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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 05 Dec 2007 12:26:15 -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/Dec/05/t1196882120ccxyptcig8etyrp.htm/, Retrieved Thu, 02 May 2024 20:35:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2504, Retrieved Thu, 02 May 2024 20:35:44 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

lamda = -0,6 D=1 d=1

Estimated Impact

235

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-12-05 19:26:15] [bebbf4ab6ac77d61a56e6916ab0650f9] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2504&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2504&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2504&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.3485	0
1	-0.544662	-4.0024	0.999904
2	-0.059321	-0.4359	0.667684
3	0.240273	1.7656	0.041555
4	-0.237364	-1.7443	0.956598
5	0.091279	0.6708	0.252616
6	0.212507	1.5616	0.062112
7	-0.334986	-2.4616	0.991472
8	0.021558	0.1584	0.43736
9	0.412135	3.0286	0.001882
10	-0.495898	-3.6441	0.999698
11	0.268188	1.9708	0.026942
12	-0.019677	-0.1446	0.557215
13	-0.18799	-1.3814	0.913583
14	0.246433	1.8109	0.03786
15	-0.055043	-0.4045	0.656273
16	-0.252102	-1.8526	0.965294
17	0.29334	2.1556	0.017795

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.3485 & 0 \tabularnewline
1 & -0.544662 & -4.0024 & 0.999904 \tabularnewline
2 & -0.059321 & -0.4359 & 0.667684 \tabularnewline
3 & 0.240273 & 1.7656 & 0.041555 \tabularnewline
4 & -0.237364 & -1.7443 & 0.956598 \tabularnewline
5 & 0.091279 & 0.6708 & 0.252616 \tabularnewline
6 & 0.212507 & 1.5616 & 0.062112 \tabularnewline
7 & -0.334986 & -2.4616 & 0.991472 \tabularnewline
8 & 0.021558 & 0.1584 & 0.43736 \tabularnewline
9 & 0.412135 & 3.0286 & 0.001882 \tabularnewline
10 & -0.495898 & -3.6441 & 0.999698 \tabularnewline
11 & 0.268188 & 1.9708 & 0.026942 \tabularnewline
12 & -0.019677 & -0.1446 & 0.557215 \tabularnewline
13 & -0.18799 & -1.3814 & 0.913583 \tabularnewline
14 & 0.246433 & 1.8109 & 0.03786 \tabularnewline
15 & -0.055043 & -0.4045 & 0.656273 \tabularnewline
16 & -0.252102 & -1.8526 & 0.965294 \tabularnewline
17 & 0.29334 & 2.1556 & 0.017795 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2504&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]7.3485[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.544662[/C][C]-4.0024[/C][C]0.999904[/C][/ROW]
[ROW][C]2[/C][C]-0.059321[/C][C]-0.4359[/C][C]0.667684[/C][/ROW]
[ROW][C]3[/C][C]0.240273[/C][C]1.7656[/C][C]0.041555[/C][/ROW]
[ROW][C]4[/C][C]-0.237364[/C][C]-1.7443[/C][C]0.956598[/C][/ROW]
[ROW][C]5[/C][C]0.091279[/C][C]0.6708[/C][C]0.252616[/C][/ROW]
[ROW][C]6[/C][C]0.212507[/C][C]1.5616[/C][C]0.062112[/C][/ROW]
[ROW][C]7[/C][C]-0.334986[/C][C]-2.4616[/C][C]0.991472[/C][/ROW]
[ROW][C]8[/C][C]0.021558[/C][C]0.1584[/C][C]0.43736[/C][/ROW]
[ROW][C]9[/C][C]0.412135[/C][C]3.0286[/C][C]0.001882[/C][/ROW]
[ROW][C]10[/C][C]-0.495898[/C][C]-3.6441[/C][C]0.999698[/C][/ROW]
[ROW][C]11[/C][C]0.268188[/C][C]1.9708[/C][C]0.026942[/C][/ROW]
[ROW][C]12[/C][C]-0.019677[/C][C]-0.1446[/C][C]0.557215[/C][/ROW]
[ROW][C]13[/C][C]-0.18799[/C][C]-1.3814[/C][C]0.913583[/C][/ROW]
[ROW][C]14[/C][C]0.246433[/C][C]1.8109[/C][C]0.03786[/C][/ROW]
[ROW][C]15[/C][C]-0.055043[/C][C]-0.4045[/C][C]0.656273[/C][/ROW]
[ROW][C]16[/C][C]-0.252102[/C][C]-1.8526[/C][C]0.965294[/C][/ROW]
[ROW][C]17[/C][C]0.29334[/C][C]2.1556[/C][C]0.017795[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2504&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2504&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	7.3485	0
1	-0.544662	-4.0024	0.999904
2	-0.059321	-0.4359	0.667684
3	0.240273	1.7656	0.041555
4	-0.237364	-1.7443	0.956598
5	0.091279	0.6708	0.252616
6	0.212507	1.5616	0.062112
7	-0.334986	-2.4616	0.991472
8	0.021558	0.1584	0.43736
9	0.412135	3.0286	0.001882
10	-0.495898	-3.6441	0.999698
11	0.268188	1.9708	0.026942
12	-0.019677	-0.1446	0.557215
13	-0.18799	-1.3814	0.913583
14	0.246433	1.8109	0.03786
15	-0.055043	-0.4045	0.656273
16	-0.252102	-1.8526	0.965294
17	0.29334	2.1556	0.017795

