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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 14 Dec 2010 14:35:40 +0000

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/2010/Dec/14/t1292337332fr7q99kpv3y973q.htm/, Retrieved Thu, 02 May 2024 20:23:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109696, Retrieved Thu, 02 May 2024 20:23:53 +0000

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User-defined keywords

Estimated Impact

108

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

-     [(Partial) Autocorrelation Function] [] [2010-12-14 14:15:36] [acfa3f91ce5598ec4ba98aad4cfba2f0]
-   P     [(Partial) Autocorrelation Function] [] [2010-12-14 14:35:40] [c474a97a96075919a678ad3d2290b00b] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109696&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109696&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109696&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.286218	4.1968	2e-05
2	0.061863	0.9071	0.182687
3	0.134829	1.977	0.024661
4	0.145195	2.129	0.017197
5	0.17733	2.6002	0.004982
6	-0.016258	-0.2384	0.405905
7	0.009927	0.1456	0.442204
8	0.130701	1.9165	0.028317
9	0.096254	1.4114	0.079791
10	-0.056391	-0.8269	0.204617
11	0.091323	1.3391	0.090984
12	0.059186	0.8678	0.193224
13	-0.038473	-0.5641	0.286631
14	0.007984	0.1171	0.453458
15	-0.049209	-0.7216	0.235677
16	0.079763	1.1696	0.121738
17	0.021397	0.3137	0.37701
18	-0.062043	-0.9097	0.181992
19	-0.006771	-0.0993	0.460502
20	-0.091443	-1.3408	0.090696
21	-0.078341	-1.1487	0.125978
22	-0.120492	-1.7668	0.039344
23	-0.103529	-1.518	0.065238

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.286218 & 4.1968 & 2e-05 \tabularnewline
2 & 0.061863 & 0.9071 & 0.182687 \tabularnewline
3 & 0.134829 & 1.977 & 0.024661 \tabularnewline
4 & 0.145195 & 2.129 & 0.017197 \tabularnewline
5 & 0.17733 & 2.6002 & 0.004982 \tabularnewline
6 & -0.016258 & -0.2384 & 0.405905 \tabularnewline
7 & 0.009927 & 0.1456 & 0.442204 \tabularnewline
8 & 0.130701 & 1.9165 & 0.028317 \tabularnewline
9 & 0.096254 & 1.4114 & 0.079791 \tabularnewline
10 & -0.056391 & -0.8269 & 0.204617 \tabularnewline
11 & 0.091323 & 1.3391 & 0.090984 \tabularnewline
12 & 0.059186 & 0.8678 & 0.193224 \tabularnewline
13 & -0.038473 & -0.5641 & 0.286631 \tabularnewline
14 & 0.007984 & 0.1171 & 0.453458 \tabularnewline
15 & -0.049209 & -0.7216 & 0.235677 \tabularnewline
16 & 0.079763 & 1.1696 & 0.121738 \tabularnewline
17 & 0.021397 & 0.3137 & 0.37701 \tabularnewline
18 & -0.062043 & -0.9097 & 0.181992 \tabularnewline
19 & -0.006771 & -0.0993 & 0.460502 \tabularnewline
