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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 03:10:47 -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/t1195812193pup5mj6ogw25a3r.htm/, Retrieved Mon, 29 Apr 2024 00:42:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6126, Retrieved Mon, 29 Apr 2024 00:42:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Q2, groep 1, totaal

Estimated Impact

221

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

-       [(Partial) Autocorrelation Function] [Q2, groep 1, totaal] [2007-11-23 10:10:47] [ce556af355e2eff84137e549c6ea8397] [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=6126&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=6126&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6126&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	8.9443	0
1	0.239736	2.1443	0.017523
2	-0.037255	-0.3332	0.630079
3	0.302062	2.7017	0.00421
4	0.049815	0.4456	0.328561
5	0.182975	1.6366	0.052823
6	0.48364	4.3258	2.2e-05
7	0.158206	1.415	0.08047
8	0.052863	0.4728	0.318815
9	0.183315	1.6396	0.052506
10	-0.188116	-1.6826	0.95182
11	0.076649	0.6856	0.247483
12	0.634837	5.6782	0
13	0.075736	0.6774	0.250053
14	-0.133564	-1.1946	0.88212
15	0.131709	1.178	0.121137
16	-0.089314	-0.7989	0.786629
17	0.022538	0.2016	0.420376
18	0.285792	2.5562	0.006237

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.239736 & 2.1443 & 0.017523 \tabularnewline
2 & -0.037255 & -0.3332 & 0.630079 \tabularnewline
3 & 0.302062 & 2.7017 & 0.00421 \tabularnewline
4 & 0.049815 & 0.4456 & 0.328561 \tabularnewline
5 & 0.182975 & 1.6366 & 0.052823 \tabularnewline
6 & 0.48364 & 4.3258 & 2.2e-05 \tabularnewline
7 & 0.158206 & 1.415 & 0.08047 \tabularnewline
8 & 0.052863 & 0.4728 & 0.318815 \tabularnewline
9 & 0.183315 & 1.6396 & 0.052506 \tabularnewline
10 & -0.188116 & -1.6826 & 0.95182 \tabularnewline
11 & 0.076649 & 0.6856 & 0.247483 \tabularnewline
12 & 0.634837 & 5.6782 & 0 \tabularnewline
13 & 0.075736 & 0.6774 & 0.250053 \tabularnewline
14 & -0.133564 & -1.1946 & 0.88212 \tabularnewline
15 & 0.131709 & 1.178 & 0.121137 \tabularnewline
16 & -0.089314 & -0.7989 & 0.786629 \tabularnewline
17 & 0.022538 & 0.2016 & 0.420376 \tabularnewline
18 & 0.285792 & 2.5562 & 0.006237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6126&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]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.239736[/C][C]2.1443[/C][C]0.017523[/C][/ROW]
[ROW][C]2[/C][C]-0.037255[/C][C]-0.3332[/C][C]0.630079[/C][/ROW]
[ROW][C]3[/C][C]0.302062[/C][C]2.7017[/C][C]0.00421[/C][/ROW]
[ROW][C]4[/C][C]0.049815[/C][C]0.4456[/C][C]0.328561[/C][/ROW]
[ROW][C]5[/C][C]0.182975[/C][C]1.6366[/C][C]0.052823[/C][/ROW]
[ROW][C]6[/C][C]0.48364[/C][C]4.3258[/C][C]2.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.158206[/C][C]1.415[/C][C]0.08047[/C][/ROW]
[ROW][C]8[/C][C]0.052863[/C][C]0.4728[/C][C]0.318815[/C][/ROW]
[ROW][C]9[/C][C]0.183315[/C][C]1.6396[/C][C]0.052506[/C][/ROW]
[ROW][C]10[/C][C]-0.188116[/C][C]-1.6826[/C][C]0.95182[/C][/ROW]
[ROW][C]11[/C][C]0.076649[/C][C]0.6856[/C][C]0.247483[/C][/ROW]
[ROW][C]12[/C][C]0.634837[/C][C]5.6782[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.075736[/C][C]0.6774[/C][C]0.250053[/C][/ROW]
[ROW][C]14[/C][C]-0.133564[/C][C]-1.1946[/C][C]0.88212[/C][/ROW]
[ROW][C]15[/C][C]0.131709[/C][C]1.178[/C][C]0.121137[/C][/ROW]
[ROW][C]16[/C][C]-0.089314[/C][C]-0.7989[/C][C]0.786629[/C][/ROW]
[ROW][C]17[/C][C]0.022538[/C][C]0.2016[/C][C]0.420376[/C][/ROW]
[ROW][C]18[/C][C]0.285792[/C][C]2.5562[/C][C]0.006237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6126&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6126&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	8.9443	0
1	0.239736	2.1443	0.017523
2	-0.037255	-0.3332	0.630079
3	0.302062	2.7017	0.00421
4	0.049815	0.4456	0.328561
5	0.182975	1.6366	0.052823
6	0.48364	4.3258	2.2e-05
7	0.158206	1.415	0.08047
8	0.052863	0.4728	0.318815
9	0.183315	1.6396	0.052506
10	-0.188116	-1.6826	0.95182
11	0.076649	0.6856	0.247483
12	0.634837	5.6782	0
13	0.075736	0.6774	0.250053
14	-0.133564	-1.1946	0.88212
15	0.131709	1.178	0.121137
16	-0.089314	-0.7989	0.786629
17	0.022538	0.2016	0.420376
18	0.285792	2.5562	0.006237

