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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 30 Dec 2009 15:33:53 -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/2009/Dec/30/t1262212556h1gcnmcm5hcs5yc.htm/, Retrieved Mon, 29 Apr 2024 07:34:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71388, Retrieved Mon, 29 Apr 2024 07:34:32 +0000

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No (this computation is public)

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Estimated Impact

113

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

-       [(Partial) Autocorrelation Function] [paper ACF] [2009-12-30 22:33:53] [3ebad5d90a5c8606f133189c73066208] [Current]

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Summary of computational 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 computational 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=71388&T=0

[TABLE]
[ROW][C]Summary of computational 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=71388&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71388&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 computational 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
1	0.933129	7.288	0
2	0.844034	6.5921	0
3	0.756732	5.9103	0
4	0.66094	5.1621	1e-06
5	0.556428	4.3458	2.7e-05
6	0.440546	3.4408	0.000526
7	0.340126	2.6565	0.005032
8	0.277782	2.1695	0.016973
9	0.225487	1.7611	0.041616
10	0.186083	1.4534	0.075625
11	0.15609	1.2191	0.11375
12	0.136862	1.0689	0.144657
13	0.148252	1.1579	0.125712
14	0.160325	1.2522	0.107643
15	0.148776	1.162	0.124885
16	0.117927	0.921	0.180328
17	0.067948	0.5307	0.298779

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.933129 & 7.288 & 0 \tabularnewline
2 & 0.844034 & 6.5921 & 0 \tabularnewline
3 & 0.756732 & 5.9103 & 0 \tabularnewline
4 & 0.66094 & 5.1621 & 1e-06 \tabularnewline
5 & 0.556428 & 4.3458 & 2.7e-05 \tabularnewline
6 & 0.440546 & 3.4408 & 0.000526 \tabularnewline
7 & 0.340126 & 2.6565 & 0.005032 \tabularnewline
8 & 0.277782 & 2.1695 & 0.016973 \tabularnewline
9 & 0.225487 & 1.7611 & 0.041616 \tabularnewline
10 & 0.186083 & 1.4534 & 0.075625 \tabularnewline
11 & 0.15609 & 1.2191 & 0.11375 \tabularnewline
12 & 0.136862 & 1.0689 & 0.144657 \tabularnewline
13 & 0.148252 & 1.1579 & 0.125712 \tabularnewline
14 & 0.160325 & 1.2522 & 0.107643 \tabularnewline
15 & 0.148776 & 1.162 & 0.124885 \tabularnewline
16 & 0.117927 & 0.921 & 0.180328 \tabularnewline
17 & 0.067948 & 0.5307 & 0.298779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71388&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]1[/C][C]0.933129[/C][C]7.288[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.844034[/C][C]6.5921[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.756732[/C][C]5.9103[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.66094[/C][C]5.1621[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.556428[/C][C]4.3458[/C][C]2.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.440546[/C][C]3.4408[/C][C]0.000526[/C][/ROW]
[ROW][C]7[/C][C]0.340126[/C][C]2.6565[/C][C]0.005032[/C][/ROW]
[ROW][C]8[/C][C]0.277782[/C][C]2.1695[/C][C]0.016973[/C][/ROW]
[ROW][C]9[/C][C]0.225487[/C][C]1.7611[/C][C]0.041616[/C][/ROW]
[ROW][C]10[/C][C]0.186083[/C][C]1.4534[/C][C]0.075625[/C][/ROW]
[ROW][C]11[/C][C]0.15609[/C][C]1.2191[/C][C]0.11375[/C][/ROW]
[ROW][C]12[/C][C]0.136862[/C][C]1.0689[/C][C]0.144657[/C][/ROW]
[ROW][C]13[/C][C]0.148252[/C][C]1.1579[/C][C]0.125712[/C][/ROW]
[ROW][C]14[/C][C]0.160325[/C][C]1.2522[/C][C]0.107643[/C][/ROW]
[ROW][C]15[/C][C]0.148776[/C][C]1.162[/C][C]0.124885[/C][/ROW]
[ROW][C]16[/C][C]0.117927[/C][C]0.921[/C][C]0.180328[/C][/ROW]
[ROW][C]17[/C][C]0.067948[/C][C]0.5307[/C][C]0.298779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71388&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71388&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
1	0.933129	7.288	0
2	0.844034	6.5921	0
3	0.756732	5.9103	0
4	0.66094	5.1621	1e-06
5	0.556428	4.3458	2.7e-05
6	0.440546	3.4408	0.000526
7	0.340126	2.6565	0.005032
8	0.277782	2.1695	0.016973
9	0.225487	1.7611	0.041616
10	0.186083	1.4534	0.075625
11	0.15609	1.2191	0.11375
12	0.136862	1.0689	0.144657
13	0.148252	1.1579	0.125712
14	0.160325	1.2522	0.107643
15	0.148776	1.162	0.124885
16	0.117927	0.921	0.180328
17	0.067948	0.5307	0.298779

