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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 11:04:21 -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/26/t1196099782684x5cng7sdu3wq.htm/, Retrieved Thu, 02 May 2024 16:33:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6601, Retrieved Thu, 02 May 2024 16:33:04 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

189

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

-       [(Partial) Autocorrelation Function] [Corr. Totaal] [2007-11-26 18:04:21] [6bdd947de0ee04552c8f0fc807f31807] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6601&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]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=6601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6601&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.641956	4.9726	3e-06
2	0.525609	4.0714	6.9e-05
3	0.660896	5.1193	2e-06
4	0.454889	3.5236	0.000411
5	0.465271	3.604	0.000319
6	0.630163	4.8812	4e-06
7	0.385459	2.9858	0.002045
8	0.372492	2.8853	0.002713
9	0.471781	3.6544	0.000272
10	0.245344	1.9004	0.031092
11	0.349944	2.7107	0.004372
12	0.505005	3.9118	0.000118
13	0.216033	1.6734	0.049729
14	0.159134	1.2326	0.111258
15	0.225276	1.745	0.043054
16	0.040104	0.3106	0.378574

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.641956 & 4.9726 & 3e-06 \tabularnewline
2 & 0.525609 & 4.0714 & 6.9e-05 \tabularnewline
3 & 0.660896 & 5.1193 & 2e-06 \tabularnewline
4 & 0.454889 & 3.5236 & 0.000411 \tabularnewline
5 & 0.465271 & 3.604 & 0.000319 \tabularnewline
6 & 0.630163 & 4.8812 & 4e-06 \tabularnewline
7 & 0.385459 & 2.9858 & 0.002045 \tabularnewline
8 & 0.372492 & 2.8853 & 0.002713 \tabularnewline
9 & 0.471781 & 3.6544 & 0.000272 \tabularnewline
10 & 0.245344 & 1.9004 & 0.031092 \tabularnewline
11 & 0.349944 & 2.7107 & 0.004372 \tabularnewline
12 & 0.505005 & 3.9118 & 0.000118 \tabularnewline
13 & 0.216033 & 1.6734 & 0.049729 \tabularnewline
14 & 0.159134 & 1.2326 & 0.111258 \tabularnewline
15 & 0.225276 & 1.745 & 0.043054 \tabularnewline
16 & 0.040104 & 0.3106 & 0.378574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6601&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.641956[/C][C]4.9726[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.525609[/C][C]4.0714[/C][C]6.9e-05[/C][/ROW]
[ROW][C]3[/C][C]0.660896[/C][C]5.1193[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.454889[/C][C]3.5236[/C][C]0.000411[/C][/ROW]
[ROW][C]5[/C][C]0.465271[/C][C]3.604[/C][C]0.000319[/C][/ROW]
[ROW][C]6[/C][C]0.630163[/C][C]4.8812[/C][C]4e-06[/C][/ROW]
[ROW][C]7[/C][C]0.385459[/C][C]2.9858[/C][C]0.002045[/C][/ROW]
[ROW][C]8[/C][C]0.372492[/C][C]2.8853[/C][C]0.002713[/C][/ROW]
[ROW][C]9[/C][C]0.471781[/C][C]3.6544[/C][C]0.000272[/C][/ROW]
[ROW][C]10[/C][C]0.245344[/C][C]1.9004[/C][C]0.031092[/C][/ROW]
[ROW][C]11[/C][C]0.349944[/C][C]2.7107[/C][C]0.004372[/C][/ROW]
[ROW][C]12[/C][C]0.505005[/C][C]3.9118[/C][C]0.000118[/C][/ROW]
[ROW][C]13[/C][C]0.216033[/C][C]1.6734[/C][C]0.049729[/C][/ROW]
[ROW][C]14[/C][C]0.159134[/C][C]1.2326[/C][C]0.111258[/C][/ROW]
[ROW][C]15[/C][C]0.225276[/C][C]1.745[/C][C]0.043054[/C][/ROW]
[ROW][C]16[/C][C]0.040104[/C][C]0.3106[/C][C]0.378574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6601&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	7.746	0
1	0.641956	4.9726	3e-06
2	0.525609	4.0714	6.9e-05
3	0.660896	5.1193	2e-06
4	0.454889	3.5236	0.000411
5	0.465271	3.604	0.000319
6	0.630163	4.8812	4e-06
7	0.385459	2.9858	0.002045
8	0.372492	2.8853	0.002713
9	0.471781	3.6544	0.000272
10	0.245344	1.9004	0.031092
11	0.349944	2.7107	0.004372
12	0.505005	3.9118	0.000118
13	0.216033	1.6734	0.049729
14	0.159134	1.2326	0.111258
15	0.225276	1.745	0.043054
16	0.040104	0.3106	0.378574