20 & -0.091443 & -1.3408 & 0.090696 \tabularnewline
21 & -0.078341 & -1.1487 & 0.125978 \tabularnewline
22 & -0.120492 & -1.7668 & 0.039344 \tabularnewline
23 & -0.103529 & -1.518 & 0.065238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109696&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]0.286218[/C][C]4.1968[/C][C]2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.061863[/C][C]0.9071[/C][C]0.182687[/C][/ROW]
[ROW][C]3[/C][C]0.134829[/C][C]1.977[/C][C]0.024661[/C][/ROW]
[ROW][C]4[/C][C]0.145195[/C][C]2.129[/C][C]0.017197[/C][/ROW]
[ROW][C]5[/C][C]0.17733[/C][C]2.6002[/C][C]0.004982[/C][/ROW]
[ROW][C]6[/C][C]-0.016258[/C][C]-0.2384[/C][C]0.405905[/C][/ROW]
[ROW][C]7[/C][C]0.009927[/C][C]0.1456[/C][C]0.442204[/C][/ROW]
[ROW][C]8[/C][C]0.130701[/C][C]1.9165[/C][C]0.028317[/C][/ROW]
[ROW][C]9[/C][C]0.096254[/C][C]1.4114[/C][C]0.079791[/C][/ROW]
[ROW][C]10[/C][C]-0.056391[/C][C]-0.8269[/C][C]0.204617[/C][/ROW]
[ROW][C]11[/C][C]0.091323[/C][C]1.3391[/C][C]0.090984[/C][/ROW]
[ROW][C]12[/C][C]0.059186[/C][C]0.8678[/C][C]0.193224[/C][/ROW]
[ROW][C]13[/C][C]-0.038473[/C][C]-0.5641[/C][C]0.286631[/C][/ROW]
[ROW][C]14[/C][C]0.007984[/C][C]0.1171[/C][C]0.453458[/C][/ROW]
[ROW][C]15[/C][C]-0.049209[/C][C]-0.7216[/C][C]0.235677[/C][/ROW]
[ROW][C]16[/C][C]0.079763[/C][C]1.1696[/C][C]0.121738[/C][/ROW]
[ROW][C]17[/C][C]0.021397[/C][C]0.3137[/C][C]0.37701[/C][/ROW]
[ROW][C]18[/C][C]-0.062043[/C][C]-0.9097[/C][C]0.181992[/C][/ROW]
[ROW][C]19[/C][C]-0.006771[/C][C]-0.0993[/C][C]0.460502[/C][/ROW]
[ROW][C]20[/C][C]-0.091443[/C][C]-1.3408[/C][C]0.090696[/C][/ROW]
[ROW][C]21[/C][C]-0.078341[/C][C]-1.1487[/C][C]0.125978[/C][/ROW]
[ROW][C]22[/C][C]-0.120492[/C][C]-1.7668[/C][C]0.039344[/C][/ROW]
[ROW][C]23[/C][C]-0.103529[/C][C]-1.518[/C][C]0.065238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109696&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109696&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	0.286218	4.1968	2e-05
2	0.061863	0.9071	0.182687
3	0.134829	1.977	0.024661
4	0.145195	2.129	0.017197
5	0.17733	2.6002	0.004982
6	-0.016258	-0.2384	0.405905
7	0.009927	0.1456	0.442204
8	0.130701	1.9165	0.028317
9	0.096254	1.4114	0.079791
10	-0.056391	-0.8269	0.204617
11	0.091323	1.3391	0.090984
12	0.059186	0.8678	0.193224
13	-0.038473	-0.5641	0.286631
14	0.007984	0.1171	0.453458
15	-0.049209	-0.7216	0.235677
16	0.079763	1.1696	0.121738
17	0.021397	0.3137	0.37701
18	-0.062043	-0.9097	0.181992
19	-0.006771	-0.0993	0.460502
20	-0.091443	-1.3408	0.090696
21	-0.078341	-1.1487	0.125978
22	-0.120492	-1.7668	0.039344
23	-0.103529	-1.518	0.065238

