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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 21 Nov 2009 10:36:22 -0700

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/2009/Nov/21/t1258825043ff219xrv4ni3qfx.htm/, Retrieved Sun, 28 Apr 2024 04:51:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=58573, Retrieved Sun, 28 Apr 2024 04:51:39 +0000

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No (this computation is public)

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Estimated Impact

129

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

-       [(Partial) Autocorrelation Function] [Parti�le autocorr...] [2009-11-21 17:36:22] [2622964eb3e61db9b0dfd11950e3a18c] [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' @ 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58573&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58573&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58573&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.330095	2.5569	0.006554
2	0.301576	2.336	0.011425
3	0.440221	3.4099	0.000584
4	0.344813	2.6709	0.004861
5	0.203495	1.5763	0.060111
6	0.186244	1.4426	0.077161
7	0.231125	1.7903	0.039227
8	0.166857	1.2925	0.100575
9	0.183852	1.4241	0.079797
10	0.258083	1.9991	0.025066
11	0.012149	0.0941	0.462669
12	0.117047	0.9066	0.184112
13	0.086758	0.672	0.252074
14	0.021208	0.1643	0.435034
15	-0.079316	-0.6144	0.270645
16	-0.058004	-0.4493	0.327417
17	-0.005189	-0.0402	0.484036

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.330095 & 2.5569 & 0.006554 \tabularnewline
2 & 0.301576 & 2.336 & 0.011425 \tabularnewline
3 & 0.440221 & 3.4099 & 0.000584 \tabularnewline
4 & 0.344813 & 2.6709 & 0.004861 \tabularnewline
5 & 0.203495 & 1.5763 & 0.060111 \tabularnewline
6 & 0.186244 & 1.4426 & 0.077161 \tabularnewline
7 & 0.231125 & 1.7903 & 0.039227 \tabularnewline
8 & 0.166857 & 1.2925 & 0.100575 \tabularnewline
9 & 0.183852 & 1.4241 & 0.079797 \tabularnewline
10 & 0.258083 & 1.9991 & 0.025066 \tabularnewline
11 & 0.012149 & 0.0941 & 0.462669 \tabularnewline
12 & 0.117047 & 0.9066 & 0.184112 \tabularnewline
13 & 0.086758 & 0.672 & 0.252074 \tabularnewline
14 & 0.021208 & 0.1643 & 0.435034 \tabularnewline
15 & -0.079316 & -0.6144 & 0.270645 \tabularnewline
16 & -0.058004 & -0.4493 & 0.327417 \tabularnewline
17 & -0.005189 & -0.0402 & 0.484036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58573&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]0.330095[/C][C]2.5569[/C][C]0.006554[/C][/ROW]
[ROW][C]2[/C][C]0.301576[/C][C]2.336[/C][C]0.011425[/C][/ROW]
[ROW][C]3[/C][C]0.440221[/C][C]3.4099[/C][C]0.000584[/C][/ROW]
[ROW][C]4[/C][C]0.344813[/C][C]2.6709[/C][C]0.004861[/C][/ROW]
[ROW][C]5[/C][C]0.203495[/C][C]1.5763[/C][C]0.060111[/C][/ROW]
[ROW][C]6[/C][C]0.186244[/C][C]1.4426[/C][C]0.077161[/C][/ROW]
[ROW][C]7[/C][C]0.231125[/C][C]1.7903[/C][C]0.039227[/C][/ROW]
[ROW][C]8[/C][C]0.166857[/C][C]1.2925[/C][C]0.100575[/C][/ROW]
[ROW][C]9[/C][C]0.183852[/C][C]1.4241[/C][C]0.079797[/C][/ROW]
[ROW][C]10[/C][C]0.258083[/C][C]1.9991[/C][C]0.025066[/C][/ROW]
[ROW][C]11[/C][C]0.012149[/C][C]0.0941[/C][C]0.462669[/C][/ROW]
[ROW][C]12[/C][C]0.117047[/C][C]0.9066[/C][C]0.184112[/C][/ROW]
[ROW][C]13[/C][C]0.086758[/C][C]0.672[/C][C]0.252074[/C][/ROW]
[ROW][C]14[/C][C]0.021208[/C][C]0.1643[/C][C]0.435034[/C][/ROW]
[ROW][C]15[/C][C]-0.079316[/C][C]-0.6144[/C][C]0.270645[/C][/ROW]
[ROW][C]16[/C][C]-0.058004[/C][C]-0.4493[/C][C]0.327417[/C][/ROW]
[ROW][C]17[/C][C]-0.005189[/C][C]-0.0402[/C][C]0.484036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58573&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58573&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	0.330095	2.5569	0.006554
2	0.301576	2.336	0.011425
3	0.440221	3.4099	0.000584
4	0.344813	2.6709	0.004861
5	0.203495	1.5763	0.060111
6	0.186244	1.4426	0.077161
7	0.231125	1.7903	0.039227
8	0.166857	1.2925	0.100575
9	0.183852	1.4241	0.079797
10	0.258083	1.9991	0.025066
11	0.012149	0.0941	0.462669
12	0.117047	0.9066	0.184112
13	0.086758	0.672	0.252074
14	0.021208	0.1643	0.435034
15	-0.079316	-0.6144	0.270645
16	-0.058004	-0.4493	0.327417
17	-0.005189	-0.0402	0.484036

