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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 06:02:18 -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/22/t1195736061ctzes8n43bbhon7.htm/, Retrieved Thu, 02 May 2024 20:47:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5963, Retrieved Thu, 02 May 2024 20:47:12 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

WS10 G29 Q2

Estimated Impact

181

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

-       [(Partial) Autocorrelation Function] [Partion auto corr] [2007-11-22 13:02:18] [7a600ca82a81f1b71fd92dcbb183f5b4] [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	4 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 & 4 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=5963&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]4 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=5963&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5963&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	4 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	11.8743	0
1	0.970411	11.523	0
2	0.93292	11.0778	0
3	0.897615	10.6586	0
4	0.857558	10.1829	0
5	0.821012	9.749	0
6	0.796953	9.4633	0
7	0.775926	9.2136	0
8	0.750177	8.9079	0
9	0.727766	8.6417	0
10	0.701231	8.3267	0
11	0.670358	7.9601	0
12	0.633685	7.5246	0
13	0.594457	7.0588	0
14	0.552665	6.5625	0
15	0.510883	6.0664	0
16	0.470195	5.5833	0
17	0.427498	5.0763	1e-06
18	0.388606	4.6144	4e-06
19	0.351573	4.1747	2.6e-05
20	0.312709	3.7132	0.000147

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 11.8743 & 0 \tabularnewline
1 & 0.970411 & 11.523 & 0 \tabularnewline
2 & 0.93292 & 11.0778 & 0 \tabularnewline
3 & 0.897615 & 10.6586 & 0 \tabularnewline
4 & 0.857558 & 10.1829 & 0 \tabularnewline
5 & 0.821012 & 9.749 & 0 \tabularnewline
6 & 0.796953 & 9.4633 & 0 \tabularnewline
7 & 0.775926 & 9.2136 & 0 \tabularnewline
8 & 0.750177 & 8.9079 & 0 \tabularnewline
9 & 0.727766 & 8.6417 & 0 \tabularnewline
10 & 0.701231 & 8.3267 & 0 \tabularnewline
11 & 0.670358 & 7.9601 & 0 \tabularnewline
12 & 0.633685 & 7.5246 & 0 \tabularnewline
13 & 0.594457 & 7.0588 & 0 \tabularnewline
14 & 0.552665 & 6.5625 & 0 \tabularnewline
15 & 0.510883 & 6.0664 & 0 \tabularnewline
16 & 0.470195 & 5.5833 & 0 \tabularnewline
17 & 0.427498 & 5.0763 & 1e-06 \tabularnewline
18 & 0.388606 & 4.6144 & 4e-06 \tabularnewline
19 & 0.351573 & 4.1747 & 2.6e-05 \tabularnewline
20 & 0.312709 & 3.7132 & 0.000147 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5963&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]11.8743[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.970411[/C][C]11.523[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.93292[/C][C]11.0778[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.897615[/C][C]10.6586[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.857558[/C][C]10.1829[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.821012[/C][C]9.749[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.796953[/C][C]9.4633[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.775926[/C][C]9.2136[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.750177[/C][C]8.9079[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.727766[/C][C]8.6417[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.701231[/C][C]8.3267[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.670358[/C][C]7.9601[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.633685[/C][C]7.5246[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.594457[/C][C]7.0588[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.552665[/C][C]6.5625[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.510883[/C][C]6.0664[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.470195[/C][C]5.5833[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.427498[/C][C]5.0763[/C][C]1e-06[/C][/ROW]
[ROW][C]18[/C][C]0.388606[/C][C]4.6144[/C][C]4e-06[/C][/ROW]
[ROW][C]19[/C][C]0.351573[/C][C]4.1747[/C][C]2.6e-05[/C][/ROW]
[ROW][C]20[/C][C]0.312709[/C][C]3.7132[/C][C]0.000147[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5963&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5963&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	11.8743	0
1	0.970411	11.523	0
2	0.93292	11.0778	0
3	0.897615	10.6586	0
4	0.857558	10.1829	0
5	0.821012	9.749	0
6	0.796953	9.4633	0
7	0.775926	9.2136	0
8	0.750177	8.9079	0
9	0.727766	8.6417	0
10	0.701231	8.3267	0
11	0.670358	7.9601	0
12	0.633685	7.5246	0
13	0.594457	7.0588	0
14	0.552665	6.5625	0
15	0.510883	6.0664	0
16	0.470195	5.5833	0
17	0.427498	5.0763	1e-06
18	0.388606	4.6144	4e-06
19	0.351573	4.1747	2.6e-05
20	0.312709	3.7132	0.000147

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.970411	11.523	0
1	-0.150545	-1.7876	0.962007
2	0.036851	0.4376	0.33118
3	-0.114941	-1.3648	0.912763
4	0.068395	0.8121	0.209039
5	0.17125	2.0335	0.02194
6	-0.002268	-0.0269	0.510724
7	-0.100632	-1.1949	0.882941
8	0.039296	0.4666	0.320748
9	-0.094707	-1.1246	0.868661
10	-0.007987	-0.0948	0.537714
11	-0.129101	-1.533	0.93624
12	-0.055631	-0.6606	0.745022
13	-0.055906	-0.6639	0.746065
14	-0.020447	-0.2428	0.59574
15	-0.045748	-0.5432	0.706085
16	-0.088648	-1.0526	0.852847
17	0.021904	0.2601	0.397583
18	-0.011628	-0.1381	0.554809
19	-0.061155	-0.7262	0.765531
20	-0.07562	-0.8979	0.814625

