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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 09:29:28 -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/2007/Nov/23/t1195834953u3bbmse13acz6q6.htm/, Retrieved Mon, 29 Apr 2024 02:37:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6223, Retrieved Mon, 29 Apr 2024 02:37:31 +0000

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No (this computation is public)

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Estimated Impact

175

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

-       [(Partial) Autocorrelation Function] [autocorr ind prod...] [2007-11-23 16:29:28] [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	2 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 & 2 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=6223&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]2 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=6223&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6223&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	2 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	8.4853	0
1	0.388515	3.2967	0.000761
2	0.19827	1.6824	0.048414
3	0.462825	3.9272	9.7e-05
4	0.127027	1.0779	0.142347
5	0.225373	1.9124	0.029905
6	0.522366	4.4324	1.6e-05
7	0.14155	1.2011	0.116826
8	0.143277	1.2157	0.114026
9	0.361715	3.0693	0.001512
10	0.045271	0.3841	0.351005
11	0.286336	2.4296	0.008805
12	0.588011	4.9894	2e-06
13	0.148693	1.2617	0.105564
14	0.120793	1.025	0.154405
15	0.233476	1.9811	0.0257
16	-0.051773	-0.4393	0.669122
17	0.12989	1.1022	0.137032

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.388515 & 3.2967 & 0.000761 \tabularnewline
2 & 0.19827 & 1.6824 & 0.048414 \tabularnewline
3 & 0.462825 & 3.9272 & 9.7e-05 \tabularnewline
4 & 0.127027 & 1.0779 & 0.142347 \tabularnewline
5 & 0.225373 & 1.9124 & 0.029905 \tabularnewline
6 & 0.522366 & 4.4324 & 1.6e-05 \tabularnewline
7 & 0.14155 & 1.2011 & 0.116826 \tabularnewline
8 & 0.143277 & 1.2157 & 0.114026 \tabularnewline
9 & 0.361715 & 3.0693 & 0.001512 \tabularnewline
10 & 0.045271 & 0.3841 & 0.351005 \tabularnewline
11 & 0.286336 & 2.4296 & 0.008805 \tabularnewline
12 & 0.588011 & 4.9894 & 2e-06 \tabularnewline
13 & 0.148693 & 1.2617 & 0.105564 \tabularnewline
14 & 0.120793 & 1.025 & 0.154405 \tabularnewline
15 & 0.233476 & 1.9811 & 0.0257 \tabularnewline
16 & -0.051773 & -0.4393 & 0.669122 \tabularnewline
17 & 0.12989 & 1.1022 & 0.137032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6223&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.388515[/C][C]3.2967[/C][C]0.000761[/C][/ROW]
[ROW][C]2[/C][C]0.19827[/C][C]1.6824[/C][C]0.048414[/C][/ROW]
[ROW][C]3[/C][C]0.462825[/C][C]3.9272[/C][C]9.7e-05[/C][/ROW]
[ROW][C]4[/C][C]0.127027[/C][C]1.0779[/C][C]0.142347[/C][/ROW]
[ROW][C]5[/C][C]0.225373[/C][C]1.9124[/C][C]0.029905[/C][/ROW]
[ROW][C]6[/C][C]0.522366[/C][C]4.4324[/C][C]1.6e-05[/C][/ROW]
[ROW][C]7[/C][C]0.14155[/C][C]1.2011[/C][C]0.116826[/C][/ROW]
[ROW][C]8[/C][C]0.143277[/C][C]1.2157[/C][C]0.114026[/C][/ROW]
[ROW][C]9[/C][C]0.361715[/C][C]3.0693[/C][C]0.001512[/C][/ROW]
[ROW][C]10[/C][C]0.045271[/C][C]0.3841[/C][C]0.351005[/C][/ROW]
[ROW][C]11[/C][C]0.286336[/C][C]2.4296[/C][C]0.008805[/C][/ROW]
[ROW][C]12[/C][C]0.588011[/C][C]4.9894[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.148693[/C][C]1.2617[/C][C]0.105564[/C][/ROW]
[ROW][C]14[/C][C]0.120793[/C][C]1.025[/C][C]0.154405[/C][/ROW]
[ROW][C]15[/C][C]0.233476[/C][C]1.9811[/C][C]0.0257[/C][/ROW]
[ROW][C]16[/C][C]-0.051773[/C][C]-0.4393[/C][C]0.669122[/C][/ROW]
[ROW][C]17[/C][C]0.12989[/C][C]1.1022[/C][C]0.137032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6223&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6223&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	8.4853	0
1	0.388515	3.2967	0.000761
2	0.19827	1.6824	0.048414
3	0.462825	3.9272	9.7e-05
4	0.127027	1.0779	0.142347
5	0.225373	1.9124	0.029905
6	0.522366	4.4324	1.6e-05
7	0.14155	1.2011	0.116826
8	0.143277	1.2157	0.114026
9	0.361715	3.0693	0.001512
10	0.045271	0.3841	0.351005
11	0.286336	2.4296	0.008805
12	0.588011	4.9894	2e-06
13	0.148693	1.2617	0.105564
14	0.120793	1.025	0.154405
15	0.233476	1.9811	0.0257
16	-0.051773	-0.4393	0.669122
17	0.12989	1.1022	0.137032

