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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, 09 Dec 2017 14:14:29 +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/2017/Dec/09/t1512825888fnxbfk3pbv255y0.htm/, Retrieved Tue, 14 May 2024 17:27:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308851, Retrieved Tue, 14 May 2024 17:27:30 +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] [] [2017-12-09 13:14:29] [20141777ecd6b11d9726230b5f8289b4] [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=308851&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=308851&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308851&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	-0.50316	-7.0979	0
2	-0.086455	-1.2196	0.112031
3	0.352907	4.9784	1e-06
4	-0.303504	-4.2814	1.4e-05
5	0.119111	1.6803	0.047237
6	0.159436	2.2491	0.0128
7	-0.234065	-3.3019	0.000569
8	0.085847	1.211	0.113663
9	0.040091	0.5656	0.286166
10	-0.084824	-1.1966	0.116446
11	0.162497	2.2923	0.011467
12	-0.207184	-2.9227	0.001936
13	0.000685	0.0097	0.496148
14	0.077442	1.0925	0.137978
15	-0.034238	-0.483	0.314818
16	-0.069963	-0.987	0.162432
17	0.057957	0.8176	0.207285
18	0.036904	0.5206	0.301616
19	-0.166359	-2.3468	0.009959
20	0.117645	1.6596	0.049286
21	0.045729	0.6451	0.259808
22	-0.264792	-3.7353	0.000122
23	0.32712	4.6146	4e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.50316 & -7.0979 & 0 \tabularnewline
2 & -0.086455 & -1.2196 & 0.112031 \tabularnewline
3 & 0.352907 & 4.9784 & 1e-06 \tabularnewline
4 & -0.303504 & -4.2814 & 1.4e-05 \tabularnewline
5 & 0.119111 & 1.6803 & 0.047237 \tabularnewline
6 & 0.159436 & 2.2491 & 0.0128 \tabularnewline
7 & -0.234065 & -3.3019 & 0.000569 \tabularnewline
8 & 0.085847 & 1.211 & 0.113663 \tabularnewline
9 & 0.040091 & 0.5656 & 0.286166 \tabularnewline
10 & -0.084824 & -1.1966 & 0.116446 \tabularnewline
11 & 0.162497 & 2.2923 & 0.011467 \tabularnewline
12 & -0.207184 & -2.9227 & 0.001936 \tabularnewline
13 & 0.000685 & 0.0097 & 0.496148 \tabularnewline
14 & 0.077442 & 1.0925 & 0.137978 \tabularnewline
15 & -0.034238 & -0.483 & 0.314818 \tabularnewline
16 & -0.069963 & -0.987 & 0.162432 \tabularnewline
17 & 0.057957 & 0.8176 & 0.207285 \tabularnewline
18 & 0.036904 & 0.5206 & 0.301616 \tabularnewline
19 & -0.166359 & -2.3468 & 0.009959 \tabularnewline
20 & 0.117645 & 1.6596 & 0.049286 \tabularnewline
21 & 0.045729 & 0.6451 & 0.259808 \tabularnewline
22 & -0.264792 & -3.7353 & 0.000122 \tabularnewline
23 & 0.32712 & 4.6146 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308851&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]-0.50316[/C][C]-7.0979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.086455[/C][C]-1.2196[/C][C]0.112031[/C][/ROW]
