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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

Thu, 03 Sep 2015 08:45:59 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Sep/03/t1441266438tdtk6h70xn27wjo.htm/, Retrieved Thu, 16 May 2024 07:45:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280551, Retrieved Thu, 16 May 2024 07:45:49 +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] [vraag 6] [2015-09-03 07:45:59] [de6a1c4dd3c7633fe50ebfd212b25713] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280551&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280551&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.718192	3.9337	0.000229
2	0.667271	3.6548	0.000488
3	0.589177	3.2271	0.00151
4	0.461304	2.5267	0.008512
5	0.432037	2.3664	0.012309
6	0.363491	1.9909	0.027833
7	0.230617	1.2631	0.108134
8	0.166932	0.9143	0.183918
9	0.009496	0.052	0.479431
10	-0.049151	-0.2692	0.394805
11	-0.095166	-0.5212	0.303011
12	-0.237303	-1.2998	0.10179
13	-0.205935	-1.128	0.134141
14	-0.276391	-1.5139	0.070264

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.718192 & 3.9337 & 0.000229 \tabularnewline
2 & 0.667271 & 3.6548 & 0.000488 \tabularnewline
3 & 0.589177 & 3.2271 & 0.00151 \tabularnewline
4 & 0.461304 & 2.5267 & 0.008512 \tabularnewline
5 & 0.432037 & 2.3664 & 0.012309 \tabularnewline
6 & 0.363491 & 1.9909 & 0.027833 \tabularnewline
7 & 0.230617 & 1.2631 & 0.108134 \tabularnewline
8 & 0.166932 & 0.9143 & 0.183918 \tabularnewline
9 & 0.009496 & 0.052 & 0.479431 \tabularnewline
10 & -0.049151 & -0.2692 & 0.394805 \tabularnewline
11 & -0.095166 & -0.5212 & 0.303011 \tabularnewline
12 & -0.237303 & -1.2998 & 0.10179 \tabularnewline
13 & -0.205935 & -1.128 & 0.134141 \tabularnewline
14 & -0.276391 & -1.5139 & 0.070264 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280551&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]0.718192[/C][C]3.9337[/C][C]0.000229[/C][/ROW]
[ROW][C]2[/C][C]0.667271[/C][C]3.6548[/C][C]0.000488[/C][/ROW]
[ROW][C]3[/C][C]0.589177[/C][C]3.2271[/C][C]0.00151[/C][/ROW]
[ROW][C]4[/C][C]0.461304[/C][C]2.5267[/C][C]0.008512[/C][/ROW]
[ROW][C]5[/C][C]0.432037[/C][C]2.3664[/C][C]0.012309[/C][/ROW]
[ROW][C]6[/C][C]0.363491[/C][C]1.9909[/C][C]0.027833[/C][/ROW]
[ROW][C]7[/C][C]0.230617[/C][C]1.2631[/C][C]0.108134[/C][/ROW]
[ROW][C]8[/C][C]0.166932[/C][C]0.9143[/C][C]0.183918[/C][/ROW]
[ROW][C]9[/C][C]0.009496[/C][C]0.052[/C][C]0.479431[/C][/ROW]
[ROW][C]10[/C][C]-0.049151[/C][C]-0.2692[/C][C]0.394805[/C][/ROW]
[ROW][C]11[/C][C]-0.095166[/C][C]-0.5212[/C][C]0.303011[/C][/ROW]
[ROW][C]12[/C][C]-0.237303[/C][C]-1.2998[/C][C]0.10179[/C][/ROW]
[ROW][C]13[/C][C]-0.205935[/C][C]-1.128[/C][C]0.134141[/C][/ROW]
[ROW][C]14[/C][C]-0.276391[/C][C]-1.5139[/C][C]0.070264[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280551&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	0.718192	3.9337	0.000229
2	0.667271	3.6548	0.000488
3	0.589177	3.2271	0.00151
4	0.461304	2.5267	0.008512
5	0.432037	2.3664	0.012309
6	0.363491	1.9909	0.027833
7	0.230617	1.2631	0.108134
8	0.166932	0.9143	0.183918
9	0.009496	0.052	0.479431
10	-0.049151	-0.2692	0.394805
11	-0.095166	-0.5212	0.303011
12	-0.237303	-1.2998	0.10179
13	-0.205935	-1.128	0.134141
14	-0.276391	-1.5139	0.070264

