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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 14 Dec 2014 09:49:58 +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/2014/Dec/14/t1418550613t3898misgixwgpa.htm/, Retrieved Sun, 19 May 2024 13:38:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267367, Retrieved Sun, 19 May 2024 13:38:10 +0000

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Estimated Impact

113

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-       [(Partial) Autocorrelation Function] [] [2014-12-14 09:49:58] [c7f962214140f976f2c4b1bb2571d9df] [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	'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267367&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267367&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.697684	6.3944	0
2	0.328643	3.0121	0.001714
3	-0.033743	-0.3093	0.378945
4	-0.331962	-3.0425	0.001565
5	-0.526292	-4.8235	3e-06
6	-0.560279	-5.135	1e-06
7	-0.480596	-4.4047	1.6e-05
8	-0.319611	-2.9293	0.002186
9	-0.023739	-0.2176	0.414145
10	0.249594	2.2876	0.012338
11	0.53167	4.8728	3e-06
12	0.67508	6.1872	0
13	0.543602	4.9822	2e-06
14	0.304914	2.7946	0.003218
15	0.018163	0.1665	0.434096
16	-0.231008	-2.1172	0.018599
17	-0.40115	-3.6766	0.000208
18	-0.462131	-4.2355	2.9e-05
19	-0.44393	-4.0687	5.3e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.697684 & 6.3944 & 0 \tabularnewline
2 & 0.328643 & 3.0121 & 0.001714 \tabularnewline
3 & -0.033743 & -0.3093 & 0.378945 \tabularnewline
4 & -0.331962 & -3.0425 & 0.001565 \tabularnewline
5 & -0.526292 & -4.8235 & 3e-06 \tabularnewline
6 & -0.560279 & -5.135 & 1e-06 \tabularnewline
7 & -0.480596 & -4.4047 & 1.6e-05 \tabularnewline
8 & -0.319611 & -2.9293 & 0.002186 \tabularnewline
9 & -0.023739 & -0.2176 & 0.414145 \tabularnewline
10 & 0.249594 & 2.2876 & 0.012338 \tabularnewline
11 & 0.53167 & 4.8728 & 3e-06 \tabularnewline
12 & 0.67508 & 6.1872 & 0 \tabularnewline
13 & 0.543602 & 4.9822 & 2e-06 \tabularnewline
14 & 0.304914 & 2.7946 & 0.003218 \tabularnewline
15 & 0.018163 & 0.1665 & 0.434096 \tabularnewline
16 & -0.231008 & -2.1172 & 0.018599 \tabularnewline
17 & -0.40115 & -3.6766 & 0.000208 \tabularnewline
18 & -0.462131 & -4.2355 & 2.9e-05 \tabularnewline
19 & -0.44393 & -4.0687 & 5.3e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267367&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]0.697684[/C][C]6.3944[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.328643[/C][C]3.0121[/C][C]0.001714[/C][/ROW]
[ROW][C]3[/C][C]-0.033743[/C][C]-0.3093[/C][C]0.378945[/C][/ROW]
[ROW][C]4[/C][C]-0.331962[/C][C]-3.0425[/C][C]0.001565[/C][/ROW]
[ROW][C]5[/C][C]-0.526292[/C][C]-4.8235[/C][C]3e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.560279[/C][C]-5.135[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.480596[/C][C]-4.4047[/C][C]1.6e-05[/C][/ROW]
[ROW][C]8[/C][C]-0.319611[/C][C]-2.9293[/C][C]0.002186[/C][/ROW]
[ROW][C]9[/C][C]-0.023739[/C][C]-0.2176[/C][C]0.414145[/C][/ROW]
[ROW][C]10[/C][C]0.249594[/C][C]2.2876[/C][C]0.012338[/C][/ROW]
[ROW][C]11[/C][C]0.53167[/C][C]4.8728[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.67508[/C][C]6.1872[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.543602[/C][C]4.9822[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.304914[/C][C]2.7946[/C][C]0.003218[/C][/ROW]
[ROW][C]15[/C][C]0.018163[/C][C]0.1665[/C][C]0.434096[/C][/ROW]
[ROW][C]16[/C][C]-0.231008[/C][C]-2.1172[/C][C]0.018599[/C][/ROW]
[ROW][C]17[/C][C]-0.40115[/C][C]-3.6766[/C][C]0.000208[/C][/ROW]
[ROW][C]18[/C][C]-0.462131[/C][C]-4.2355[/C][C]2.9e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.44393[/C][C]-4.0687[/C][C]5.3e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267367&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	0.697684	6.3944	0
2	0.328643	3.0121	0.001714
3	-0.033743	-0.3093	0.378945
4	-0.331962	-3.0425	0.001565
5	-0.526292	-4.8235	3e-06
6	-0.560279	-5.135	1e-06
7	-0.480596	-4.4047	1.6e-05
8	-0.319611	-2.9293	0.002186
9	-0.023739	-0.2176	0.414145
10	0.249594	2.2876	0.012338
11	0.53167	4.8728	3e-06
12	0.67508	6.1872	0
13	0.543602	4.9822	2e-06
14	0.304914	2.7946	0.003218
15	0.018163	0.1665	0.434096
16	-0.231008	-2.1172	0.018599
17	-0.40115	-3.6766	0.000208
18	-0.462131	-4.2355	2.9e-05
19	-0.44393	-4.0687	5.3e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.697684	6.3944	0
2	-0.308083	-2.8236	0.002964
3	-0.25559	-2.3425	0.01076
4	-0.232424	-2.1302	0.01804
5	-0.218748	-2.0049	0.024099
6	-0.112444	-1.0306	0.152852
7	-0.148918	-1.3649	0.087972
8	-0.12753	-1.1688	0.122889
9	0.150259	1.3771	0.086062
10	0.036374	0.3334	0.369842
11	0.31969	2.93	0.002182
12	0.203946	1.8692	0.03254
13	-0.129593	-1.1877	0.119142
14	0.104536	0.9581	0.170384
15	0.007337	0.0672	0.473273
16	0.064419	0.5904	0.27825
17	0.078278	0.7174	0.237549
18	-0.070973	-0.6505	0.25858
19	-0.02829	-0.2593	0.398027