[ROW][C]3[/C][C]0.352907[/C][C]4.9784[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.303504[/C][C]-4.2814[/C][C]1.4e-05[/C][/ROW]
[ROW][C]5[/C][C]0.119111[/C][C]1.6803[/C][C]0.047237[/C][/ROW]
[ROW][C]6[/C][C]0.159436[/C][C]2.2491[/C][C]0.0128[/C][/ROW]
[ROW][C]7[/C][C]-0.234065[/C][C]-3.3019[/C][C]0.000569[/C][/ROW]
[ROW][C]8[/C][C]0.085847[/C][C]1.211[/C][C]0.113663[/C][/ROW]
[ROW][C]9[/C][C]0.040091[/C][C]0.5656[/C][C]0.286166[/C][/ROW]
[ROW][C]10[/C][C]-0.084824[/C][C]-1.1966[/C][C]0.116446[/C][/ROW]
[ROW][C]11[/C][C]0.162497[/C][C]2.2923[/C][C]0.011467[/C][/ROW]
[ROW][C]12[/C][C]-0.207184[/C][C]-2.9227[/C][C]0.001936[/C][/ROW]
[ROW][C]13[/C][C]0.000685[/C][C]0.0097[/C][C]0.496148[/C][/ROW]
[ROW][C]14[/C][C]0.077442[/C][C]1.0925[/C][C]0.137978[/C][/ROW]
[ROW][C]15[/C][C]-0.034238[/C][C]-0.483[/C][C]0.314818[/C][/ROW]
[ROW][C]16[/C][C]-0.069963[/C][C]-0.987[/C][C]0.162432[/C][/ROW]
[ROW][C]17[/C][C]0.057957[/C][C]0.8176[/C][C]0.207285[/C][/ROW]
[ROW][C]18[/C][C]0.036904[/C][C]0.5206[/C][C]0.301616[/C][/ROW]
[ROW][C]19[/C][C]-0.166359[/C][C]-2.3468[/C][C]0.009959[/C][/ROW]
[ROW][C]20[/C][C]0.117645[/C][C]1.6596[/C][C]0.049286[/C][/ROW]
[ROW][C]21[/C][C]0.045729[/C][C]0.6451[/C][C]0.259808[/C][/ROW]
[ROW][C]22[/C][C]-0.264792[/C][C]-3.7353[/C][C]0.000122[/C][/ROW]
[ROW][C]23[/C][C]0.32712[/C][C]4.6146[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308851&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308851&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	-0.50316	-7.0979	0
2	-0.086455	-1.2196	0.112031
3	0.352907	4.9784	1e-06
4	-0.303504	-4.2814	1.4e-05
5	0.119111	1.6803	0.047237
6	0.159436	2.2491	0.0128
7	-0.234065	-3.3019	0.000569
8	0.085847	1.211	0.113663
9	0.040091	0.5656	0.286166
10	-0.084824	-1.1966	0.116446
11	0.162497	2.2923	0.011467
12	-0.207184	-2.9227	0.001936
13	0.000685	0.0097	0.496148
14	0.077442	1.0925	0.137978
15	-0.034238	-0.483	0.314818
16	-0.069963	-0.987	0.162432
17	0.057957	0.8176	0.207285
18	0.036904	0.5206	0.301616
19	-0.166359	-2.3468	0.009959
20	0.117645	1.6596	0.049286
21	0.045729	0.6451	0.259808
22	-0.264792	-3.7353	0.000122
23	0.32712	4.6146	4e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.50316	-7.0979	0
2	-0.454755	-6.4151	0
3	0.102654	1.4481	0.074581
4	-0.073067	-1.0307	0.151957
5	0.042774	0.6034	0.273463
6	0.186422	2.6298	0.004606
7	0.065596	0.9253	0.177955
8	-0.044138	-0.6226	0.267115
9	-0.076666	-1.0815	0.14039
10	-0.031013	-0.4375	0.331117
11	0.148513	2.095	0.018717
12	-0.124261	-1.7529	0.040579
13	-0.186802	-2.6352	0.004536
14	-0.206226	-2.9092	0.002018
15	0.008571	0.1209	0.451942
16	-0.131074	-1.849	0.032969
17	-0.077391	-1.0917	0.138135
18	0.167138	2.3578	0.009678
19	-0.03138	-0.4427	0.329244
20	-0.115518	-1.6296	0.052386
21	0.007292	0.1029	0.459086
22	-0.205396	-2.8975	0.002092
23	0.160107	2.2586	0.012497