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.718192	3.9337	0.000229
2	0.31283	1.7134	0.048475
3	0.080568	0.4413	0.331085
4	-0.12602	-0.6902	0.247674
5	0.064442	0.353	0.363292
6	0.007972	0.0437	0.482731
7	-0.194445	-1.065	0.147682
8	-0.07984	-0.4373	0.332513
9	-0.213723	-1.1706	0.125485
10	-0.012117	-0.0664	0.473762
11	0.014417	0.079	0.468792
12	-0.214036	-1.1723	0.125147
13	0.121411	0.665	0.255567
14	-0.031517	-0.1726	0.432052

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.718192 & 3.9337 & 0.000229 \tabularnewline
2 & 0.31283 & 1.7134 & 0.048475 \tabularnewline
3 & 0.080568 & 0.4413 & 0.331085 \tabularnewline
4 & -0.12602 & -0.6902 & 0.247674 \tabularnewline
5 & 0.064442 & 0.353 & 0.363292 \tabularnewline
6 & 0.007972 & 0.0437 & 0.482731 \tabularnewline
7 & -0.194445 & -1.065 & 0.147682 \tabularnewline
8 & -0.07984 & -0.4373 & 0.332513 \tabularnewline
9 & -0.213723 & -1.1706 & 0.125485 \tabularnewline
10 & -0.012117 & -0.0664 & 0.473762 \tabularnewline
11 & 0.014417 & 0.079 & 0.468792 \tabularnewline
12 & -0.214036 & -1.1723 & 0.125147 \tabularnewline
13 & 0.121411 & 0.665 & 0.255567 \tabularnewline
14 & -0.031517 & -0.1726 & 0.432052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280551&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]0.718192[/C][C]3.9337[/C][C]0.000229[/C][/ROW]
[ROW][C]2[/C][C]0.31283[/C][C]1.7134[/C][C]0.048475[/C][/ROW]
[ROW][C]3[/C][C]0.080568[/C][C]0.4413[/C][C]0.331085[/C][/ROW]
[ROW][C]4[/C][C]-0.12602[/C][C]-0.6902[/C][C]0.247674[/C][/ROW]
[ROW][C]5[/C][C]0.064442[/C][C]0.353[/C][C]0.363292[/C][/ROW]
[ROW][C]6[/C][C]0.007972[/C][C]0.0437[/C][C]0.482731[/C][/ROW]
[ROW][C]7[/C][C]-0.194445[/C][C]-1.065[/C][C]0.147682[/C][/ROW]
[ROW][C]8[/C][C]-0.07984[/C][C]-0.4373[/C][C]0.332513[/C][/ROW]
[ROW][C]9[/C][C]-0.213723[/C][C]-1.1706[/C][C]0.125485[/C][/ROW]
[ROW][C]10[/C][C]-0.012117[/C][C]-0.0664[/C][C]0.473762[/C][/ROW]
[ROW][C]11[/C][C]0.014417[/C][C]0.079[/C][C]0.468792[/C][/ROW]
[ROW][C]12[/C][C]-0.214036[/C][C]-1.1723[/C][C]0.125147[/C][/ROW]
[ROW][C]13[/C][C]0.121411[/C][C]0.665[/C][C]0.255567[/C][/ROW]
[ROW][C]14[/C][C]-0.031517[/C][C]-0.1726[/C][C]0.432052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280551&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280551&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	0.718192	3.9337	0.000229
2	0.31283	1.7134	0.048475
3	0.080568	0.4413	0.331085
4	-0.12602	-0.6902	0.247674
5	0.064442	0.353	0.363292
6	0.007972	0.0437	0.482731
7	-0.194445	-1.065	0.147682
8	-0.07984	-0.4373	0.332513
9	-0.213723	-1.1706	0.125485
10	-0.012117	-0.0664	0.473762
11	0.014417	0.079	0.468792
12	-0.214036	-1.1723	0.125147
13	0.121411	0.665	0.255567
14	-0.031517	-0.1726	0.432052

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 = 50 ; par2 = 0.34 ; par3 = 0 ; par4 = 0.10 ;

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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Figures (Output of Computation)

Input Parameters & R Code