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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2007 05:09:58 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/01/t11965104213yl1zt1xz0kmapr.htm/, Retrieved Sun, 19 May 2024 04:31:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2223, Retrieved Sun, 19 May 2024 04:31:53 +0000

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No (this computation is public)

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Estimated Impact

237

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

-       [(Partial) Autocorrelation Function] [autocorrelation w...] [2007-12-01 12:09:58] [bd02e85be52eb1cb060a2c60779eb820] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2223&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2223&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	10.3923	0
1	0.974832	10.1307	0
2	0.94839	9.856	0
3	0.920593	9.5671	0
4	0.891533	9.2651	0
5	0.86181	8.9562	0
6	0.831054	8.6366	0
7	0.800395	8.3179	0
8	0.768737	7.9889	0
9	0.737238	7.6616	0
10	0.704584	7.3223	0
11	0.671777	6.9813	0
12	0.638554	6.636	0
13	0.605124	6.2886	0
14	0.571588	5.9401	0
15	0.538454	5.5958	0
16	0.505201	5.2502	0
17	0.470803	4.8927	2e-06
18	0.436361	4.5348	7e-06
19	0.403451	4.1928	2.8e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.3923 & 0 \tabularnewline
1 & 0.974832 & 10.1307 & 0 \tabularnewline
2 & 0.94839 & 9.856 & 0 \tabularnewline
3 & 0.920593 & 9.5671 & 0 \tabularnewline
4 & 0.891533 & 9.2651 & 0 \tabularnewline
5 & 0.86181 & 8.9562 & 0 \tabularnewline
6 & 0.831054 & 8.6366 & 0 \tabularnewline
7 & 0.800395 & 8.3179 & 0 \tabularnewline
8 & 0.768737 & 7.9889 & 0 \tabularnewline
9 & 0.737238 & 7.6616 & 0 \tabularnewline
10 & 0.704584 & 7.3223 & 0 \tabularnewline
11 & 0.671777 & 6.9813 & 0 \tabularnewline
12 & 0.638554 & 6.636 & 0 \tabularnewline
13 & 0.605124 & 6.2886 & 0 \tabularnewline
14 & 0.571588 & 5.9401 & 0 \tabularnewline
15 & 0.538454 & 5.5958 & 0 \tabularnewline
16 & 0.505201 & 5.2502 & 0 \tabularnewline
17 & 0.470803 & 4.8927 & 2e-06 \tabularnewline
18 & 0.436361 & 4.5348 & 7e-06 \tabularnewline
19 & 0.403451 & 4.1928 & 2.8e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2223&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]0[/C][C]1[/C][C]10.3923[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.974832[/C][C]10.1307[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.94839[/C][C]9.856[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.920593[/C][C]9.5671[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.891533[/C][C]9.2651[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.86181[/C][C]8.9562[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.831054[/C][C]8.6366[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.800395[/C][C]8.3179[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.768737[/C][C]7.9889[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.737238[/C][C]7.6616[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.704584[/C][C]7.3223[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.671777[/C][C]6.9813[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.638554[/C][C]6.636[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.605124[/C][C]6.2886[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.571588[/C][C]5.9401[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.538454[/C][C]5.5958[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.505201[/C][C]5.2502[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.470803[/C][C]4.8927[/C][C]2e-06[/C][/ROW]
[ROW][C]18[/C][C]0.436361[/C][C]4.5348[/C][C]7e-06[/C][/ROW]
[ROW][C]19[/C][C]0.403451[/C][C]4.1928[/C][C]2.8e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2223&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
0	1	10.3923	0
1	0.974832	10.1307	0
2	0.94839	9.856	0
3	0.920593	9.5671	0
4	0.891533	9.2651	0
5	0.86181	8.9562	0
6	0.831054	8.6366	0
7	0.800395	8.3179	0
8	0.768737	7.9889	0
9	0.737238	7.6616	0
10	0.704584	7.3223	0
11	0.671777	6.9813	0
12	0.638554	6.636	0
13	0.605124	6.2886	0
14	0.571588	5.9401	0
15	0.538454	5.5958	0
16	0.505201	5.2502	0
17	0.470803	4.8927	2e-06
18	0.436361	4.5348	7e-06
19	0.403451	4.1928	2.8e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.974832	10.1307	0
1	-0.038351	-0.3986	0.654498
2	-0.040265	-0.4184	0.661773
3	-0.038659	-0.4018	0.655672
4	-0.026951	-0.2801	0.610027
5	-0.035086	-0.3646	0.641947
6	-0.012799	-0.133	0.552782
7	-0.035893	-0.373	0.645065
8	-0.012987	-0.135	0.553554
9	-0.040553	-0.4214	0.662864
10	-0.020415	-0.2122	0.583809
11	-0.026945	-0.28	0.610003
12	-0.022528	-0.2341	0.592331
13	-0.022357	-0.2323	0.591644
14	-0.01148	-0.1193	0.54737
15	-0.024288	-0.2524	0.599397
16	-0.044551	-0.463	0.677847
17	-0.023879	-0.2482	0.59776
18	0.008838	0.0918	0.463496
19	-0.023553	-0.2448	0.596449