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.641956	4.9726	3e-06
1	0.193066	1.4955	0.070015
2	0.467654	3.6224	0.000301
3	-0.231016	-1.7894	0.960705
4	0.267886	2.075	0.02114
5	0.227663	1.7635	0.041457
6	-0.266499	-2.0643	0.978339
7	0.106783	0.8271	0.205717
8	-0.060528	-0.4688	0.679561
9	-0.137214	-1.0629	0.853947
10	0.295325	2.2876	0.012851
11	0.061708	0.478	0.317199
12	-0.268584	-2.0804	0.979118
13	-0.241464	-1.8704	0.966844
14	-0.074598	-0.5778	0.717231
15	0.066516	0.5152	0.304142
16	0.040378	0.3128	0.377772

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.641956 & 4.9726 & 3e-06 \tabularnewline
1 & 0.193066 & 1.4955 & 0.070015 \tabularnewline
2 & 0.467654 & 3.6224 & 0.000301 \tabularnewline
3 & -0.231016 & -1.7894 & 0.960705 \tabularnewline
4 & 0.267886 & 2.075 & 0.02114 \tabularnewline
5 & 0.227663 & 1.7635 & 0.041457 \tabularnewline
6 & -0.266499 & -2.0643 & 0.978339 \tabularnewline
7 & 0.106783 & 0.8271 & 0.205717 \tabularnewline
8 & -0.060528 & -0.4688 & 0.679561 \tabularnewline
9 & -0.137214 & -1.0629 & 0.853947 \tabularnewline
10 & 0.295325 & 2.2876 & 0.012851 \tabularnewline
11 & 0.061708 & 0.478 & 0.317199 \tabularnewline
12 & -0.268584 & -2.0804 & 0.979118 \tabularnewline
13 & -0.241464 & -1.8704 & 0.966844 \tabularnewline
14 & -0.074598 & -0.5778 & 0.717231 \tabularnewline
15 & 0.066516 & 0.5152 & 0.304142 \tabularnewline
16 & 0.040378 & 0.3128 & 0.377772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6601&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]0.641956[/C][C]4.9726[/C][C]3e-06[/C][/ROW]
[ROW][C]1[/C][C]0.193066[/C][C]1.4955[/C][C]0.070015[/C][/ROW]
[ROW][C]2[/C][C]0.467654[/C][C]3.6224[/C][C]0.000301[/C][/ROW]
[ROW][C]3[/C][C]-0.231016[/C][C]-1.7894[/C][C]0.960705[/C][/ROW]
[ROW][C]4[/C][C]0.267886[/C][C]2.075[/C][C]0.02114[/C][/ROW]
[ROW][C]5[/C][C]0.227663[/C][C]1.7635[/C][C]0.041457[/C][/ROW]
[ROW][C]6[/C][C]-0.266499[/C][C]-2.0643[/C][C]0.978339[/C][/ROW]
[ROW][C]7[/C][C]0.106783[/C][C]0.8271[/C][C]0.205717[/C][/ROW]
[ROW][C]8[/C][C]-0.060528[/C][C]-0.4688[/C][C]0.679561[/C][/ROW]
[ROW][C]9[/C][C]-0.137214[/C][C]-1.0629[/C][C]0.853947[/C][/ROW]
[ROW][C]10[/C][C]0.295325[/C][C]2.2876[/C][C]0.012851[/C][/ROW]
[ROW][C]11[/C][C]0.061708[/C][C]0.478[/C][C]0.317199[/C][/ROW]
[ROW][C]12[/C][C]-0.268584[/C][C]-2.0804[/C][C]0.979118[/C][/ROW]
[ROW][C]13[/C][C]-0.241464[/C][C]-1.8704[/C][C]0.966844[/C][/ROW]
[ROW][C]14[/C][C]-0.074598[/C][C]-0.5778[/C][C]0.717231[/C][/ROW]
[ROW][C]15[/C][C]0.066516[/C][C]0.5152[/C][C]0.304142[/C][/ROW]
[ROW][C]16[/C][C]0.040378[/C][C]0.3128[/C][C]0.377772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6601&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6601&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	0.641956	4.9726	3e-06
1	0.193066	1.4955	0.070015
2	0.467654	3.6224	0.000301
3	-0.231016	-1.7894	0.960705
4	0.267886	2.075	0.02114
5	0.227663	1.7635	0.041457
6	-0.266499	-2.0643	0.978339
7	0.106783	0.8271	0.205717
8	-0.060528	-0.4688	0.679561
9	-0.137214	-1.0629	0.853947
10	0.295325	2.2876	0.012851
11	0.061708	0.478	0.317199
12	-0.268584	-2.0804	0.979118
13	-0.241464	-1.8704	0.966844
14	-0.074598	-0.5778	0.717231
15	0.066516	0.5152	0.304142
16	0.040378	0.3128	0.377772

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

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Input Parameters & R Code