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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 17 Nov 2016 10:50:53 +0100

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/2016/Nov/17/t14793762630xvtxyd6p5q7oh1.htm/, Retrieved Sun, 05 May 2024 10:39:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296795, Retrieved Sun, 05 May 2024 10:39:53 +0000

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

-       [(Partial) Autocorrelation Function] [] [2016-11-17 09:50:53] [219800a2f11ddd28e3280d87dbde8c8d] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296795&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=296795&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296795&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.021323	-0.2422	0.40451
2	-0.074754	-0.849	0.198715
3	-0.141664	-1.609	0.055031
4	0.010153	0.1153	0.454189
5	0.083467	0.948	0.17245
6	-0.102982	-1.1697	0.122149
7	-0.053219	-0.6044	0.273303
8	-0.020134	-0.2287	0.409738
9	0.0026	0.0295	0.488242
10	-0.077745	-0.883	0.189435
11	-0.026846	-0.3049	0.380463
12	-0.037708	-0.4283	0.334582
13	0.021812	0.2477	0.402367
14	-0.044397	-0.5043	0.307472
15	-0.039276	-0.4461	0.32814
16	-0.031658	-0.3596	0.35988
17	-0.058811	-0.668	0.252673
18	0.015975	0.1814	0.428153
19	0.032961	0.3744	0.354374
20	0.14759	1.6763	0.048051
21	-0.069516	-0.7895	0.215621

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.021323 & -0.2422 & 0.40451 \tabularnewline
2 & -0.074754 & -0.849 & 0.198715 \tabularnewline
3 & -0.141664 & -1.609 & 0.055031 \tabularnewline
4 & 0.010153 & 0.1153 & 0.454189 \tabularnewline
5 & 0.083467 & 0.948 & 0.17245 \tabularnewline
6 & -0.102982 & -1.1697 & 0.122149 \tabularnewline
7 & -0.053219 & -0.6044 & 0.273303 \tabularnewline
8 & -0.020134 & -0.2287 & 0.409738 \tabularnewline
9 & 0.0026 & 0.0295 & 0.488242 \tabularnewline
10 & -0.077745 & -0.883 & 0.189435 \tabularnewline
11 & -0.026846 & -0.3049 & 0.380463 \tabularnewline
12 & -0.037708 & -0.4283 & 0.334582 \tabularnewline
13 & 0.021812 & 0.2477 & 0.402367 \tabularnewline
14 & -0.044397 & -0.5043 & 0.307472 \tabularnewline
15 & -0.039276 & -0.4461 & 0.32814 \tabularnewline
16 & -0.031658 & -0.3596 & 0.35988 \tabularnewline
17 & -0.058811 & -0.668 & 0.252673 \tabularnewline
18 & 0.015975 & 0.1814 & 0.428153 \tabularnewline