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.974832 & 10.1307 & 0 \tabularnewline
1 & -0.038351 & -0.3986 & 0.654498 \tabularnewline
2 & -0.040265 & -0.4184 & 0.661773 \tabularnewline
3 & -0.038659 & -0.4018 & 0.655672 \tabularnewline
4 & -0.026951 & -0.2801 & 0.610027 \tabularnewline
5 & -0.035086 & -0.3646 & 0.641947 \tabularnewline
6 & -0.012799 & -0.133 & 0.552782 \tabularnewline
7 & -0.035893 & -0.373 & 0.645065 \tabularnewline
8 & -0.012987 & -0.135 & 0.553554 \tabularnewline
9 & -0.040553 & -0.4214 & 0.662864 \tabularnewline
10 & -0.020415 & -0.2122 & 0.583809 \tabularnewline
11 & -0.026945 & -0.28 & 0.610003 \tabularnewline
12 & -0.022528 & -0.2341 & 0.592331 \tabularnewline
13 & -0.022357 & -0.2323 & 0.591644 \tabularnewline
14 & -0.01148 & -0.1193 & 0.54737 \tabularnewline
15 & -0.024288 & -0.2524 & 0.599397 \tabularnewline
16 & -0.044551 & -0.463 & 0.677847 \tabularnewline
17 & -0.023879 & -0.2482 & 0.59776 \tabularnewline
18 & 0.008838 & 0.0918 & 0.463496 \tabularnewline
19 & -0.023553 & -0.2448 & 0.596449 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2223&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]0[/C][C]0.974832[/C][C]10.1307[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.038351[/C][C]-0.3986[/C][C]0.654498[/C][/ROW]
[ROW][C]2[/C][C]-0.040265[/C][C]-0.4184[/C][C]0.661773[/C][/ROW]
[ROW][C]3[/C][C]-0.038659[/C][C]-0.4018[/C][C]0.655672[/C][/ROW]
[ROW][C]4[/C][C]-0.026951[/C][C]-0.2801[/C][C]0.610027[/C][/ROW]
[ROW][C]5[/C][C]-0.035086[/C][C]-0.3646[/C][C]0.641947[/C][/ROW]
[ROW][C]6[/C][C]-0.012799[/C][C]-0.133[/C][C]0.552782[/C][/ROW]
[ROW][C]7[/C][C]-0.035893[/C][C]-0.373[/C][C]0.645065[/C][/ROW]
[ROW][C]8[/C][C]-0.012987[/C][C]-0.135[/C][C]0.553554[/C][/ROW]
[ROW][C]9[/C][C]-0.040553[/C][C]-0.4214[/C][C]0.662864[/C][/ROW]
[ROW][C]10[/C][C]-0.020415[/C][C]-0.2122[/C][C]0.583809[/C][/ROW]
[ROW][C]11[/C][C]-0.026945[/C][C]-0.28[/C][C]0.610003[/C][/ROW]
[ROW][C]12[/C][C]-0.022528[/C][C]-0.2341[/C][C]0.592331[/C][/ROW]
[ROW][C]13[/C][C]-0.022357[/C][C]-0.2323[/C][C]0.591644[/C][/ROW]
[ROW][C]14[/C][C]-0.01148[/C][C]-0.1193[/C][C]0.54737[/C][/ROW]
[ROW][C]15[/C][C]-0.024288[/C][C]-0.2524[/C][C]0.599397[/C][/ROW]
[ROW][C]16[/C][C]-0.044551[/C][C]-0.463[/C][C]0.677847[/C][/ROW]
[ROW][C]17[/C][C]-0.023879[/C][C]-0.2482[/C][C]0.59776[/C][/ROW]
[ROW][C]18[/C][C]0.008838[/C][C]0.0918[/C][C]0.463496[/C][/ROW]
[ROW][C]19[/C][C]-0.023553[/C][C]-0.2448[/C][C]0.596449[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2223&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2223&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
0	0.974832	10.1307	0
1	-0.038351	-0.3986	0.654498
2	-0.040265	-0.4184	0.661773
3	-0.038659	-0.4018	0.655672
4	-0.026951	-0.2801	0.610027
5	-0.035086	-0.3646	0.641947
6	-0.012799	-0.133	0.552782
7	-0.035893	-0.373	0.645065
8	-0.012987	-0.135	0.553554
9	-0.040553	-0.4214	0.662864
10	-0.020415	-0.2122	0.583809
11	-0.026945	-0.28	0.610003
12	-0.022528	-0.2341	0.592331
13	-0.022357	-0.2323	0.591644
14	-0.01148	-0.1193	0.54737
15	-0.024288	-0.2524	0.599397
16	-0.044551	-0.463	0.677847
17	-0.023879	-0.2482	0.59776
18	0.008838	0.0918	0.463496
19	-0.023553	-0.2448	0.596449

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(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)

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Input Parameters & R Code