabularnewline
11 & 0.522362 & 4.0462 & 7.6e-05 \tabularnewline
12 & 0.476355 & 3.6898 & 0.000243 \tabularnewline
13 & 0.428048 & 3.3156 & 0.000778 \tabularnewline
14 & 0.365905 & 2.8343 & 0.003124 \tabularnewline
15 & 0.308747 & 2.3915 & 0.009965 \tabularnewline
16 & 0.251001 & 1.9442 & 0.028279 \tabularnewline
17 & 0.198149 & 1.5349 & 0.065038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167489&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]0.95151[/C][C]7.3704[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.90284[/C][C]6.9934[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.856359[/C][C]6.6333[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.804288[/C][C]6.23[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.758939[/C][C]5.8787[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.718494[/C][C]5.5654[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.682174[/C][C]5.2841[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.639221[/C][C]4.9514[/C][C]3e-06[/C][/ROW]
[ROW][C]9[/C][C]0.605475[/C][C]4.69[/C][C]8e-06[/C][/ROW]
[ROW][C]10[/C][C]0.568419[/C][C]4.403[/C][C]2.2e-05[/C][/ROW]
[ROW][C]11[/C][C]0.522362[/C][C]4.0462[/C][C]7.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.476355[/C][C]3.6898[/C][C]0.000243[/C][/ROW]
[ROW][C]13[/C][C]0.428048[/C][C]3.3156[/C][C]0.000778[/C][/ROW]
[ROW][C]14[/C][C]0.365905[/C][C]2.8343[/C][C]0.003124[/C][/ROW]
[ROW][C]15[/C][C]0.308747[/C][C]2.3915[/C][C]0.009965[/C][/ROW]
[ROW][C]16[/C][C]0.251001[/C][C]1.9442[/C][C]0.028279[/C][/ROW]
[ROW][C]17[/C][C]0.198149[/C][C]1.5349[/C][C]0.065038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167489&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167489&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	0.95151	7.3704	0
2	0.90284	6.9934	0
3	0.856359	6.6333	0
4	0.804288	6.23	0
5	0.758939	5.8787	0
6	0.718494	5.5654	0
7	0.682174	5.2841	1e-06
8	0.639221	4.9514	3e-06
9	0.605475	4.69	8e-06
10	0.568419	4.403	2.2e-05
11	0.522362	4.0462	7.6e-05
12	0.476355	3.6898	0.000243
13	0.428048	3.3156	0.000778
14	0.365905	2.8343	0.003124
15	0.308747	2.3915	0.009965
16	0.251001	1.9442	0.028279
17	0.198149	1.5349	0.065038

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.95151	7.3704	0
2	-0.026742	-0.2071	0.418301
3	-0.002433	-0.0188	0.492514
4	-0.084253	-0.6526	0.258246
5	0.043463	0.3367	0.368772
6	0.023092	0.1789	0.42932
7	0.026309	0.2038	0.419604
8	-0.099385	-0.7698	0.222209
9	0.074724	0.5788	0.282442
10	-0.061891	-0.4794	0.316695
11	-0.098028	-0.7593	0.225317
12	-0.047624	-0.3689	0.356753
13	-0.045094	-0.3493	0.364044
14	-0.179664	-1.3917	0.084579
15	0.012567	0.0973	0.46139
16	-0.08424	-0.6525	0.25828
17	0.031666	0.2453	0.403537

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95151 & 7.3704 & 0 \tabularnewline
2 & -0.026742 & -0.2071 & 0.418301 \tabularnewline
3 & -0.002433 & -0.0188 & 0.492514 \tabularnewline
4 & -0.084253 & -0.6526 & 0.258246 \tabularnewline
5 & 0.043463 & 0.3367 & 0.368772 \tabularnewline
6 & 0.023092 & 0.1789 & 0.42932 \tabularnewline
7 & 0.026309 & 0.2038 & 0.419604 \tabularnewline
8 & -0.099385 & -0.7698 & 0.222209 \tabularnewline
9 & 0.074724 & 0.5788 & 0.282442 \tabularnewline
10 & -0.061891 & -0.4794 & 0.316695 \tabularnewline
11 & -0.098028 & -0.7593 & 0.225317 \tabularnewline
12 & -0.047624 & -0.3689 & 0.356753 \tabularnewline
13 & -0.045094 & -0.3493 & 0.364044 \tabularnewline
14 & -0.179664 & -1.3917 & 0.084579 \tabularnewline
15 & 0.012567 & 0.0973 & 0.46139 \tabularnewline
16 & -0.08424 & -0.6525 & 0.25828 \tabularnewline
17 & 0.031666 & 0.2453 & 0.403537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167489&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]0.95151[/C][C]7.3704[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.026742[/C][C]-0.2071[/C][C]0.418301[/C][/ROW]
[ROW][C]3[/C][C]-0.002433[/C][C]-0.0188[/C][C]0.492514[/C][/ROW]
[ROW][C]4[/C][C]-0.084253[/C][C]-0.6526[/C][C]0.258246[/C][/ROW]
[ROW][C]5[/C][C]0.043463[/C][C]0.3367[/C][C]0.368772[/C][/ROW]
[ROW][C]6[/C][C]0.023092[/C][C]0.1789[/C][C]0.42932[/C][/ROW]
[ROW][C]7[/C][C]0.026309[/C][C]0.2038[/C][C]0.419604[/C][/ROW]
[ROW][C]8[/C][C]-0.099385[/C][C]-0.7698[/C][C]0.222209[/C][/ROW]
[ROW][C]9[/C][C]0.074724[/C][C]0.5788[/C][C]0.282442[/C][/ROW]
[ROW][C]10[/C][C]-0.061891[/C][C]-0.4794[/C][C]0.316695[/C][/ROW]
[ROW][C]11[/C][C]-0.098028[/C][C]-0.7593[/C][C]0.225317[/C][/ROW]
[ROW][C]12[/C][C]-0.047624[/C][C]-0.3689[/C][C]0.356753[/C][/ROW]
[ROW][C]13[/C][C]-0.045094[/C][C]-0.3493[/C][C]0.364044[/C][/ROW]
[ROW][C]14[/C][C]-0.179664[/C][C]-1.3917[/C][C]0.084579[/C][/ROW]
[ROW][C]15[/C][C]0.012567[/C][C]0.0973[/C][C]0.46139[/C][/ROW]
[ROW][C]16[/C][C]-0.08424[/C][C]-0.6525[/C][C]0.25828[/C][/ROW]
[ROW][C]17[/C][C]0.031666[/C][C]0.2453[/C][C]0.403537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167489&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167489&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	0.95151	7.3704	0
2	-0.026742	-0.2071	0.418301
3	-0.002433	-0.0188	0.492514
4	-0.084253	-0.6526	0.258246
5	0.043463	0.3367	0.368772
6	0.023092	0.1789	0.42932
7	0.026309	0.2038	0.419604
8	-0.099385	-0.7698	0.222209
9	0.074724	0.5788	0.282442
10	-0.061891	-0.4794	0.316695
11	-0.098028	-0.7593	0.225317
12	-0.047624	-0.3689	0.356753
13	-0.045094	-0.3493	0.364044
14	-0.179664	-1.3917	0.084579
15	0.012567	0.0973	0.46139
16	-0.08424	-0.6525	0.25828
17	0.031666	0.2453	0.403537

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 = 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code