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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 03 Dec 2007 03:45:58 -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/03/t11966780412rycsl4pyv67xff.htm/, Retrieved Sat, 04 May 2024 02:44:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2311, Retrieved Sat, 04 May 2024 02:44:24 +0000

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Estimated Impact

240

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

-     [(Partial) Autocorrelation Function] [Q2, groep 1] [2007-11-23 10:24:00] [896fe76e31044e3fb614abd7cf3ce8b6]
-   PD    [(Partial) Autocorrelation Function] [w8] [2007-12-03 10:45:58] [d41d8cd98f00b204e9800998ecf8427e] [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=2311&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=2311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2311&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	7.4162	0
1	-0.520869	-3.8629	0.999851
2	-0.002644	-0.0196	0.507788
3	0.136178	1.0099	0.158477
4	-0.223226	-1.6555	0.948239
5	0.238999	1.7725	0.040928
6	-0.029399	-0.218	0.585892
7	-0.21993	-1.631	0.945702
8	0.173347	1.2856	0.101989
9	0.071166	0.5278	0.299887
10	-0.123003	-0.9122	0.817181
11	0.189515	1.4055	0.082751
12	-0.419853	-3.1137	0.998534
13	0.261123	1.9365	0.028973
14	-0.002878	-0.0213	0.508477
15	-0.074796	-0.5547	0.709327
16	0.061992	0.4597	0.323756
17	-0.10928	-0.8104	0.789411
18	0.165546	1.2277	0.112391

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.4162 & 0 \tabularnewline
1 & -0.520869 & -3.8629 & 0.999851 \tabularnewline
2 & -0.002644 & -0.0196 & 0.507788 \tabularnewline
3 & 0.136178 & 1.0099 & 0.158477 \tabularnewline
4 & -0.223226 & -1.6555 & 0.948239 \tabularnewline
5 & 0.238999 & 1.7725 & 0.040928 \tabularnewline
6 & -0.029399 & -0.218 & 0.585892 \tabularnewline
7 & -0.21993 & -1.631 & 0.945702 \tabularnewline
8 & 0.173347 & 1.2856 & 0.101989 \tabularnewline
9 & 0.071166 & 0.5278 & 0.299887 \tabularnewline
10 & -0.123003 & -0.9122 & 0.817181 \tabularnewline
11 & 0.189515 & 1.4055 & 0.082751 \tabularnewline
12 & -0.419853 & -3.1137 & 0.998534 \tabularnewline
13 & 0.261123 & 1.9365 & 0.028973 \tabularnewline
14 & -0.002878 & -0.0213 & 0.508477 \tabularnewline
15 & -0.074796 & -0.5547 & 0.709327 \tabularnewline
16 & 0.061992 & 0.4597 & 0.323756 \tabularnewline
17 & -0.10928 & -0.8104 & 0.789411 \tabularnewline
18 & 0.165546 & 1.2277 & 0.112391 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2311&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]7.4162[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.520869[/C][C]-3.8629[/C][C]0.999851[/C][/ROW]
[ROW][C]2[/C][C]-0.002644[/C][C]-0.0196[/C][C]0.507788[/C][/ROW]
[ROW][C]3[/C][C]0.136178[/C][C]1.0099[/C][C]0.158477[/C][/ROW]
[ROW][C]4[/C][C]-0.223226[/C][C]-1.6555[/C][C]0.948239[/C][/ROW]
[ROW][C]5[/C][C]0.238999[/C][C]1.7725[/C][C]0.040928[/C][/ROW]
[ROW][C]6[/C][C]-0.029399[/C][C]-0.218[/C][C]0.585892[/C][/ROW]
[ROW][C]7[/C][C]-0.21993[/C][C]-1.631[/C][C]0.945702[/C][/ROW]
[ROW][C]8[/C][C]0.173347[/C][C]1.2856[/C][C]0.101989[/C][/ROW]
[ROW][C]9[/C][C]0.071166[/C][C]0.5278[/C][C]0.299887[/C][/ROW]
[ROW][C]10[/C][C]-0.123003[/C][C]-0.9122[/C][C]0.817181[/C][/ROW]
[ROW][C]11[/C][C]0.189515[/C][C]1.4055[/C][C]0.082751[/C][/ROW]
[ROW][C]12[/C][C]-0.419853[/C][C]-3.1137[/C][C]0.998534[/C][/ROW]
[ROW][C]13[/C][C]0.261123[/C][C]1.9365[/C][C]0.028973[/C][/ROW]
[ROW][C]14[/C][C]-0.002878[/C][C]-0.0213[/C][C]0.508477[/C][/ROW]
[ROW][C]15[/C][C]-0.074796[/C][C]-0.5547[/C][C]0.709327[/C][/ROW]
[ROW][C]16[/C][C]0.061992[/C][C]0.4597[/C][C]0.323756[/C][/ROW]
[ROW][C]17[/C][C]-0.10928[/C][C]-0.8104[/C][C]0.789411[/C][/ROW]
[ROW][C]18[/C][C]0.165546[/C][C]1.2277[/C][C]0.112391[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2311&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	7.4162	0
1	-0.520869	-3.8629	0.999851
2	-0.002644	-0.0196	0.507788
3	0.136178	1.0099	0.158477
4	-0.223226	-1.6555	0.948239
5	0.238999	1.7725	0.040928
6	-0.029399	-0.218	0.585892
7	-0.21993	-1.631	0.945702
8	0.173347	1.2856	0.101989
9	0.071166	0.5278	0.299887
10	-0.123003	-0.9122	0.817181
11	0.189515	1.4055	0.082751
12	-0.419853	-3.1137	0.998534
13	0.261123	1.9365	0.028973
14	-0.002878	-0.0213	0.508477
15	-0.074796	-0.5547	0.709327
16	0.061992	0.4597	0.323756
17	-0.10928	-0.8104	0.789411
18	0.165546	1.2277	0.112391

