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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Dec 2011 15:04:38 -0500

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/2011/Dec/01/t13227700356292fp3amfvdqll.htm/, Retrieved Tue, 23 Apr 2024 14:58:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149984, Retrieved Tue, 23 Apr 2024 14:58:50 +0000

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User-defined keywords

Estimated Impact

134

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

-     [(Partial) Autocorrelation Function] [] [2011-12-01 19:58:02] [ee8c3a74bf3b349877806e9a50913c60]
- R P   [(Partial) Autocorrelation Function] [] [2011-12-01 20:01:46] [ee8c3a74bf3b349877806e9a50913c60]
-   P       [(Partial) Autocorrelation Function] [] [2011-12-01 20:04:38] [7dc03dd48c8acabd98b217fada4a6bc0] [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	'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=149984&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=149984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149984&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	-0.224534	-2.4494	0.007884
2	0.148043	1.615	0.054484
3	0.129572	1.4135	0.080065
4	0.086604	0.9447	0.173353
5	0.087095	0.9501	0.171994
6	0.084891	0.9261	0.178147
7	0.029202	0.3186	0.375311
8	0.034344	0.3746	0.354296
9	0.09276	1.0119	0.156821
10	-0.039605	-0.432	0.333247
11	0.246153	2.6852	0.004142
12	-0.393521	-4.2928	1.8e-05
13	0.170042	1.8549	0.03304
14	0.00444	0.0484	0.480724
15	-0.062788	-0.6849	0.247359
16	-0.039483	-0.4307	0.333728
17	0.00714	0.0779	0.469026
18	-0.036945	-0.403	0.343827
19	0.018841	0.2055	0.418754
20	0.07176	0.7828	0.217646
21	-0.099447	-1.0848	0.140094