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.388515	3.2967	0.000761
1	0.05574	0.473	0.318834
2	0.435284	3.6935	0.000214
3	-0.262431	-2.2268	0.985455
4	0.353644	3.0008	0.001849
5	0.216265	1.8351	0.035313
6	-0.146054	-1.2393	0.890372
7	0.049665	0.4214	0.337352
8	0.06321	0.5364	0.296684
9	-0.090932	-0.7716	0.778556
10	0.35066	2.9755	0.00199
11	0.2173	1.8438	0.03466
12	-0.124435	-1.0559	0.852721
13	-0.161261	-1.3683	0.91227
14	-0.132946	-1.1281	0.868486
15	-0.034076	-0.2891	0.613348
16	-0.032377	-0.2747	0.607843
17	-0.128215	-1.0879	0.859874

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.388515 & 3.2967 & 0.000761 \tabularnewline
1 & 0.05574 & 0.473 & 0.318834 \tabularnewline
2 & 0.435284 & 3.6935 & 0.000214 \tabularnewline
3 & -0.262431 & -2.2268 & 0.985455 \tabularnewline
4 & 0.353644 & 3.0008 & 0.001849 \tabularnewline
5 & 0.216265 & 1.8351 & 0.035313 \tabularnewline
6 & -0.146054 & -1.2393 & 0.890372 \tabularnewline
7 & 0.049665 & 0.4214 & 0.337352 \tabularnewline
8 & 0.06321 & 0.5364 & 0.296684 \tabularnewline
9 & -0.090932 & -0.7716 & 0.778556 \tabularnewline
10 & 0.35066 & 2.9755 & 0.00199 \tabularnewline
11 & 0.2173 & 1.8438 & 0.03466 \tabularnewline
12 & -0.124435 & -1.0559 & 0.852721 \tabularnewline
13 & -0.161261 & -1.3683 & 0.91227 \tabularnewline
14 & -0.132946 & -1.1281 & 0.868486 \tabularnewline
15 & -0.034076 & -0.2891 & 0.613348 \tabularnewline
16 & -0.032377 & -0.2747 & 0.607843 \tabularnewline
17 & -0.128215 & -1.0879 & 0.859874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6223&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]0.388515[/C][C]3.2967[/C][C]0.000761[/C][/ROW]
[ROW][C]1[/C][C]0.05574[/C][C]0.473[/C][C]0.318834[/C][/ROW]
[ROW][C]2[/C][C]0.435284[/C][C]3.6935[/C][C]0.000214[/C][/ROW]
[ROW][C]3[/C][C]-0.262431[/C][C]-2.2268[/C][C]0.985455[/C][/ROW]
[ROW][C]4[/C][C]0.353644[/C][C]3.0008[/C][C]0.001849[/C][/ROW]
[ROW][C]5[/C][C]0.216265[/C][C]1.8351[/C][C]0.035313[/C][/ROW]
[ROW][C]6[/C][C]-0.146054[/C][C]-1.2393[/C][C]0.890372[/C][/ROW]
[ROW][C]7[/C][C]0.049665[/C][C]0.4214[/C][C]0.337352[/C][/ROW]
[ROW][C]8[/C][C]0.06321[/C][C]0.5364[/C][C]0.296684[/C][/ROW]
[ROW][C]9[/C][C]-0.090932[/C][C]-0.7716[/C][C]0.778556[/C][/ROW]
[ROW][C]10[/C][C]0.35066[/C][C]2.9755[/C][C]0.00199[/C][/ROW]
[ROW][C]11[/C][C]0.2173[/C][C]1.8438[/C][C]0.03466[/C][/ROW]
[ROW][C]12[/C][C]-0.124435[/C][C]-1.0559[/C][C]0.852721[/C][/ROW]
[ROW][C]13[/C][C]-0.161261[/C][C]-1.3683[/C][C]0.91227[/C][/ROW]
[ROW][C]14[/C][C]-0.132946[/C][C]-1.1281[/C][C]0.868486[/C][/ROW]
[ROW][C]15[/C][C]-0.034076[/C][C]-0.2891[/C][C]0.613348[/C][/ROW]
[ROW][C]16[/C][C]-0.032377[/C][C]-0.2747[/C][C]0.607843[/C][/ROW]
[ROW][C]17[/C][C]-0.128215[/C][C]-1.0879[/C][C]0.859874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6223&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6223&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	0.388515	3.2967	0.000761
1	0.05574	0.473	0.318834
2	0.435284	3.6935	0.000214
3	-0.262431	-2.2268	0.985455
4	0.353644	3.0008	0.001849
5	0.216265	1.8351	0.035313
6	-0.146054	-1.2393	0.890372
7	0.049665	0.4214	0.337352
8	0.06321	0.5364	0.296684
9	-0.090932	-0.7716	0.778556
10	0.35066	2.9755	0.00199
11	0.2173	1.8438	0.03466
12	-0.124435	-1.0559	0.852721
13	-0.161261	-1.3683	0.91227
14	-0.132946	-1.1281	0.868486
15	-0.034076	-0.2891	0.613348
16	-0.032377	-0.2747	0.607843
17	-0.128215	-1.0879	0.859874

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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