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.933129	7.288	0
2	-0.20651	-1.6129	0.055965
3	-0.006511	-0.0509	0.479805
4	-0.127706	-0.9974	0.161251
5	-0.105228	-0.8219	0.20718
6	-0.149189	-1.1652	0.124236
7	0.073316	0.5726	0.284504
8	0.203587	1.5901	0.058495
9	-0.029091	-0.2272	0.410511
10	0.060637	0.4736	0.318742
11	-0.035611	-0.2781	0.390926
12	-0.012998	-0.1015	0.459737
13	0.158539	1.2382	0.110188
14	-0.03968	-0.3099	0.378844
15	-0.157537	-1.2304	0.111635
16	-0.16881	-1.3184	0.096142
17	-0.172228	-1.3451	0.091779

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.933129 & 7.288 & 0 \tabularnewline
2 & -0.20651 & -1.6129 & 0.055965 \tabularnewline
3 & -0.006511 & -0.0509 & 0.479805 \tabularnewline
4 & -0.127706 & -0.9974 & 0.161251 \tabularnewline
5 & -0.105228 & -0.8219 & 0.20718 \tabularnewline
6 & -0.149189 & -1.1652 & 0.124236 \tabularnewline
7 & 0.073316 & 0.5726 & 0.284504 \tabularnewline
8 & 0.203587 & 1.5901 & 0.058495 \tabularnewline
9 & -0.029091 & -0.2272 & 0.410511 \tabularnewline
10 & 0.060637 & 0.4736 & 0.318742 \tabularnewline
11 & -0.035611 & -0.2781 & 0.390926 \tabularnewline
12 & -0.012998 & -0.1015 & 0.459737 \tabularnewline
13 & 0.158539 & 1.2382 & 0.110188 \tabularnewline
14 & -0.03968 & -0.3099 & 0.378844 \tabularnewline
15 & -0.157537 & -1.2304 & 0.111635 \tabularnewline
16 & -0.16881 & -1.3184 & 0.096142 \tabularnewline
17 & -0.172228 & -1.3451 & 0.091779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71388&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]1[/C][C]0.933129[/C][C]7.288[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.20651[/C][C]-1.6129[/C][C]0.055965[/C][/ROW]
[ROW][C]3[/C][C]-0.006511[/C][C]-0.0509[/C][C]0.479805[/C][/ROW]
[ROW][C]4[/C][C]-0.127706[/C][C]-0.9974[/C][C]0.161251[/C][/ROW]
[ROW][C]5[/C][C]-0.105228[/C][C]-0.8219[/C][C]0.20718[/C][/ROW]
[ROW][C]6[/C][C]-0.149189[/C][C]-1.1652[/C][C]0.124236[/C][/ROW]
[ROW][C]7[/C][C]0.073316[/C][C]0.5726[/C][C]0.284504[/C][/ROW]
[ROW][C]8[/C][C]0.203587[/C][C]1.5901[/C][C]0.058495[/C][/ROW]
[ROW][C]9[/C][C]-0.029091[/C][C]-0.2272[/C][C]0.410511[/C][/ROW]
[ROW][C]10[/C][C]0.060637[/C][C]0.4736[/C][C]0.318742[/C][/ROW]
[ROW][C]11[/C][C]-0.035611[/C][C]-0.2781[/C][C]0.390926[/C][/ROW]
[ROW][C]12[/C][C]-0.012998[/C][C]-0.1015[/C][C]0.459737[/C][/ROW]
[ROW][C]13[/C][C]0.158539[/C][C]1.2382[/C][C]0.110188[/C][/ROW]
[ROW][C]14[/C][C]-0.03968[/C][C]-0.3099[/C][C]0.378844[/C][/ROW]
[ROW][C]15[/C][C]-0.157537[/C][C]-1.2304[/C][C]0.111635[/C][/ROW]
[ROW][C]16[/C][C]-0.16881[/C][C]-1.3184[/C][C]0.096142[/C][/ROW]
[ROW][C]17[/C][C]-0.172228[/C][C]-1.3451[/C][C]0.091779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71388&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71388&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
1	0.933129	7.288	0
2	-0.20651	-1.6129	0.055965
3	-0.006511	-0.0509	0.479805
4	-0.127706	-0.9974	0.161251
5	-0.105228	-0.8219	0.20718
6	-0.149189	-1.1652	0.124236
7	0.073316	0.5726	0.284504
8	0.203587	1.5901	0.058495
9	-0.029091	-0.2272	0.410511
10	0.060637	0.4736	0.318742
11	-0.035611	-0.2781	0.390926
12	-0.012998	-0.1015	0.459737
13	0.158539	1.2382	0.110188
14	-0.03968	-0.3099	0.378844
15	-0.157537	-1.2304	0.111635
16	-0.16881	-1.3184	0.096142
17	-0.172228	-1.3451	0.091779

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 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code