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.224534 & -2.4494 & 0.007884 \tabularnewline
2 & 0.148043 & 1.615 & 0.054484 \tabularnewline
3 & 0.129572 & 1.4135 & 0.080065 \tabularnewline
4 & 0.086604 & 0.9447 & 0.173353 \tabularnewline
5 & 0.087095 & 0.9501 & 0.171994 \tabularnewline
6 & 0.084891 & 0.9261 & 0.178147 \tabularnewline
7 & 0.029202 & 0.3186 & 0.375311 \tabularnewline
8 & 0.034344 & 0.3746 & 0.354296 \tabularnewline
9 & 0.09276 & 1.0119 & 0.156821 \tabularnewline
10 & -0.039605 & -0.432 & 0.333247 \tabularnewline
11 & 0.246153 & 2.6852 & 0.004142 \tabularnewline
12 & -0.393521 & -4.2928 & 1.8e-05 \tabularnewline
13 & 0.170042 & 1.8549 & 0.03304 \tabularnewline
14 & 0.00444 & 0.0484 & 0.480724 \tabularnewline
15 & -0.062788 & -0.6849 & 0.247359 \tabularnewline
16 & -0.039483 & -0.4307 & 0.333728 \tabularnewline
17 & 0.00714 & 0.0779 & 0.469026 \tabularnewline
18 & -0.036945 & -0.403 & 0.343827 \tabularnewline
19 & 0.018841 & 0.2055 & 0.418754 \tabularnewline
20 & 0.07176 & 0.7828 & 0.217646 \tabularnewline
21 & -0.099447 & -1.0848 & 0.140094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149984&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]-0.224534[/C][C]-2.4494[/C][C]0.007884[/C][/ROW]
[ROW][C]2[/C][C]0.148043[/C][C]1.615[/C][C]0.054484[/C][/ROW]
[ROW][C]3[/C][C]0.129572[/C][C]1.4135[/C][C]0.080065[/C][/ROW]
[ROW][C]4[/C][C]0.086604[/C][C]0.9447[/C][C]0.173353[/C][/ROW]
[ROW][C]5[/C][C]0.087095[/C][C]0.9501[/C][C]0.171994[/C][/ROW]
[ROW][C]6[/C][C]0.084891[/C][C]0.9261[/C][C]0.178147[/C][/ROW]
[ROW][C]7[/C][C]0.029202[/C][C]0.3186[/C][C]0.375311[/C][/ROW]
[ROW][C]8[/C][C]0.034344[/C][C]0.3746[/C][C]0.354296[/C][/ROW]
[ROW][C]9[/C][C]0.09276[/C][C]1.0119[/C][C]0.156821[/C][/ROW]
[ROW][C]10[/C][C]-0.039605[/C][C]-0.432[/C][C]0.333247[/C][/ROW]
[ROW][C]11[/C][C]0.246153[/C][C]2.6852[/C][C]0.004142[/C][/ROW]
[ROW][C]12[/C][C]-0.393521[/C][C]-4.2928[/C][C]1.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.170042[/C][C]1.8549[/C][C]0.03304[/C][/ROW]
[ROW][C]14[/C][C]0.00444[/C][C]0.0484[/C][C]0.480724[/C][/ROW]
[ROW][C]15[/C][C]-0.062788[/C][C]-0.6849[/C][C]0.247359[/C][/ROW]
[ROW][C]16[/C][C]-0.039483[/C][C]-0.4307[/C][C]0.333728[/C][/ROW]
[ROW][C]17[/C][C]0.00714[/C][C]0.0779[/C][C]0.469026[/C][/ROW]
[ROW][C]18[/C][C]-0.036945[/C][C]-0.403[/C][C]0.343827[/C][/ROW]
[ROW][C]19[/C][C]0.018841[/C][C]0.2055[/C][C]0.418754[/C][/ROW]
[ROW][C]20[/C][C]0.07176[/C][C]0.7828[/C][C]0.217646[/C][/ROW]
[ROW][C]21[/C][C]-0.099447[/C][C]-1.0848[/C][C]0.140094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149984&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	-0.224534	-2.4494	0.007884
2	0.148043	1.615	0.054484
3	0.129572	1.4135	0.080065
4	0.086604	0.9447	0.173353
5	0.087095	0.9501	0.171994
6	0.084891	0.9261	0.178147
7	0.029202	0.3186	0.375311
8	0.034344	0.3746	0.354296
9	0.09276	1.0119	0.156821
10	-0.039605	-0.432	0.333247
11	0.246153	2.6852	0.004142
12	-0.393521	-4.2928	1.8e-05
13	0.170042	1.8549	0.03304
14	0.00444	0.0484	0.480724
15	-0.062788	-0.6849	0.247359
16	-0.039483	-0.4307	0.333728
17	0.00714	0.0779	0.469026
18	-0.036945	-0.403	0.343827
19	0.018841	0.2055	0.418754
20	0.07176	0.7828	0.217646
21	-0.099447	-1.0848	0.140094

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.224534	-2.4494	0.007884
2	0.102811	1.1215	0.13216
3	0.194221	2.1187	0.018098
4	0.152515	1.6637	0.049397
5	0.106155	1.158	0.124589
6	0.079334	0.8654	0.194271
7	0.005813	0.0634	0.474774
8	-0.027115	-0.2958	0.383952
9	0.045526	0.4966	0.310182
10	-0.047651	-0.5198	0.302082
11	0.21227	2.3156	0.011147
12	-0.371909	-4.057	4.5e-05
13	-0.068095	-0.7428	0.229523
14	0.040456	0.4413	0.32989
15	0.005886	0.0642	0.474454
16	-0.040822	-0.4453	0.328452
17	0.01444	0.1575	0.43755
18	0.024525	0.2675	0.394761
19	0.044501	0.4854	0.314126
20	0.110542	1.2059	0.115129
21	0.005876	0.0641	0.474499