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.970411 & 11.523 & 0 \tabularnewline
1 & -0.150545 & -1.7876 & 0.962007 \tabularnewline
2 & 0.036851 & 0.4376 & 0.33118 \tabularnewline
3 & -0.114941 & -1.3648 & 0.912763 \tabularnewline
4 & 0.068395 & 0.8121 & 0.209039 \tabularnewline
5 & 0.17125 & 2.0335 & 0.02194 \tabularnewline
6 & -0.002268 & -0.0269 & 0.510724 \tabularnewline
7 & -0.100632 & -1.1949 & 0.882941 \tabularnewline
8 & 0.039296 & 0.4666 & 0.320748 \tabularnewline
9 & -0.094707 & -1.1246 & 0.868661 \tabularnewline
10 & -0.007987 & -0.0948 & 0.537714 \tabularnewline
11 & -0.129101 & -1.533 & 0.93624 \tabularnewline
12 & -0.055631 & -0.6606 & 0.745022 \tabularnewline
13 & -0.055906 & -0.6639 & 0.746065 \tabularnewline
14 & -0.020447 & -0.2428 & 0.59574 \tabularnewline
15 & -0.045748 & -0.5432 & 0.706085 \tabularnewline
16 & -0.088648 & -1.0526 & 0.852847 \tabularnewline
17 & 0.021904 & 0.2601 & 0.397583 \tabularnewline
18 & -0.011628 & -0.1381 & 0.554809 \tabularnewline
19 & -0.061155 & -0.7262 & 0.765531 \tabularnewline
20 & -0.07562 & -0.8979 & 0.814625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5963&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]0.970411[/C][C]11.523[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.150545[/C][C]-1.7876[/C][C]0.962007[/C][/ROW]
[ROW][C]2[/C][C]0.036851[/C][C]0.4376[/C][C]0.33118[/C][/ROW]
[ROW][C]3[/C][C]-0.114941[/C][C]-1.3648[/C][C]0.912763[/C][/ROW]
[ROW][C]4[/C][C]0.068395[/C][C]0.8121[/C][C]0.209039[/C][/ROW]
[ROW][C]5[/C][C]0.17125[/C][C]2.0335[/C][C]0.02194[/C][/ROW]
[ROW][C]6[/C][C]-0.002268[/C][C]-0.0269[/C][C]0.510724[/C][/ROW]
[ROW][C]7[/C][C]-0.100632[/C][C]-1.1949[/C][C]0.882941[/C][/ROW]
[ROW][C]8[/C][C]0.039296[/C][C]0.4666[/C][C]0.320748[/C][/ROW]
[ROW][C]9[/C][C]-0.094707[/C][C]-1.1246[/C][C]0.868661[/C][/ROW]
[ROW][C]10[/C][C]-0.007987[/C][C]-0.0948[/C][C]0.537714[/C][/ROW]
[ROW][C]11[/C][C]-0.129101[/C][C]-1.533[/C][C]0.93624[/C][/ROW]
[ROW][C]12[/C][C]-0.055631[/C][C]-0.6606[/C][C]0.745022[/C][/ROW]
[ROW][C]13[/C][C]-0.055906[/C][C]-0.6639[/C][C]0.746065[/C][/ROW]
[ROW][C]14[/C][C]-0.020447[/C][C]-0.2428[/C][C]0.59574[/C][/ROW]
[ROW][C]15[/C][C]-0.045748[/C][C]-0.5432[/C][C]0.706085[/C][/ROW]
[ROW][C]16[/C][C]-0.088648[/C][C]-1.0526[/C][C]0.852847[/C][/ROW]
[ROW][C]17[/C][C]0.021904[/C][C]0.2601[/C][C]0.397583[/C][/ROW]
[ROW][C]18[/C][C]-0.011628[/C][C]-0.1381[/C][C]0.554809[/C][/ROW]
[ROW][C]19[/C][C]-0.061155[/C][C]-0.7262[/C][C]0.765531[/C][/ROW]
[ROW][C]20[/C][C]-0.07562[/C][C]-0.8979[/C][C]0.814625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5963&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5963&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	0.970411	11.523	0
1	-0.150545	-1.7876	0.962007
2	0.036851	0.4376	0.33118
3	-0.114941	-1.3648	0.912763
4	0.068395	0.8121	0.209039
5	0.17125	2.0335	0.02194
6	-0.002268	-0.0269	0.510724
7	-0.100632	-1.1949	0.882941
8	0.039296	0.4666	0.320748
9	-0.094707	-1.1246	0.868661
10	-0.007987	-0.0948	0.537714
11	-0.129101	-1.533	0.93624
12	-0.055631	-0.6606	0.745022
13	-0.055906	-0.6639	0.746065
14	-0.020447	-0.2428	0.59574
15	-0.045748	-0.5432	0.706085
16	-0.088648	-1.0526	0.852847
17	0.021904	0.2601	0.397583
18	-0.011628	-0.1381	0.554809
19	-0.061155	-0.7262	0.765531
20	-0.07562	-0.8979	0.814625

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code