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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 06:37:14 -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/t11958246339cgy55voxuofgph.htm/, Retrieved Sun, 28 Apr 2024 23:13:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6168, Retrieved Sun, 28 Apr 2024 23:13:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

223

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

-     [(Partial) Autocorrelation Function] [Partiel Autocorre...] [2007-11-22 13:00:02] [ced1562ed3c62c3bc1f3b66b8f83b537]
-   PD    [(Partial) Autocorrelation Function] [WS 9] [2007-11-23 13:37:14] [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	3 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 & 3 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=6168&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]3 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=6168&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6168&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	3 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	0.105476	0.895	0.186887
2	-0.177777	-1.5085	0.932097
3	-0.094147	-0.7989	0.786503
4	-0.134954	-1.1451	0.872026
5	0.175107	1.4858	0.070845
6	0.328515	2.7875	0.003394
7	0.19989	1.6961	0.047091
8	-0.233642	-1.9825	0.974381
9	-0.156548	-1.3284	0.905872
10	-0.112831	-0.9574	0.829216
11	0.101715	0.8631	0.195479
12	0.488658	4.1464	4.6e-05
13	0.053776	0.4563	0.324773
14	-0.109118	-0.9259	0.821204
15	-0.158783	-1.3473	0.908948
16	-0.161594	-1.3712	0.91271
17	0.101128	0.8581	0.196842

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.105476 & 0.895 & 0.186887 \tabularnewline
2 & -0.177777 & -1.5085 & 0.932097 \tabularnewline
3 & -0.094147 & -0.7989 & 0.786503 \tabularnewline
4 & -0.134954 & -1.1451 & 0.872026 \tabularnewline
5 & 0.175107 & 1.4858 & 0.070845 \tabularnewline
6 & 0.328515 & 2.7875 & 0.003394 \tabularnewline
7 & 0.19989 & 1.6961 & 0.047091 \tabularnewline
8 & -0.233642 & -1.9825 & 0.974381 \tabularnewline
9 & -0.156548 & -1.3284 & 0.905872 \tabularnewline
10 & -0.112831 & -0.9574 & 0.829216 \tabularnewline
11 & 0.101715 & 0.8631 & 0.195479 \tabularnewline
12 & 0.488658 & 4.1464 & 4.6e-05 \tabularnewline
13 & 0.053776 & 0.4563 & 0.324773 \tabularnewline
14 & -0.109118 & -0.9259 & 0.821204 \tabularnewline
15 & -0.158783 & -1.3473 & 0.908948 \tabularnewline
16 & -0.161594 & -1.3712 & 0.91271 \tabularnewline
17 & 0.101128 & 0.8581 & 0.196842 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6168&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]0.105476[/C][C]0.895[/C][C]0.186887[/C][/ROW]
[ROW][C]2[/C][C]-0.177777[/C][C]-1.5085[/C][C]0.932097[/C][/ROW]
[ROW][C]3[/C][C]-0.094147[/C][C]-0.7989[/C][C]0.786503[/C][/ROW]
[ROW][C]4[/C][C]-0.134954[/C][C]-1.1451[/C][C]0.872026[/C][/ROW]
[ROW][C]5[/C][C]0.175107[/C][C]1.4858[/C][C]0.070845[/C][/ROW]
[ROW][C]6[/C][C]0.328515[/C][C]2.7875[/C][C]0.003394[/C][/ROW]
[ROW][C]7[/C][C]0.19989[/C][C]1.6961[/C][C]0.047091[/C][/ROW]
[ROW][C]8[/C][C]-0.233642[/C][C]-1.9825[/C][C]0.974381[/C][/ROW]
[ROW][C]9[/C][C]-0.156548[/C][C]-1.3284[/C][C]0.905872[/C][/ROW]
[ROW][C]10[/C][C]-0.112831[/C][C]-0.9574[/C][C]0.829216[/C][/ROW]
[ROW][C]11[/C][C]0.101715[/C][C]0.8631[/C][C]0.195479[/C][/ROW]
[ROW][C]12[/C][C]0.488658[/C][C]4.1464[/C][C]4.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.053776[/C][C]0.4563[/C][C]0.324773[/C][/ROW]
[ROW][C]14[/C][C]-0.109118[/C][C]-0.9259[/C][C]0.821204[/C][/ROW]
[ROW][C]15[/C][C]-0.158783[/C][C]-1.3473[/C][C]0.908948[/C][/ROW]
[ROW][C]16[/C][C]-0.161594[/C][C]-1.3712[/C][C]0.91271[/C][/ROW]
[ROW][C]17[/C][C]0.101128[/C][C]0.8581[/C][C]0.196842[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6168&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6168&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	0.105476	0.895	0.186887
2	-0.177777	-1.5085	0.932097
3	-0.094147	-0.7989	0.786503
4	-0.134954	-1.1451	0.872026
5	0.175107	1.4858	0.070845
6	0.328515	2.7875	0.003394
7	0.19989	1.6961	0.047091
8	-0.233642	-1.9825	0.974381
9	-0.156548	-1.3284	0.905872
10	-0.112831	-0.9574	0.829216
11	0.101715	0.8631	0.195479
12	0.488658	4.1464	4.6e-05
13	0.053776	0.4563	0.324773
14	-0.109118	-0.9259	0.821204
15	-0.158783	-1.3473	0.908948
16	-0.161594	-1.3712	0.91271
17	0.101128	0.8581	0.196842