19 & 0.032961 & 0.3744 & 0.354374 \tabularnewline
20 & 0.14759 & 1.6763 & 0.048051 \tabularnewline
21 & -0.069516 & -0.7895 & 0.215621 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296795&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]-0.021323[/C][C]-0.2422[/C][C]0.40451[/C][/ROW]
[ROW][C]2[/C][C]-0.074754[/C][C]-0.849[/C][C]0.198715[/C][/ROW]
[ROW][C]3[/C][C]-0.141664[/C][C]-1.609[/C][C]0.055031[/C][/ROW]
[ROW][C]4[/C][C]0.010153[/C][C]0.1153[/C][C]0.454189[/C][/ROW]
[ROW][C]5[/C][C]0.083467[/C][C]0.948[/C][C]0.17245[/C][/ROW]
[ROW][C]6[/C][C]-0.102982[/C][C]-1.1697[/C][C]0.122149[/C][/ROW]
[ROW][C]7[/C][C]-0.053219[/C][C]-0.6044[/C][C]0.273303[/C][/ROW]
[ROW][C]8[/C][C]-0.020134[/C][C]-0.2287[/C][C]0.409738[/C][/ROW]
[ROW][C]9[/C][C]0.0026[/C][C]0.0295[/C][C]0.488242[/C][/ROW]
[ROW][C]10[/C][C]-0.077745[/C][C]-0.883[/C][C]0.189435[/C][/ROW]
[ROW][C]11[/C][C]-0.026846[/C][C]-0.3049[/C][C]0.380463[/C][/ROW]
[ROW][C]12[/C][C]-0.037708[/C][C]-0.4283[/C][C]0.334582[/C][/ROW]
[ROW][C]13[/C][C]0.021812[/C][C]0.2477[/C][C]0.402367[/C][/ROW]
[ROW][C]14[/C][C]-0.044397[/C][C]-0.5043[/C][C]0.307472[/C][/ROW]
[ROW][C]15[/C][C]-0.039276[/C][C]-0.4461[/C][C]0.32814[/C][/ROW]
[ROW][C]16[/C][C]-0.031658[/C][C]-0.3596[/C][C]0.35988[/C][/ROW]
[ROW][C]17[/C][C]-0.058811[/C][C]-0.668[/C][C]0.252673[/C][/ROW]
[ROW][C]18[/C][C]0.015975[/C][C]0.1814[/C][C]0.428153[/C][/ROW]
[ROW][C]19[/C][C]0.032961[/C][C]0.3744[/C][C]0.354374[/C][/ROW]
[ROW][C]20[/C][C]0.14759[/C][C]1.6763[/C][C]0.048051[/C][/ROW]
[ROW][C]21[/C][C]-0.069516[/C][C]-0.7895[/C][C]0.215621[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296795&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296795&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	-0.021323	-0.2422	0.40451
2	-0.074754	-0.849	0.198715
3	-0.141664	-1.609	0.055031
4	0.010153	0.1153	0.454189
5	0.083467	0.948	0.17245
6	-0.102982	-1.1697	0.122149
7	-0.053219	-0.6044	0.273303
8	-0.020134	-0.2287	0.409738
9	0.0026	0.0295	0.488242
10	-0.077745	-0.883	0.189435
11	-0.026846	-0.3049	0.380463
12	-0.037708	-0.4283	0.334582
13	0.021812	0.2477	0.402367
14	-0.044397	-0.5043	0.307472
15	-0.039276	-0.4461	0.32814
16	-0.031658	-0.3596	0.35988
17	-0.058811	-0.668	0.252673
18	0.015975	0.1814	0.428153
19	0.032961	0.3744	0.354374
20	0.14759	1.6763	0.048051
21	-0.069516	-0.7895	0.215621