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.520869	-3.8629	0.999851
1	-0.375944	-2.7881	0.996367
2	-0.098344	-0.7293	0.765554
3	-0.279185	-2.0705	0.978443
4	-0.006712	-0.0498	0.519761
5	0.119223	0.8842	0.190224
6	-0.148707	-1.1028	0.862551
7	-0.131597	-0.976	0.833319
8	0.155474	1.153	0.126943
9	0.074132	0.5498	0.292349
10	0.225227	1.6703	0.050269
11	-0.311494	-2.3101	0.98767
12	-0.193315	-1.4337	0.921336
13	-0.268726	-1.9929	0.97438
14	-0.116479	-0.8638	0.804284
15	-0.145958	-1.0825	0.858113
16	-0.137385	-1.0189	0.843638
17	0.091878	0.6814	0.249244
18	-0.131646	-0.9763	0.833407

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.520869 & -3.8629 & 0.999851 \tabularnewline
1 & -0.375944 & -2.7881 & 0.996367 \tabularnewline
2 & -0.098344 & -0.7293 & 0.765554 \tabularnewline
3 & -0.279185 & -2.0705 & 0.978443 \tabularnewline
4 & -0.006712 & -0.0498 & 0.519761 \tabularnewline
5 & 0.119223 & 0.8842 & 0.190224 \tabularnewline
6 & -0.148707 & -1.1028 & 0.862551 \tabularnewline
7 & -0.131597 & -0.976 & 0.833319 \tabularnewline
8 & 0.155474 & 1.153 & 0.126943 \tabularnewline
9 & 0.074132 & 0.5498 & 0.292349 \tabularnewline
10 & 0.225227 & 1.6703 & 0.050269 \tabularnewline
11 & -0.311494 & -2.3101 & 0.98767 \tabularnewline
12 & -0.193315 & -1.4337 & 0.921336 \tabularnewline
13 & -0.268726 & -1.9929 & 0.97438 \tabularnewline
14 & -0.116479 & -0.8638 & 0.804284 \tabularnewline
15 & -0.145958 & -1.0825 & 0.858113 \tabularnewline
16 & -0.137385 & -1.0189 & 0.843638 \tabularnewline
17 & 0.091878 & 0.6814 & 0.249244 \tabularnewline
18 & -0.131646 & -0.9763 & 0.833407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2311&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]-0.520869[/C][C]-3.8629[/C][C]0.999851[/C][/ROW]
[ROW][C]1[/C][C]-0.375944[/C][C]-2.7881[/C][C]0.996367[/C][/ROW]
[ROW][C]2[/C][C]-0.098344[/C][C]-0.7293[/C][C]0.765554[/C][/ROW]
[ROW][C]3[/C][C]-0.279185[/C][C]-2.0705[/C][C]0.978443[/C][/ROW]
[ROW][C]4[/C][C]-0.006712[/C][C]-0.0498[/C][C]0.519761[/C][/ROW]
[ROW][C]5[/C][C]0.119223[/C][C]0.8842[/C][C]0.190224[/C][/ROW]
[ROW][C]6[/C][C]-0.148707[/C][C]-1.1028[/C][C]0.862551[/C][/ROW]
[ROW][C]7[/C][C]-0.131597[/C][C]-0.976[/C][C]0.833319[/C][/ROW]
[ROW][C]8[/C][C]0.155474[/C][C]1.153[/C][C]0.126943[/C][/ROW]
[ROW][C]9[/C][C]0.074132[/C][C]0.5498[/C][C]0.292349[/C][/ROW]
[ROW][C]10[/C][C]0.225227[/C][C]1.6703[/C][C]0.050269[/C][/ROW]
[ROW][C]11[/C][C]-0.311494[/C][C]-2.3101[/C][C]0.98767[/C][/ROW]
[ROW][C]12[/C][C]-0.193315[/C][C]-1.4337[/C][C]0.921336[/C][/ROW]
[ROW][C]13[/C][C]-0.268726[/C][C]-1.9929[/C][C]0.97438[/C][/ROW]
[ROW][C]14[/C][C]-0.116479[/C][C]-0.8638[/C][C]0.804284[/C][/ROW]
[ROW][C]15[/C][C]-0.145958[/C][C]-1.0825[/C][C]0.858113[/C][/ROW]
[ROW][C]16[/C][C]-0.137385[/C][C]-1.0189[/C][C]0.843638[/C][/ROW]
[ROW][C]17[/C][C]0.091878[/C][C]0.6814[/C][C]0.249244[/C][/ROW]
[ROW][C]18[/C][C]-0.131646[/C][C]-0.9763[/C][C]0.833407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2311&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	-0.520869	-3.8629	0.999851
1	-0.375944	-2.7881	0.996367
2	-0.098344	-0.7293	0.765554
3	-0.279185	-2.0705	0.978443
4	-0.006712	-0.0498	0.519761
5	0.119223	0.8842	0.190224
6	-0.148707	-1.1028	0.862551
7	-0.131597	-0.976	0.833319
8	0.155474	1.153	0.126943
9	0.074132	0.5498	0.292349
10	0.225227	1.6703	0.050269
11	-0.311494	-2.3101	0.98767
12	-0.193315	-1.4337	0.921336
13	-0.268726	-1.9929	0.97438
14	-0.116479	-0.8638	0.804284
15	-0.145958	-1.0825	0.858113
16	-0.137385	-1.0189	0.843638
17	0.091878	0.6814	0.249244
18	-0.131646	-0.9763	0.833407

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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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