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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 04:26:20 -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/28/t1196248617cd6u3pwokzgkpml.htm/, Retrieved Thu, 02 May 2024 09:19:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7022, Retrieved Thu, 02 May 2024 09:19:06 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

200

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

-       [(Partial) Autocorrelation Function] [Inducing Stationa...] [2007-11-28 11:26:20] [157a0cf3c12a7482b4e6935b4c49d48f] [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=7022&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=7022&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7022&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	7.746	0
1	0.892695	6.9148	0
2	0.754081	5.8411	0
3	0.590335	4.5727	1.2e-05
4	0.416439	3.2257	0.001018
5	0.27423	2.1242	0.018893
6	0.123489	0.9565	0.171319
7	0.0084	0.0651	0.47417
8	-0.088594	-0.6862	0.7524
9	-0.16129	-1.2493	0.891805
10	-0.188346	-1.4589	0.925099
11	-0.209165	-1.6202	0.944781
12	-0.224942	-1.7424	0.956718
13	-0.187944	-1.4558	0.92467
14	-0.137901	-1.0682	0.855141
15	-0.061717	-0.4781	0.682827
16	0.019905	0.1542	0.438992
17	0.091474	0.7086	0.240672

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.892695 & 6.9148 & 0 \tabularnewline
2 & 0.754081 & 5.8411 & 0 \tabularnewline
3 & 0.590335 & 4.5727 & 1.2e-05 \tabularnewline
4 & 0.416439 & 3.2257 & 0.001018 \tabularnewline
5 & 0.27423 & 2.1242 & 0.018893 \tabularnewline
6 & 0.123489 & 0.9565 & 0.171319 \tabularnewline
7 & 0.0084 & 0.0651 & 0.47417 \tabularnewline
8 & -0.088594 & -0.6862 & 0.7524 \tabularnewline
9 & -0.16129 & -1.2493 & 0.891805 \tabularnewline
10 & -0.188346 & -1.4589 & 0.925099 \tabularnewline
11 & -0.209165 & -1.6202 & 0.944781 \tabularnewline
12 & -0.224942 & -1.7424 & 0.956718 \tabularnewline
13 & -0.187944 & -1.4558 & 0.92467 \tabularnewline
14 & -0.137901 & -1.0682 & 0.855141 \tabularnewline
15 & -0.061717 & -0.4781 & 0.682827 \tabularnewline
16 & 0.019905 & 0.1542 & 0.438992 \tabularnewline
17 & 0.091474 & 0.7086 & 0.240672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7022&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.892695[/C][C]6.9148[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.754081[/C][C]5.8411[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.590335[/C][C]4.5727[/C][C]1.2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.416439[/C][C]3.2257[/C][C]0.001018[/C][/ROW]
[ROW][C]5[/C][C]0.27423[/C][C]2.1242[/C][C]0.018893[/C][/ROW]
[ROW][C]6[/C][C]0.123489[/C][C]0.9565[/C][C]0.171319[/C][/ROW]
[ROW][C]7[/C][C]0.0084[/C][C]0.0651[/C][C]0.47417[/C][/ROW]
[ROW][C]8[/C][C]-0.088594[/C][C]-0.6862[/C][C]0.7524[/C][/ROW]
[ROW][C]9[/C][C]-0.16129[/C][C]-1.2493[/C][C]0.891805[/C][/ROW]
[ROW][C]10[/C][C]-0.188346[/C][C]-1.4589[/C][C]0.925099[/C][/ROW]
[ROW][C]11[/C][C]-0.209165[/C][C]-1.6202[/C][C]0.944781[/C][/ROW]
[ROW][C]12[/C][C]-0.224942[/C][C]-1.7424[/C][C]0.956718[/C][/ROW]
[ROW][C]13[/C][C]-0.187944[/C][C]-1.4558[/C][C]0.92467[/C][/ROW]
[ROW][C]14[/C][C]-0.137901[/C][C]-1.0682[/C][C]0.855141[/C][/ROW]
[ROW][C]15[/C][C]-0.061717[/C][C]-0.4781[/C][C]0.682827[/C][/ROW]
[ROW][C]16[/C][C]0.019905[/C][C]0.1542[/C][C]0.438992[/C][/ROW]
[ROW][C]17[/C][C]0.091474[/C][C]0.7086[/C][C]0.240672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7022&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7022&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	7.746	0
1	0.892695	6.9148	0
2	0.754081	5.8411	0
3	0.590335	4.5727	1.2e-05
4	0.416439	3.2257	0.001018
5	0.27423	2.1242	0.018893
6	0.123489	0.9565	0.171319
7	0.0084	0.0651	0.47417
8	-0.088594	-0.6862	0.7524
9	-0.16129	-1.2493	0.891805
10	-0.188346	-1.4589	0.925099
11	-0.209165	-1.6202	0.944781
12	-0.224942	-1.7424	0.956718
13	-0.187944	-1.4558	0.92467
14	-0.137901	-1.0682	0.855141
15	-0.061717	-0.4781	0.682827
16	0.019905	0.1542	0.438992
17	0.091474	0.7086	0.240672