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.544662	-4.0024	0.999904
1	-0.506123	-3.7192	0.999762
2	-0.160665	-1.1806	0.87854
3	-0.286604	-2.1061	0.98007
4	-0.251017	-1.8446	0.964707
5	0.155488	1.1426	0.129124
6	-0.00982	-0.0722	0.528631
7	-0.332704	-2.4449	0.991108
8	0.260111	1.9114	0.030632
9	-0.031664	-0.2327	0.591555
10	0.008113	0.0596	0.476341
11	-0.055753	-0.4097	0.658177
12	-0.028807	-0.2117	0.583427
13	-0.036081	-0.2651	0.604045
14	-0.059459	-0.4369	0.668049
15	-0.196586	-1.4446	0.922827
16	-0.077752	-0.5714	0.714937
17	0.075763	0.5567	0.290002

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.544662 & -4.0024 & 0.999904 \tabularnewline
1 & -0.506123 & -3.7192 & 0.999762 \tabularnewline
2 & -0.160665 & -1.1806 & 0.87854 \tabularnewline
3 & -0.286604 & -2.1061 & 0.98007 \tabularnewline
4 & -0.251017 & -1.8446 & 0.964707 \tabularnewline
5 & 0.155488 & 1.1426 & 0.129124 \tabularnewline
6 & -0.00982 & -0.0722 & 0.528631 \tabularnewline
7 & -0.332704 & -2.4449 & 0.991108 \tabularnewline
8 & 0.260111 & 1.9114 & 0.030632 \tabularnewline
9 & -0.031664 & -0.2327 & 0.591555 \tabularnewline
10 & 0.008113 & 0.0596 & 0.476341 \tabularnewline
11 & -0.055753 & -0.4097 & 0.658177 \tabularnewline
12 & -0.028807 & -0.2117 & 0.583427 \tabularnewline
13 & -0.036081 & -0.2651 & 0.604045 \tabularnewline
14 & -0.059459 & -0.4369 & 0.668049 \tabularnewline
15 & -0.196586 & -1.4446 & 0.922827 \tabularnewline
16 & -0.077752 & -0.5714 & 0.714937 \tabularnewline
17 & 0.075763 & 0.5567 & 0.290002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2504&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]-0.544662[/C][C]-4.0024[/C][C]0.999904[/C][/ROW]
[ROW][C]1[/C][C]-0.506123[/C][C]-3.7192[/C][C]0.999762[/C][/ROW]
[ROW][C]2[/C][C]-0.160665[/C][C]-1.1806[/C][C]0.87854[/C][/ROW]
[ROW][C]3[/C][C]-0.286604[/C][C]-2.1061[/C][C]0.98007[/C][/ROW]
[ROW][C]4[/C][C]-0.251017[/C][C]-1.8446[/C][C]0.964707[/C][/ROW]
[ROW][C]5[/C][C]0.155488[/C][C]1.1426[/C][C]0.129124[/C][/ROW]
[ROW][C]6[/C][C]-0.00982[/C][C]-0.0722[/C][C]0.528631[/C][/ROW]
[ROW][C]7[/C][C]-0.332704[/C][C]-2.4449[/C][C]0.991108[/C][/ROW]
[ROW][C]8[/C][C]0.260111[/C][C]1.9114[/C][C]0.030632[/C][/ROW]
[ROW][C]9[/C][C]-0.031664[/C][C]-0.2327[/C][C]0.591555[/C][/ROW]
[ROW][C]10[/C][C]0.008113[/C][C]0.0596[/C][C]0.476341[/C][/ROW]
[ROW][C]11[/C][C]-0.055753[/C][C]-0.4097[/C][C]0.658177[/C][/ROW]
[ROW][C]12[/C][C]-0.028807[/C][C]-0.2117[/C][C]0.583427[/C][/ROW]
[ROW][C]13[/C][C]-0.036081[/C][C]-0.2651[/C][C]0.604045[/C][/ROW]
[ROW][C]14[/C][C]-0.059459[/C][C]-0.4369[/C][C]0.668049[/C][/ROW]
[ROW][C]15[/C][C]-0.196586[/C][C]-1.4446[/C][C]0.922827[/C][/ROW]
[ROW][C]16[/C][C]-0.077752[/C][C]-0.5714[/C][C]0.714937[/C][/ROW]
[ROW][C]17[/C][C]0.075763[/C][C]0.5567[/C][C]0.290002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2504&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2504&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	-0.544662	-4.0024	0.999904
1	-0.506123	-3.7192	0.999762
2	-0.160665	-1.1806	0.87854
3	-0.286604	-2.1061	0.98007
4	-0.251017	-1.8446	0.964707
5	0.155488	1.1426	0.129124
6	-0.00982	-0.0722	0.528631
7	-0.332704	-2.4449	0.991108
8	0.260111	1.9114	0.030632
9	-0.031664	-0.2327	0.591555
10	0.008113	0.0596	0.476341
11	-0.055753	-0.4097	0.658177
12	-0.028807	-0.2117	0.583427
13	-0.036081	-0.2651	0.604045
14	-0.059459	-0.4369	0.668049
15	-0.196586	-1.4446	0.922827
16	-0.077752	-0.5714	0.714937
17	0.075763	0.5567	0.290002

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -0.6 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -0.6 ; par3 = 1 ; par4 = 1 ; 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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