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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

Sat, 03 Dec 2011 08:59:15 -0500

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/2011/Dec/03/t132292076526hyaclptmf4w5x.htm/, Retrieved Sun, 28 Apr 2024 20:24:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150456, Retrieved Sun, 28 Apr 2024 20:24:35 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2011-12-03 13:59:15] [ce4468323d272130d499477f5e05a6d2] [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	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150456&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150456&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150456&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.505065	6.6623	0
2	0.478564	6.3127	0
3	0.326519	4.3071	1.4e-05
4	0.275644	3.636	0.000182
5	0.170614	2.2506	0.012833
6	0.187691	2.4758	0.007125
7	0.15954	2.1045	0.018386
8	0.106945	1.4107	0.080059
9	0.008856	0.1168	0.453569
10	-0.105636	-1.3934	0.082632
11	-0.087061	-1.1484	0.126186
12	-0.32429	-4.2777	1.6e-05
13	-0.105208	-1.3878	0.083488
14	-0.117482	-1.5497	0.061516
15	0.057695	0.761	0.223829
16	-0.048326	-0.6375	0.26233
17	-0.076118	-1.0041	0.158371
18	-0.067674	-0.8927	0.18663
19	-0.07844	-1.0347	0.151124
20	-0.113887	-1.5023	0.06742
21	-0.059222	-0.7812	0.217876
22	-0.01285	-0.1695	0.432798

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.505065 & 6.6623 & 0 \tabularnewline
2 & 0.478564 & 6.3127 & 0 \tabularnewline
3 & 0.326519 & 4.3071 & 1.4e-05 \tabularnewline
4 & 0.275644 & 3.636 & 0.000182 \tabularnewline
5 & 0.170614 & 2.2506 & 0.012833 \tabularnewline
6 & 0.187691 & 2.4758 & 0.007125 \tabularnewline
7 & 0.15954 & 2.1045 & 0.018386 \tabularnewline
8 & 0.106945 & 1.4107 & 0.080059 \tabularnewline
9 & 0.008856 & 0.1168 & 0.453569 \tabularnewline
10 & -0.105636 & -1.3934 & 0.082632 \tabularnewline
11 & -0.087061 & -1.1484 & 0.126186 \tabularnewline
12 & -0.32429 & -4.2777 & 1.6e-05 \tabularnewline
13 & -0.105208 & -1.3878 & 0.083488 \tabularnewline
14 & -0.117482 & -1.5497 & 0.061516 \tabularnewline
15 & 0.057695 & 0.761 & 0.223829 \tabularnewline
16 & -0.048326 & -0.6375 & 0.26233 \tabularnewline
17 & -0.076118 & -1.0041 & 0.158371 \tabularnewline
18 & -0.067674 & -0.8927 & 0.18663 \tabularnewline
19 & -0.07844 & -1.0347 & 0.151124 \tabularnewline
20 & -0.113887 & -1.5023 & 0.06742 \tabularnewline