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.330095	2.5569	0.006554
2	0.216168	1.6744	0.049626
3	0.342401	2.6522	0.005108
4	0.149363	1.157	0.125937
5	-0.047172	-0.3654	0.358051
6	-0.078098	-0.6049	0.273748
7	0.031685	0.2454	0.403479
8	0.026232	0.2032	0.419836
9	0.099727	0.7725	0.221431
10	0.156301	1.2107	0.115378
11	-0.227761	-1.7642	0.041392
12	-0.02701	-0.2092	0.417493
13	-0.095138	-0.7369	0.232017
14	-0.00106	-0.0082	0.496737
15	-0.098405	-0.7622	0.224451
16	-0.062434	-0.4836	0.31521
17	0.017245	0.1336	0.447091

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.330095 & 2.5569 & 0.006554 \tabularnewline
2 & 0.216168 & 1.6744 & 0.049626 \tabularnewline
3 & 0.342401 & 2.6522 & 0.005108 \tabularnewline
4 & 0.149363 & 1.157 & 0.125937 \tabularnewline
5 & -0.047172 & -0.3654 & 0.358051 \tabularnewline
6 & -0.078098 & -0.6049 & 0.273748 \tabularnewline
7 & 0.031685 & 0.2454 & 0.403479 \tabularnewline
8 & 0.026232 & 0.2032 & 0.419836 \tabularnewline
9 & 0.099727 & 0.7725 & 0.221431 \tabularnewline
10 & 0.156301 & 1.2107 & 0.115378 \tabularnewline
11 & -0.227761 & -1.7642 & 0.041392 \tabularnewline
12 & -0.02701 & -0.2092 & 0.417493 \tabularnewline
13 & -0.095138 & -0.7369 & 0.232017 \tabularnewline
14 & -0.00106 & -0.0082 & 0.496737 \tabularnewline
15 & -0.098405 & -0.7622 & 0.224451 \tabularnewline
16 & -0.062434 & -0.4836 & 0.31521 \tabularnewline
17 & 0.017245 & 0.1336 & 0.447091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=58573&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]0.330095[/C][C]2.5569[/C][C]0.006554[/C][/ROW]
[ROW][C]2[/C][C]0.216168[/C][C]1.6744[/C][C]0.049626[/C][/ROW]
[ROW][C]3[/C][C]0.342401[/C][C]2.6522[/C][C]0.005108[/C][/ROW]
[ROW][C]4[/C][C]0.149363[/C][C]1.157[/C][C]0.125937[/C][/ROW]
[ROW][C]5[/C][C]-0.047172[/C][C]-0.3654[/C][C]0.358051[/C][/ROW]
[ROW][C]6[/C][C]-0.078098[/C][C]-0.6049[/C][C]0.273748[/C][/ROW]
[ROW][C]7[/C][C]0.031685[/C][C]0.2454[/C][C]0.403479[/C][/ROW]
[ROW][C]8[/C][C]0.026232[/C][C]0.2032[/C][C]0.419836[/C][/ROW]
[ROW][C]9[/C][C]0.099727[/C][C]0.7725[/C][C]0.221431[/C][/ROW]
[ROW][C]10[/C][C]0.156301[/C][C]1.2107[/C][C]0.115378[/C][/ROW]
[ROW][C]11[/C][C]-0.227761[/C][C]-1.7642[/C][C]0.041392[/C][/ROW]
[ROW][C]12[/C][C]-0.02701[/C][C]-0.2092[/C][C]0.417493[/C][/ROW]
[ROW][C]13[/C][C]-0.095138[/C][C]-0.7369[/C][C]0.232017[/C][/ROW]
[ROW][C]14[/C][C]-0.00106[/C][C]-0.0082[/C][C]0.496737[/C][/ROW]
[ROW][C]15[/C][C]-0.098405[/C][C]-0.7622[/C][C]0.224451[/C][/ROW]
[ROW][C]16[/C][C]-0.062434[/C][C]-0.4836[/C][C]0.31521[/C][/ROW]
[ROW][C]17[/C][C]0.017245[/C][C]0.1336[/C][C]0.447091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=58573&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=58573&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	0.330095	2.5569	0.006554
2	0.216168	1.6744	0.049626
3	0.342401	2.6522	0.005108
4	0.149363	1.157	0.125937
5	-0.047172	-0.3654	0.358051
6	-0.078098	-0.6049	0.273748
7	0.031685	0.2454	0.403479
8	0.026232	0.2032	0.419836
9	0.099727	0.7725	0.221431
10	0.156301	1.2107	0.115378
11	-0.227761	-1.7642	0.041392
12	-0.02701	-0.2092	0.417493
13	-0.095138	-0.7369	0.232017
14	-0.00106	-0.0082	0.496737
15	-0.098405	-0.7622	0.224451
16	-0.062434	-0.4836	0.31521
17	0.017245	0.1336	0.447091

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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