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.892695	6.9148	0
1	-0.210853	-1.6333	0.946175
2	-0.188288	-1.4585	0.925038
3	-0.131525	-1.0188	0.843804
4	0.065022	0.5037	0.308174
5	-0.188741	-1.462	0.925518
6	0.044305	0.3432	0.366328
7	-0.064054	-0.4962	0.689204
8	0.002533	0.0196	0.492207
9	0.065644	0.5085	0.306493
10	-0.066517	-0.5152	0.695861
11	-0.11141	-0.863	0.804208
12	0.249348	1.9314	0.029078
13	0.010563	0.0818	0.467529
14	0.059545	0.4612	0.323149
15	0.024121	0.1868	0.426207
16	0.039894	0.309	0.37919
17	0.016845	0.1305	0.448312

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.892695 & 6.9148 & 0 \tabularnewline
1 & -0.210853 & -1.6333 & 0.946175 \tabularnewline
2 & -0.188288 & -1.4585 & 0.925038 \tabularnewline
3 & -0.131525 & -1.0188 & 0.843804 \tabularnewline
4 & 0.065022 & 0.5037 & 0.308174 \tabularnewline
5 & -0.188741 & -1.462 & 0.925518 \tabularnewline
6 & 0.044305 & 0.3432 & 0.366328 \tabularnewline
7 & -0.064054 & -0.4962 & 0.689204 \tabularnewline
8 & 0.002533 & 0.0196 & 0.492207 \tabularnewline
9 & 0.065644 & 0.5085 & 0.306493 \tabularnewline
10 & -0.066517 & -0.5152 & 0.695861 \tabularnewline
11 & -0.11141 & -0.863 & 0.804208 \tabularnewline
12 & 0.249348 & 1.9314 & 0.029078 \tabularnewline
13 & 0.010563 & 0.0818 & 0.467529 \tabularnewline
14 & 0.059545 & 0.4612 & 0.323149 \tabularnewline
15 & 0.024121 & 0.1868 & 0.426207 \tabularnewline
16 & 0.039894 & 0.309 & 0.37919 \tabularnewline
17 & 0.016845 & 0.1305 & 0.448312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7022&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]0.892695[/C][C]6.9148[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.210853[/C][C]-1.6333[/C][C]0.946175[/C][/ROW]
[ROW][C]2[/C][C]-0.188288[/C][C]-1.4585[/C][C]0.925038[/C][/ROW]
[ROW][C]3[/C][C]-0.131525[/C][C]-1.0188[/C][C]0.843804[/C][/ROW]
[ROW][C]4[/C][C]0.065022[/C][C]0.5037[/C][C]0.308174[/C][/ROW]
[ROW][C]5[/C][C]-0.188741[/C][C]-1.462[/C][C]0.925518[/C][/ROW]
[ROW][C]6[/C][C]0.044305[/C][C]0.3432[/C][C]0.366328[/C][/ROW]
[ROW][C]7[/C][C]-0.064054[/C][C]-0.4962[/C][C]0.689204[/C][/ROW]
[ROW][C]8[/C][C]0.002533[/C][C]0.0196[/C][C]0.492207[/C][/ROW]
[ROW][C]9[/C][C]0.065644[/C][C]0.5085[/C][C]0.306493[/C][/ROW]
[ROW][C]10[/C][C]-0.066517[/C][C]-0.5152[/C][C]0.695861[/C][/ROW]
[ROW][C]11[/C][C]-0.11141[/C][C]-0.863[/C][C]0.804208[/C][/ROW]
[ROW][C]12[/C][C]0.249348[/C][C]1.9314[/C][C]0.029078[/C][/ROW]
[ROW][C]13[/C][C]0.010563[/C][C]0.0818[/C][C]0.467529[/C][/ROW]
[ROW][C]14[/C][C]0.059545[/C][C]0.4612[/C][C]0.323149[/C][/ROW]
[ROW][C]15[/C][C]0.024121[/C][C]0.1868[/C][C]0.426207[/C][/ROW]
[ROW][C]16[/C][C]0.039894[/C][C]0.309[/C][C]0.37919[/C][/ROW]
[ROW][C]17[/C][C]0.016845[/C][C]0.1305[/C][C]0.448312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7022&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7022&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	0.892695	6.9148	0
1	-0.210853	-1.6333	0.946175
2	-0.188288	-1.4585	0.925038
3	-0.131525	-1.0188	0.843804
4	0.065022	0.5037	0.308174
5	-0.188741	-1.462	0.925518
6	0.044305	0.3432	0.366328
7	-0.064054	-0.4962	0.689204
8	0.002533	0.0196	0.492207
9	0.065644	0.5085	0.306493
10	-0.066517	-0.5152	0.695861
11	-0.11141	-0.863	0.804208
12	0.249348	1.9314	0.029078
13	0.010563	0.0818	0.467529
14	0.059545	0.4612	0.323149
15	0.024121	0.1868	0.426207
16	0.039894	0.309	0.37919
17	0.016845	0.1305	0.448312

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1.2 ; par3 = 0 ; 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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