21 & -0.059222 & -0.7812 & 0.217876 \tabularnewline
22 & -0.01285 & -0.1695 & 0.432798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150456&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]0.505065[/C][C]6.6623[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.478564[/C][C]6.3127[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.326519[/C][C]4.3071[/C][C]1.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.275644[/C][C]3.636[/C][C]0.000182[/C][/ROW]
[ROW][C]5[/C][C]0.170614[/C][C]2.2506[/C][C]0.012833[/C][/ROW]
[ROW][C]6[/C][C]0.187691[/C][C]2.4758[/C][C]0.007125[/C][/ROW]
[ROW][C]7[/C][C]0.15954[/C][C]2.1045[/C][C]0.018386[/C][/ROW]
[ROW][C]8[/C][C]0.106945[/C][C]1.4107[/C][C]0.080059[/C][/ROW]
[ROW][C]9[/C][C]0.008856[/C][C]0.1168[/C][C]0.453569[/C][/ROW]
[ROW][C]10[/C][C]-0.105636[/C][C]-1.3934[/C][C]0.082632[/C][/ROW]
[ROW][C]11[/C][C]-0.087061[/C][C]-1.1484[/C][C]0.126186[/C][/ROW]
[ROW][C]12[/C][C]-0.32429[/C][C]-4.2777[/C][C]1.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.105208[/C][C]-1.3878[/C][C]0.083488[/C][/ROW]
[ROW][C]14[/C][C]-0.117482[/C][C]-1.5497[/C][C]0.061516[/C][/ROW]
[ROW][C]15[/C][C]0.057695[/C][C]0.761[/C][C]0.223829[/C][/ROW]
[ROW][C]16[/C][C]-0.048326[/C][C]-0.6375[/C][C]0.26233[/C][/ROW]
[ROW][C]17[/C][C]-0.076118[/C][C]-1.0041[/C][C]0.158371[/C][/ROW]
[ROW][C]18[/C][C]-0.067674[/C][C]-0.8927[/C][C]0.18663[/C][/ROW]
[ROW][C]19[/C][C]-0.07844[/C][C]-1.0347[/C][C]0.151124[/C][/ROW]
[ROW][C]20[/C][C]-0.113887[/C][C]-1.5023[/C][C]0.06742[/C][/ROW]
[ROW][C]21[/C][C]-0.059222[/C][C]-0.7812[/C][C]0.217876[/C][/ROW]
[ROW][C]22[/C][C]-0.01285[/C][C]-0.1695[/C][C]0.432798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150456&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150456&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	0.505065	6.6623	0
2	0.478564	6.3127	0
3	0.326519	4.3071	1.4e-05
4	0.275644	3.636	0.000182
5	0.170614	2.2506	0.012833
6	0.187691	2.4758	0.007125
7	0.15954	2.1045	0.018386
8	0.106945	1.4107	0.080059
9	0.008856	0.1168	0.453569
10	-0.105636	-1.3934	0.082632
11	-0.087061	-1.1484	0.126186
12	-0.32429	-4.2777	1.6e-05
13	-0.105208	-1.3878	0.083488
14	-0.117482	-1.5497	0.061516
15	0.057695	0.761	0.223829
16	-0.048326	-0.6375	0.26233
17	-0.076118	-1.0041	0.158371
18	-0.067674	-0.8927	0.18663
19	-0.07844	-1.0347	0.151124
20	-0.113887	-1.5023	0.06742
21	-0.059222	-0.7812	0.217876
22	-0.01285	-0.1695	0.432798