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.239736	2.1443	0.017523
1	-0.100505	-0.8989	0.814309
2	0.360111	3.2209	0.000924
3	-0.165547	-1.4807	0.928693
4	0.365741	3.2713	0.000791
5	0.260001	2.3255	0.011289
6	0.070671	0.6321	0.264561
7	0.013062	0.1168	0.453642
8	-0.015758	-0.1409	0.555864
9	-0.406403	-3.635	0.999755
10	0.188981	1.6903	0.047432
11	0.448067	4.0076	6.8e-05
12	-0.170433	-1.5244	0.934324
13	-0.158283	-1.4157	0.919631
14	-0.068046	-0.6086	0.72775
15	0.057586	0.5151	0.303964
16	-0.057159	-0.5112	0.694705
17	-0.079799	-0.7137	0.761269
18	0.013664	0.1222	0.451517

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.239736 & 2.1443 & 0.017523 \tabularnewline
1 & -0.100505 & -0.8989 & 0.814309 \tabularnewline
2 & 0.360111 & 3.2209 & 0.000924 \tabularnewline
3 & -0.165547 & -1.4807 & 0.928693 \tabularnewline
4 & 0.365741 & 3.2713 & 0.000791 \tabularnewline
5 & 0.260001 & 2.3255 & 0.011289 \tabularnewline
6 & 0.070671 & 0.6321 & 0.264561 \tabularnewline
7 & 0.013062 & 0.1168 & 0.453642 \tabularnewline
8 & -0.015758 & -0.1409 & 0.555864 \tabularnewline
9 & -0.406403 & -3.635 & 0.999755 \tabularnewline
10 & 0.188981 & 1.6903 & 0.047432 \tabularnewline
11 & 0.448067 & 4.0076 & 6.8e-05 \tabularnewline
12 & -0.170433 & -1.5244 & 0.934324 \tabularnewline
13 & -0.158283 & -1.4157 & 0.919631 \tabularnewline
14 & -0.068046 & -0.6086 & 0.72775 \tabularnewline
15 & 0.057586 & 0.5151 & 0.303964 \tabularnewline
16 & -0.057159 & -0.5112 & 0.694705 \tabularnewline
17 & -0.079799 & -0.7137 & 0.761269 \tabularnewline
18 & 0.013664 & 0.1222 & 0.451517 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6126&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]0.239736[/C][C]2.1443[/C][C]0.017523[/C][/ROW]
[ROW][C]1[/C][C]-0.100505[/C][C]-0.8989[/C][C]0.814309[/C][/ROW]
[ROW][C]2[/C][C]0.360111[/C][C]3.2209[/C][C]0.000924[/C][/ROW]
[ROW][C]3[/C][C]-0.165547[/C][C]-1.4807[/C][C]0.928693[/C][/ROW]
[ROW][C]4[/C][C]0.365741[/C][C]3.2713[/C][C]0.000791[/C][/ROW]
[ROW][C]5[/C][C]0.260001[/C][C]2.3255[/C][C]0.011289[/C][/ROW]
[ROW][C]6[/C][C]0.070671[/C][C]0.6321[/C][C]0.264561[/C][/ROW]
[ROW][C]7[/C][C]0.013062[/C][C]0.1168[/C][C]0.453642[/C][/ROW]
[ROW][C]8[/C][C]-0.015758[/C][C]-0.1409[/C][C]0.555864[/C][/ROW]
[ROW][C]9[/C][C]-0.406403[/C][C]-3.635[/C][C]0.999755[/C][/ROW]
[ROW][C]10[/C][C]0.188981[/C][C]1.6903[/C][C]0.047432[/C][/ROW]
[ROW][C]11[/C][C]0.448067[/C][C]4.0076[/C][C]6.8e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.170433[/C][C]-1.5244[/C][C]0.934324[/C][/ROW]
[ROW][C]13[/C][C]-0.158283[/C][C]-1.4157[/C][C]0.919631[/C][/ROW]
[ROW][C]14[/C][C]-0.068046[/C][C]-0.6086[/C][C]0.72775[/C][/ROW]
[ROW][C]15[/C][C]0.057586[/C][C]0.5151[/C][C]0.303964[/C][/ROW]
[ROW][C]16[/C][C]-0.057159[/C][C]-0.5112[/C][C]0.694705[/C][/ROW]
[ROW][C]17[/C][C]-0.079799[/C][C]-0.7137[/C][C]0.761269[/C][/ROW]
[ROW][C]18[/C][C]0.013664[/C][C]0.1222[/C][C]0.451517[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6126&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6126&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	0.239736	2.1443	0.017523
1	-0.100505	-0.8989	0.814309
2	0.360111	3.2209	0.000924
3	-0.165547	-1.4807	0.928693
4	0.365741	3.2713	0.000791
5	0.260001	2.3255	0.011289
6	0.070671	0.6321	0.264561
7	0.013062	0.1168	0.453642
8	-0.015758	-0.1409	0.555864
9	-0.406403	-3.635	0.999755
10	0.188981	1.6903	0.047432
11	0.448067	4.0076	6.8e-05
12	-0.170433	-1.5244	0.934324
13	-0.158283	-1.4157	0.919631
14	-0.068046	-0.6086	0.72775
15	0.057586	0.5151	0.303964
16	-0.057159	-0.5112	0.694705
17	-0.079799	-0.7137	0.761269
18	0.013664	0.1222	0.451517

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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