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.224534 & -2.4494 & 0.007884 \tabularnewline
2 & 0.102811 & 1.1215 & 0.13216 \tabularnewline
3 & 0.194221 & 2.1187 & 0.018098 \tabularnewline
4 & 0.152515 & 1.6637 & 0.049397 \tabularnewline
5 & 0.106155 & 1.158 & 0.124589 \tabularnewline
6 & 0.079334 & 0.8654 & 0.194271 \tabularnewline
7 & 0.005813 & 0.0634 & 0.474774 \tabularnewline
8 & -0.027115 & -0.2958 & 0.383952 \tabularnewline
9 & 0.045526 & 0.4966 & 0.310182 \tabularnewline
10 & -0.047651 & -0.5198 & 0.302082 \tabularnewline
11 & 0.21227 & 2.3156 & 0.011147 \tabularnewline
12 & -0.371909 & -4.057 & 4.5e-05 \tabularnewline
13 & -0.068095 & -0.7428 & 0.229523 \tabularnewline
14 & 0.040456 & 0.4413 & 0.32989 \tabularnewline
15 & 0.005886 & 0.0642 & 0.474454 \tabularnewline
16 & -0.040822 & -0.4453 & 0.328452 \tabularnewline
17 & 0.01444 & 0.1575 & 0.43755 \tabularnewline
18 & 0.024525 & 0.2675 & 0.394761 \tabularnewline
19 & 0.044501 & 0.4854 & 0.314126 \tabularnewline
20 & 0.110542 & 1.2059 & 0.115129 \tabularnewline
21 & 0.005876 & 0.0641 & 0.474499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149984&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]-0.224534[/C][C]-2.4494[/C][C]0.007884[/C][/ROW]
[ROW][C]2[/C][C]0.102811[/C][C]1.1215[/C][C]0.13216[/C][/ROW]
[ROW][C]3[/C][C]0.194221[/C][C]2.1187[/C][C]0.018098[/C][/ROW]
[ROW][C]4[/C][C]0.152515[/C][C]1.6637[/C][C]0.049397[/C][/ROW]
[ROW][C]5[/C][C]0.106155[/C][C]1.158[/C][C]0.124589[/C][/ROW]
[ROW][C]6[/C][C]0.079334[/C][C]0.8654[/C][C]0.194271[/C][/ROW]
[ROW][C]7[/C][C]0.005813[/C][C]0.0634[/C][C]0.474774[/C][/ROW]
[ROW][C]8[/C][C]-0.027115[/C][C]-0.2958[/C][C]0.383952[/C][/ROW]
[ROW][C]9[/C][C]0.045526[/C][C]0.4966[/C][C]0.310182[/C][/ROW]
[ROW][C]10[/C][C]-0.047651[/C][C]-0.5198[/C][C]0.302082[/C][/ROW]
[ROW][C]11[/C][C]0.21227[/C][C]2.3156[/C][C]0.011147[/C][/ROW]
[ROW][C]12[/C][C]-0.371909[/C][C]-4.057[/C][C]4.5e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.068095[/C][C]-0.7428[/C][C]0.229523[/C][/ROW]
[ROW][C]14[/C][C]0.040456[/C][C]0.4413[/C][C]0.32989[/C][/ROW]
[ROW][C]15[/C][C]0.005886[/C][C]0.0642[/C][C]0.474454[/C][/ROW]
[ROW][C]16[/C][C]-0.040822[/C][C]-0.4453[/C][C]0.328452[/C][/ROW]
[ROW][C]17[/C][C]0.01444[/C][C]0.1575[/C][C]0.43755[/C][/ROW]
[ROW][C]18[/C][C]0.024525[/C][C]0.2675[/C][C]0.394761[/C][/ROW]
[ROW][C]19[/C][C]0.044501[/C][C]0.4854[/C][C]0.314126[/C][/ROW]
[ROW][C]20[/C][C]0.110542[/C][C]1.2059[/C][C]0.115129[/C][/ROW]
[ROW][C]21[/C][C]0.005876[/C][C]0.0641[/C][C]0.474499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149984&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	-0.224534	-2.4494	0.007884
2	0.102811	1.1215	0.13216
3	0.194221	2.1187	0.018098
4	0.152515	1.6637	0.049397
5	0.106155	1.158	0.124589
6	0.079334	0.8654	0.194271
7	0.005813	0.0634	0.474774
8	-0.027115	-0.2958	0.383952
9	0.045526	0.4966	0.310182
10	-0.047651	-0.5198	0.302082
11	0.21227	2.3156	0.011147
12	-0.371909	-4.057	4.5e-05
13	-0.068095	-0.7428	0.229523
14	0.040456	0.4413	0.32989
15	0.005886	0.0642	0.474454
16	-0.040822	-0.4453	0.328452
17	0.01444	0.1575	0.43755
18	0.024525	0.2675	0.394761
19	0.044501	0.4854	0.314126
20	0.110542	1.2059	0.115129
21	0.005876	0.0641	0.474499

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 = 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)
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