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.505065	6.6623	0
2	0.300001	3.9573	5.5e-05
3	0.008563	0.113	0.455097
4	0.021536	0.2841	0.388346
5	-0.047699	-0.6292	0.265022
6	0.071721	0.9461	0.172715
7	0.048974	0.646	0.25956
8	-0.04921	-0.6491	0.258558
9	-0.128562	-1.6958	0.045852
10	-0.17816	-2.3501	0.009945
11	0.031566	0.4164	0.338821
12	-0.307423	-4.0552	3.8e-05
13	0.236925	3.1253	0.001041
14	0.101094	1.3335	0.092052
15	0.221297	2.9191	0.001987
16	-0.100666	-1.3279	0.09298
17	-0.208386	-2.7488	0.003306
18	0.077627	1.024	0.153636
19	-0.010752	-0.1418	0.443688
20	-0.040106	-0.529	0.298729
21	-0.069782	-0.9205	0.179295
22	-0.049429	-0.652	0.257627

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.505065 & 6.6623 & 0 \tabularnewline
2 & 0.300001 & 3.9573 & 5.5e-05 \tabularnewline
3 & 0.008563 & 0.113 & 0.455097 \tabularnewline
4 & 0.021536 & 0.2841 & 0.388346 \tabularnewline
5 & -0.047699 & -0.6292 & 0.265022 \tabularnewline
6 & 0.071721 & 0.9461 & 0.172715 \tabularnewline
7 & 0.048974 & 0.646 & 0.25956 \tabularnewline
8 & -0.04921 & -0.6491 & 0.258558 \tabularnewline
9 & -0.128562 & -1.6958 & 0.045852 \tabularnewline
10 & -0.17816 & -2.3501 & 0.009945 \tabularnewline
11 & 0.031566 & 0.4164 & 0.338821 \tabularnewline
12 & -0.307423 & -4.0552 & 3.8e-05 \tabularnewline
13 & 0.236925 & 3.1253 & 0.001041 \tabularnewline
14 & 0.101094 & 1.3335 & 0.092052 \tabularnewline
15 & 0.221297 & 2.9191 & 0.001987 \tabularnewline
16 & -0.100666 & -1.3279 & 0.09298 \tabularnewline
17 & -0.208386 & -2.7488 & 0.003306 \tabularnewline
18 & 0.077627 & 1.024 & 0.153636 \tabularnewline
19 & -0.010752 & -0.1418 & 0.443688 \tabularnewline
20 & -0.040106 & -0.529 & 0.298729 \tabularnewline
21 & -0.069782 & -0.9205 & 0.179295 \tabularnewline
22 & -0.049429 & -0.652 & 0.257627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150456&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]0.505065[/C][C]6.6623[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.300001[/C][C]3.9573[/C][C]5.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.008563[/C][C]0.113[/C][C]0.455097[/C][/ROW]
[ROW][C]4[/C][C]0.021536[/C][C]0.2841[/C][C]0.388346[/C][/ROW]
[ROW][C]5[/C][C]-0.047699[/C][C]-0.6292[/C][C]0.265022[/C][/ROW]
[ROW][C]6[/C][C]0.071721[/C][C]0.9461[/C][C]0.172715[/C][/ROW]
[ROW][C]7[/C][C]0.048974[/C][C]0.646[/C][C]0.25956[/C][/ROW]
[ROW][C]8[/C][C]-0.04921[/C][C]-0.6491[/C][C]0.258558[/C][/ROW]
[ROW][C]9[/C][C]-0.128562[/C][C]-1.6958[/C][C]0.045852[/C][/ROW]
[ROW][C]10[/C][C]-0.17816[/C][C]-2.3501[/C][C]0.009945[/C][/ROW]
[ROW][C]11[/C][C]0.031566[/C][C]0.4164[/C][C]0.338821[/C][/ROW]
[ROW][C]12[/C][C]-0.307423[/C][C]-4.0552[/C][C]3.8e-05[/C][/ROW]
[ROW][C]13[/C][C]0.236925[/C][C]3.1253[/C][C]0.001041[/C][/ROW]
[ROW][C]14[/C][C]0.101094[/C][C]1.3335[/C][C]0.092052[/C][/ROW]
[ROW][C]15[/C][C]0.221297[/C][C]2.9191[/C][C]0.001987[/C][/ROW]
[ROW][C]16[/C][C]-0.100666[/C][C]-1.3279[/C][C]0.09298[/C][/ROW]
[ROW][C]17[/C][C]-0.208386[/C][C]-2.7488[/C][C]0.003306[/C][/ROW]
[ROW][C]18[/C][C]0.077627[/C][C]1.024[/C][C]0.153636[/C][/ROW]
[ROW][C]19[/C][C]-0.010752[/C][C]-0.1418[/C][C]0.443688[/C][/ROW]
[ROW][C]20[/C][C]-0.040106[/C][C]-0.529[/C][C]0.298729[/C][/ROW]
[ROW][C]21[/C][C]-0.069782[/C][C]-0.9205[/C][C]0.179295[/C][/ROW]
[ROW][C]22[/C][C]-0.049429[/C][C]-0.652[/C][C]0.257627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150456&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150456&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	0.505065	6.6623	0
2	0.300001	3.9573	5.5e-05
3	0.008563	0.113	0.455097
4	0.021536	0.2841	0.388346
5	-0.047699	-0.6292	0.265022
6	0.071721	0.9461	0.172715
7	0.048974	0.646	0.25956
8	-0.04921	-0.6491	0.258558
9	-0.128562	-1.6958	0.045852
10	-0.17816	-2.3501	0.009945
11	0.031566	0.4164	0.338821
12	-0.307423	-4.0552	3.8e-05
13	0.236925	3.1253	0.001041
14	0.101094	1.3335	0.092052
15	0.221297	2.9191	0.001987
16	-0.100666	-1.3279	0.09298
17	-0.208386	-2.7488	0.003306
18	0.077627	1.024	0.153636
19	-0.010752	-0.1418	0.443688
20	-0.040106	-0.529	0.298729
21	-0.069782	-0.9205	0.179295
22	-0.049429	-0.652	0.257627

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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