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.286218	4.1968	2e-05
2	-0.021847	-0.3203	0.37451
3	0.134027	1.9652	0.025338
4	0.078546	1.1517	0.125359
5	0.127529	1.8699	0.031425
6	-0.124627	-1.8274	0.034514
7	0.032382	0.4748	0.3177
8	0.087698	1.2859	0.099929
9	0.029642	0.4346	0.332134
10	-0.116055	-1.7017	0.045129
11	0.163446	2.3966	0.008702
12	-0.055441	-0.8129	0.208581
13	-0.074759	-1.0962	0.137113
14	0.033149	0.4861	0.313708
15	-0.040848	-0.599	0.274918
16	0.062599	0.9179	0.179853
17	-0.019624	-0.2877	0.38691
18	-0.015052	-0.2207	0.412766
19	-0.019266	-0.2825	0.388917
20	-0.130485	-1.9133	0.02852
21	-0.006037	-0.0885	0.464774
22	-0.09957	-1.46	0.072877
23	-0.026421	-0.3874	0.349416

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.286218 & 4.1968 & 2e-05 \tabularnewline
2 & -0.021847 & -0.3203 & 0.37451 \tabularnewline
3 & 0.134027 & 1.9652 & 0.025338 \tabularnewline
4 & 0.078546 & 1.1517 & 0.125359 \tabularnewline
5 & 0.127529 & 1.8699 & 0.031425 \tabularnewline
6 & -0.124627 & -1.8274 & 0.034514 \tabularnewline
7 & 0.032382 & 0.4748 & 0.3177 \tabularnewline
8 & 0.087698 & 1.2859 & 0.099929 \tabularnewline
9 & 0.029642 & 0.4346 & 0.332134 \tabularnewline
10 & -0.116055 & -1.7017 & 0.045129 \tabularnewline
11 & 0.163446 & 2.3966 & 0.008702 \tabularnewline
12 & -0.055441 & -0.8129 & 0.208581 \tabularnewline
13 & -0.074759 & -1.0962 & 0.137113 \tabularnewline
14 & 0.033149 & 0.4861 & 0.313708 \tabularnewline
15 & -0.040848 & -0.599 & 0.274918 \tabularnewline
16 & 0.062599 & 0.9179 & 0.179853 \tabularnewline
17 & -0.019624 & -0.2877 & 0.38691 \tabularnewline
18 & -0.015052 & -0.2207 & 0.412766 \tabularnewline
19 & -0.019266 & -0.2825 & 0.388917 \tabularnewline
20 & -0.130485 & -1.9133 & 0.02852 \tabularnewline
21 & -0.006037 & -0.0885 & 0.464774 \tabularnewline
22 & -0.09957 & -1.46 & 0.072877 \tabularnewline
23 & -0.026421 & -0.3874 & 0.349416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109696&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]0.286218[/C][C]4.1968[/C][C]2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.021847[/C][C]-0.3203[/C][C]0.37451[/C][/ROW]
[ROW][C]3[/C][C]0.134027[/C][C]1.9652[/C][C]0.025338[/C][/ROW]
[ROW][C]4[/C][C]0.078546[/C][C]1.1517[/C][C]0.125359[/C][/ROW]
[ROW][C]5[/C][C]0.127529[/C][C]1.8699[/C][C]0.031425[/C][/ROW]
[ROW][C]6[/C][C]-0.124627[/C][C]-1.8274[/C][C]0.034514[/C][/ROW]
[ROW][C]7[/C][C]0.032382[/C][C]0.4748[/C][C]0.3177[/C][/ROW]
[ROW][C]8[/C][C]0.087698[/C][C]1.2859[/C][C]0.099929[/C][/ROW]
[ROW][C]9[/C][C]0.029642[/C][C]0.4346[/C][C]0.332134[/C][/ROW]
[ROW][C]10[/C][C]-0.116055[/C][C]-1.7017[/C][C]0.045129[/C][/ROW]
[ROW][C]11[/C][C]0.163446[/C][C]2.3966[/C][C]0.008702[/C][/ROW]
[ROW][C]12[/C][C]-0.055441[/C][C]-0.8129[/C][C]0.208581[/C][/ROW]
[ROW][C]13[/C][C]-0.074759[/C][C]-1.0962[/C][C]0.137113[/C][/ROW]
[ROW][C]14[/C][C]0.033149[/C][C]0.4861[/C][C]0.313708[/C][/ROW]
[ROW][C]15[/C][C]-0.040848[/C][C]-0.599[/C][C]0.274918[/C][/ROW]
[ROW][C]16[/C][C]0.062599[/C][C]0.9179[/C][C]0.179853[/C][/ROW]
[ROW][C]17[/C][C]-0.019624[/C][C]-0.2877[/C][C]0.38691[/C][/ROW]
[ROW][C]18[/C][C]-0.015052[/C][C]-0.2207[/C][C]0.412766[/C][/ROW]
[ROW][C]19[/C][C]-0.019266[/C][C]-0.2825[/C][C]0.388917[/C][/ROW]
[ROW][C]20[/C][C]-0.130485[/C][C]-1.9133[/C][C]0.02852[/C][/ROW]
[ROW][C]21[/C][C]-0.006037[/C][C]-0.0885[/C][C]0.464774[/C][/ROW]
[ROW][C]22[/C][C]-0.09957[/C][C]-1.46[/C][C]0.072877[/C][/ROW]
[ROW][C]23[/C][C]-0.026421[/C][C]-0.3874[/C][C]0.349416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109696&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109696&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	0.286218	4.1968	2e-05
2	-0.021847	-0.3203	0.37451
3	0.134027	1.9652	0.025338
4	0.078546	1.1517	0.125359
5	0.127529	1.8699	0.031425
6	-0.124627	-1.8274	0.034514
7	0.032382	0.4748	0.3177
8	0.087698	1.2859	0.099929
9	0.029642	0.4346	0.332134
10	-0.116055	-1.7017	0.045129
11	0.163446	2.3966	0.008702
12	-0.055441	-0.8129	0.208581
13	-0.074759	-1.0962	0.137113
14	0.033149	0.4861	0.313708
15	-0.040848	-0.599	0.274918
16	0.062599	0.9179	0.179853
17	-0.019624	-0.2877	0.38691
18	-0.015052	-0.2207	0.412766
19	-0.019266	-0.2825	0.388917
20	-0.130485	-1.9133	0.02852
21	-0.006037	-0.0885	0.464774
22	-0.09957	-1.46	0.072877
23	-0.026421	-0.3874	0.349416

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code