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.50316 & -7.0979 & 0 \tabularnewline
2 & -0.454755 & -6.4151 & 0 \tabularnewline
3 & 0.102654 & 1.4481 & 0.074581 \tabularnewline
4 & -0.073067 & -1.0307 & 0.151957 \tabularnewline
5 & 0.042774 & 0.6034 & 0.273463 \tabularnewline
6 & 0.186422 & 2.6298 & 0.004606 \tabularnewline
7 & 0.065596 & 0.9253 & 0.177955 \tabularnewline
8 & -0.044138 & -0.6226 & 0.267115 \tabularnewline
9 & -0.076666 & -1.0815 & 0.14039 \tabularnewline
10 & -0.031013 & -0.4375 & 0.331117 \tabularnewline
11 & 0.148513 & 2.095 & 0.018717 \tabularnewline
12 & -0.124261 & -1.7529 & 0.040579 \tabularnewline
13 & -0.186802 & -2.6352 & 0.004536 \tabularnewline
14 & -0.206226 & -2.9092 & 0.002018 \tabularnewline
15 & 0.008571 & 0.1209 & 0.451942 \tabularnewline
16 & -0.131074 & -1.849 & 0.032969 \tabularnewline
17 & -0.077391 & -1.0917 & 0.138135 \tabularnewline
18 & 0.167138 & 2.3578 & 0.009678 \tabularnewline
19 & -0.03138 & -0.4427 & 0.329244 \tabularnewline
20 & -0.115518 & -1.6296 & 0.052386 \tabularnewline
21 & 0.007292 & 0.1029 & 0.459086 \tabularnewline
22 & -0.205396 & -2.8975 & 0.002092 \tabularnewline
23 & 0.160107 & 2.2586 & 0.012497 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308851&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]-0.50316[/C][C]-7.0979[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.454755[/C][C]-6.4151[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.102654[/C][C]1.4481[/C][C]0.074581[/C][/ROW]
[ROW][C]4[/C][C]-0.073067[/C][C]-1.0307[/C][C]0.151957[/C][/ROW]
[ROW][C]5[/C][C]0.042774[/C][C]0.6034[/C][C]0.273463[/C][/ROW]
[ROW][C]6[/C][C]0.186422[/C][C]2.6298[/C][C]0.004606[/C][/ROW]
[ROW][C]7[/C][C]0.065596[/C][C]0.9253[/C][C]0.177955[/C][/ROW]
[ROW][C]8[/C][C]-0.044138[/C][C]-0.6226[/C][C]0.267115[/C][/ROW]
[ROW][C]9[/C][C]-0.076666[/C][C]-1.0815[/C][C]0.14039[/C][/ROW]
[ROW][C]10[/C][C]-0.031013[/C][C]-0.4375[/C][C]0.331117[/C][/ROW]
[ROW][C]11[/C][C]0.148513[/C][C]2.095[/C][C]0.018717[/C][/ROW]
[ROW][C]12[/C][C]-0.124261[/C][C]-1.7529[/C][C]0.040579[/C][/ROW]
[ROW][C]13[/C][C]-0.186802[/C][C]-2.6352[/C][C]0.004536[/C][/ROW]
[ROW][C]14[/C][C]-0.206226[/C][C]-2.9092[/C][C]0.002018[/C][/ROW]
[ROW][C]15[/C][C]0.008571[/C][C]0.1209[/C][C]0.451942[/C][/ROW]
[ROW][C]16[/C][C]-0.131074[/C][C]-1.849[/C][C]0.032969[/C][/ROW]
[ROW][C]17[/C][C]-0.077391[/C][C]-1.0917[/C][C]0.138135[/C][/ROW]
[ROW][C]18[/C][C]0.167138[/C][C]2.3578[/C][C]0.009678[/C][/ROW]
[ROW][C]19[/C][C]-0.03138[/C][C]-0.4427[/C][C]0.329244[/C][/ROW]
[ROW][C]20[/C][C]-0.115518[/C][C]-1.6296[/C][C]0.052386[/C][/ROW]
[ROW][C]21[/C][C]0.007292[/C][C]0.1029[/C][C]0.459086[/C][/ROW]
[ROW][C]22[/C][C]-0.205396[/C][C]-2.8975[/C][C]0.002092[/C][/ROW]
[ROW][C]23[/C][C]0.160107[/C][C]2.2586[/C][C]0.012497[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308851&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308851&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	-0.50316	-7.0979	0
2	-0.454755	-6.4151	0
3	0.102654	1.4481	0.074581
4	-0.073067	-1.0307	0.151957
5	0.042774	0.6034	0.273463
6	0.186422	2.6298	0.004606
7	0.065596	0.9253	0.177955
8	-0.044138	-0.6226	0.267115
9	-0.076666	-1.0815	0.14039
10	-0.031013	-0.4375	0.331117
11	0.148513	2.095	0.018717
12	-0.124261	-1.7529	0.040579
13	-0.186802	-2.6352	0.004536
14	-0.206226	-2.9092	0.002018
15	0.008571	0.1209	0.451942
16	-0.131074	-1.849	0.032969
17	-0.077391	-1.0917	0.138135
18	0.167138	2.3578	0.009678
19	-0.03138	-0.4427	0.329244
20	-0.115518	-1.6296	0.052386
21	0.007292	0.1029	0.459086
22	-0.205396	-2.8975	0.002092
23	0.160107	2.2586	0.012497

Figure 1

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Figure 2

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Figure 3

PNG link

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PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

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

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code