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.105476	0.895	0.186887
1	-0.191027	-1.6209	0.945297
2	-0.054226	-0.4601	0.676592
3	-0.159088	-1.3499	0.909363
4	0.194175	1.6476	0.051893
5	0.25211	2.1392	0.017905
6	0.2269	1.9253	0.029071
7	-0.205262	-1.7417	0.957085
8	0.004209	0.0357	0.485805
9	-0.163321	-1.3858	0.914962
10	0.078064	0.6624	0.254916
11	0.32638	2.7694	0.003569
12	-0.020583	-0.1747	0.56908
13	0.082285	0.6982	0.243647
14	-0.045595	-0.3869	0.650011
15	-0.112857	-0.9576	0.829272
16	-0.059392	-0.504	0.692085
17	-0.046117	-0.3913	0.651641

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.105476 & 0.895 & 0.186887 \tabularnewline
1 & -0.191027 & -1.6209 & 0.945297 \tabularnewline
2 & -0.054226 & -0.4601 & 0.676592 \tabularnewline
3 & -0.159088 & -1.3499 & 0.909363 \tabularnewline
4 & 0.194175 & 1.6476 & 0.051893 \tabularnewline
5 & 0.25211 & 2.1392 & 0.017905 \tabularnewline
6 & 0.2269 & 1.9253 & 0.029071 \tabularnewline
7 & -0.205262 & -1.7417 & 0.957085 \tabularnewline
8 & 0.004209 & 0.0357 & 0.485805 \tabularnewline
9 & -0.163321 & -1.3858 & 0.914962 \tabularnewline
10 & 0.078064 & 0.6624 & 0.254916 \tabularnewline
11 & 0.32638 & 2.7694 & 0.003569 \tabularnewline
12 & -0.020583 & -0.1747 & 0.56908 \tabularnewline
13 & 0.082285 & 0.6982 & 0.243647 \tabularnewline
14 & -0.045595 & -0.3869 & 0.650011 \tabularnewline
15 & -0.112857 & -0.9576 & 0.829272 \tabularnewline
16 & -0.059392 & -0.504 & 0.692085 \tabularnewline
17 & -0.046117 & -0.3913 & 0.651641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6168&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]0.105476[/C][C]0.895[/C][C]0.186887[/C][/ROW]
[ROW][C]1[/C][C]-0.191027[/C][C]-1.6209[/C][C]0.945297[/C][/ROW]
[ROW][C]2[/C][C]-0.054226[/C][C]-0.4601[/C][C]0.676592[/C][/ROW]
[ROW][C]3[/C][C]-0.159088[/C][C]-1.3499[/C][C]0.909363[/C][/ROW]
[ROW][C]4[/C][C]0.194175[/C][C]1.6476[/C][C]0.051893[/C][/ROW]
[ROW][C]5[/C][C]0.25211[/C][C]2.1392[/C][C]0.017905[/C][/ROW]
[ROW][C]6[/C][C]0.2269[/C][C]1.9253[/C][C]0.029071[/C][/ROW]
[ROW][C]7[/C][C]-0.205262[/C][C]-1.7417[/C][C]0.957085[/C][/ROW]
[ROW][C]8[/C][C]0.004209[/C][C]0.0357[/C][C]0.485805[/C][/ROW]
[ROW][C]9[/C][C]-0.163321[/C][C]-1.3858[/C][C]0.914962[/C][/ROW]
[ROW][C]10[/C][C]0.078064[/C][C]0.6624[/C][C]0.254916[/C][/ROW]
[ROW][C]11[/C][C]0.32638[/C][C]2.7694[/C][C]0.003569[/C][/ROW]
[ROW][C]12[/C][C]-0.020583[/C][C]-0.1747[/C][C]0.56908[/C][/ROW]
[ROW][C]13[/C][C]0.082285[/C][C]0.6982[/C][C]0.243647[/C][/ROW]
[ROW][C]14[/C][C]-0.045595[/C][C]-0.3869[/C][C]0.650011[/C][/ROW]
[ROW][C]15[/C][C]-0.112857[/C][C]-0.9576[/C][C]0.829272[/C][/ROW]
[ROW][C]16[/C][C]-0.059392[/C][C]-0.504[/C][C]0.692085[/C][/ROW]
[ROW][C]17[/C][C]-0.046117[/C][C]-0.3913[/C][C]0.651641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6168&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6168&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	0.105476	0.895	0.186887
1	-0.191027	-1.6209	0.945297
2	-0.054226	-0.4601	0.676592
3	-0.159088	-1.3499	0.909363
4	0.194175	1.6476	0.051893
5	0.25211	2.1392	0.017905
6	0.2269	1.9253	0.029071
7	-0.205262	-1.7417	0.957085
8	0.004209	0.0357	0.485805
9	-0.163321	-1.3858	0.914962
10	0.078064	0.6624	0.254916
11	0.32638	2.7694	0.003569
12	-0.020583	-0.1747	0.56908
13	0.082285	0.6982	0.243647
14	-0.045595	-0.3869	0.650011
15	-0.112857	-0.9576	0.829272
16	-0.059392	-0.504	0.692085
17	-0.046117	-0.3913	0.651641

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 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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