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.697684 & 6.3944 & 0 \tabularnewline
2 & -0.308083 & -2.8236 & 0.002964 \tabularnewline
3 & -0.25559 & -2.3425 & 0.01076 \tabularnewline
4 & -0.232424 & -2.1302 & 0.01804 \tabularnewline
5 & -0.218748 & -2.0049 & 0.024099 \tabularnewline
6 & -0.112444 & -1.0306 & 0.152852 \tabularnewline
7 & -0.148918 & -1.3649 & 0.087972 \tabularnewline
8 & -0.12753 & -1.1688 & 0.122889 \tabularnewline
9 & 0.150259 & 1.3771 & 0.086062 \tabularnewline
10 & 0.036374 & 0.3334 & 0.369842 \tabularnewline
11 & 0.31969 & 2.93 & 0.002182 \tabularnewline
12 & 0.203946 & 1.8692 & 0.03254 \tabularnewline
13 & -0.129593 & -1.1877 & 0.119142 \tabularnewline
14 & 0.104536 & 0.9581 & 0.170384 \tabularnewline
15 & 0.007337 & 0.0672 & 0.473273 \tabularnewline
16 & 0.064419 & 0.5904 & 0.27825 \tabularnewline
17 & 0.078278 & 0.7174 & 0.237549 \tabularnewline
18 & -0.070973 & -0.6505 & 0.25858 \tabularnewline
19 & -0.02829 & -0.2593 & 0.398027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267367&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]0.697684[/C][C]6.3944[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.308083[/C][C]-2.8236[/C][C]0.002964[/C][/ROW]
[ROW][C]3[/C][C]-0.25559[/C][C]-2.3425[/C][C]0.01076[/C][/ROW]
[ROW][C]4[/C][C]-0.232424[/C][C]-2.1302[/C][C]0.01804[/C][/ROW]
[ROW][C]5[/C][C]-0.218748[/C][C]-2.0049[/C][C]0.024099[/C][/ROW]
[ROW][C]6[/C][C]-0.112444[/C][C]-1.0306[/C][C]0.152852[/C][/ROW]
[ROW][C]7[/C][C]-0.148918[/C][C]-1.3649[/C][C]0.087972[/C][/ROW]
[ROW][C]8[/C][C]-0.12753[/C][C]-1.1688[/C][C]0.122889[/C][/ROW]
[ROW][C]9[/C][C]0.150259[/C][C]1.3771[/C][C]0.086062[/C][/ROW]
[ROW][C]10[/C][C]0.036374[/C][C]0.3334[/C][C]0.369842[/C][/ROW]
[ROW][C]11[/C][C]0.31969[/C][C]2.93[/C][C]0.002182[/C][/ROW]
[ROW][C]12[/C][C]0.203946[/C][C]1.8692[/C][C]0.03254[/C][/ROW]
[ROW][C]13[/C][C]-0.129593[/C][C]-1.1877[/C][C]0.119142[/C][/ROW]
[ROW][C]14[/C][C]0.104536[/C][C]0.9581[/C][C]0.170384[/C][/ROW]
[ROW][C]15[/C][C]0.007337[/C][C]0.0672[/C][C]0.473273[/C][/ROW]
[ROW][C]16[/C][C]0.064419[/C][C]0.5904[/C][C]0.27825[/C][/ROW]
[ROW][C]17[/C][C]0.078278[/C][C]0.7174[/C][C]0.237549[/C][/ROW]
[ROW][C]18[/C][C]-0.070973[/C][C]-0.6505[/C][C]0.25858[/C][/ROW]
[ROW][C]19[/C][C]-0.02829[/C][C]-0.2593[/C][C]0.398027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267367&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267367&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	0.697684	6.3944	0
2	-0.308083	-2.8236	0.002964
3	-0.25559	-2.3425	0.01076
4	-0.232424	-2.1302	0.01804
5	-0.218748	-2.0049	0.024099
6	-0.112444	-1.0306	0.152852
7	-0.148918	-1.3649	0.087972
8	-0.12753	-1.1688	0.122889
9	0.150259	1.3771	0.086062
10	0.036374	0.3334	0.369842
11	0.31969	2.93	0.002182
12	0.203946	1.8692	0.03254
13	-0.129593	-1.1877	0.119142
14	0.104536	0.9581	0.170384
15	0.007337	0.0672	0.473273
16	0.064419	0.5904	0.27825
17	0.078278	0.7174	0.237549
18	-0.070973	-0.6505	0.25858
19	-0.02829	-0.2593	0.398027

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code