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.021323	-0.2422	0.40451
2	-0.075243	-0.8546	0.19718
3	-0.145875	-1.6568	0.049993
4	-0.003737	-0.0424	0.483103
5	0.063377	0.7198	0.236468
6	-0.121963	-1.3852	0.084187
7	-0.050409	-0.5725	0.283978
8	-0.018622	-0.2115	0.416415
9	-0.040822	-0.4637	0.321839
10	-0.107804	-1.2244	0.111513
11	-0.028207	-0.3204	0.374602
12	-0.068701	-0.7803	0.218323
13	-0.02715	-0.3084	0.379153
14	-0.073619	-0.8362	0.202307
15	-0.061698	-0.7008	0.242359
16	-0.075301	-0.8553	0.196998
17	-0.113393	-1.2879	0.100044
18	-0.048501	-0.5509	0.291337
19	-0.013692	-0.1555	0.438332
20	0.098445	1.1181	0.132796
21	-0.096224	-1.0929	0.138237

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.021323 & -0.2422 & 0.40451 \tabularnewline
2 & -0.075243 & -0.8546 & 0.19718 \tabularnewline
3 & -0.145875 & -1.6568 & 0.049993 \tabularnewline
4 & -0.003737 & -0.0424 & 0.483103 \tabularnewline
5 & 0.063377 & 0.7198 & 0.236468 \tabularnewline
6 & -0.121963 & -1.3852 & 0.084187 \tabularnewline
7 & -0.050409 & -0.5725 & 0.283978 \tabularnewline
8 & -0.018622 & -0.2115 & 0.416415 \tabularnewline
9 & -0.040822 & -0.4637 & 0.321839 \tabularnewline
10 & -0.107804 & -1.2244 & 0.111513 \tabularnewline
11 & -0.028207 & -0.3204 & 0.374602 \tabularnewline
12 & -0.068701 & -0.7803 & 0.218323 \tabularnewline
13 & -0.02715 & -0.3084 & 0.379153 \tabularnewline
14 & -0.073619 & -0.8362 & 0.202307 \tabularnewline
15 & -0.061698 & -0.7008 & 0.242359 \tabularnewline
16 & -0.075301 & -0.8553 & 0.196998 \tabularnewline
17 & -0.113393 & -1.2879 & 0.100044 \tabularnewline
18 & -0.048501 & -0.5509 & 0.291337 \tabularnewline
19 & -0.013692 & -0.1555 & 0.438332 \tabularnewline
20 & 0.098445 & 1.1181 & 0.132796 \tabularnewline
21 & -0.096224 & -1.0929 & 0.138237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296795&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]-0.021323[/C][C]-0.2422[/C][C]0.40451[/C][/ROW]
[ROW][C]2[/C][C]-0.075243[/C][C]-0.8546[/C][C]0.19718[/C][/ROW]
[ROW][C]3[/C][C]-0.145875[/C][C]-1.6568[/C][C]0.049993[/C][/ROW]
[ROW][C]4[/C][C]-0.003737[/C][C]-0.0424[/C][C]0.483103[/C][/ROW]
[ROW][C]5[/C][C]0.063377[/C][C]0.7198[/C][C]0.236468[/C][/ROW]
[ROW][C]6[/C][C]-0.121963[/C][C]-1.3852[/C][C]0.084187[/C][/ROW]
[ROW][C]7[/C][C]-0.050409[/C][C]-0.5725[/C][C]0.283978[/C][/ROW]
[ROW][C]8[/C][C]-0.018622[/C][C]-0.2115[/C][C]0.416415[/C][/ROW]
[ROW][C]9[/C][C]-0.040822[/C][C]-0.4637[/C][C]0.321839[/C][/ROW]
[ROW][C]10[/C][C]-0.107804[/C][C]-1.2244[/C][C]0.111513[/C][/ROW]
[ROW][C]11[/C][C]-0.028207[/C][C]-0.3204[/C][C]0.374602[/C][/ROW]
[ROW][C]12[/C][C]-0.068701[/C][C]-0.7803[/C][C]0.218323[/C][/ROW]
[ROW][C]13[/C][C]-0.02715[/C][C]-0.3084[/C][C]0.379153[/C][/ROW]
[ROW][C]14[/C][C]-0.073619[/C][C]-0.8362[/C][C]0.202307[/C][/ROW]
[ROW][C]15[/C][C]-0.061698[/C][C]-0.7008[/C][C]0.242359[/C][/ROW]
[ROW][C]16[/C][C]-0.075301[/C][C]-0.8553[/C][C]0.196998[/C][/ROW]
[ROW][C]17[/C][C]-0.113393[/C][C]-1.2879[/C][C]0.100044[/C][/ROW]
[ROW][C]18[/C][C]-0.048501[/C][C]-0.5509[/C][C]0.291337[/C][/ROW]
[ROW][C]19[/C][C]-0.013692[/C][C]-0.1555[/C][C]0.438332[/C][/ROW]
[ROW][C]20[/C][C]0.098445[/C][C]1.1181[/C][C]0.132796[/C][/ROW]
[ROW][C]21[/C][C]-0.096224[/C][C]-1.0929[/C][C]0.138237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296795&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296795&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	-0.021323	-0.2422	0.40451
2	-0.075243	-0.8546	0.19718
3	-0.145875	-1.6568	0.049993
4	-0.003737	-0.0424	0.483103
5	0.063377	0.7198	0.236468
6	-0.121963	-1.3852	0.084187
7	-0.050409	-0.5725	0.283978
8	-0.018622	-0.2115	0.416415
9	-0.040822	-0.4637	0.321839
10	-0.107804	-1.2244	0.111513
11	-0.028207	-0.3204	0.374602
12	-0.068701	-0.7803	0.218323
13	-0.02715	-0.3084	0.379153
14	-0.073619	-0.8362	0.202307
15	-0.061698	-0.7008	0.242359
16	-0.075301	-0.8553	0.196998
17	-0.113393	-1.2879	0.100044
18	-0.048501	-0.5509	0.291337
19	-0.013692	-0.1555	0.438332
20	0.098445	1.1181	0.132796
21	-0.096224	-1.0929	0.138237

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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