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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

Wed, 21 Dec 2016 16:06:39 +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/Dec/21/t1482332858y2zoro8zonr6h2l.htm/, Retrieved Fri, 17 May 2024 16:39:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302369, Retrieved Fri, 17 May 2024 16:39:25 +0000

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User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2016-12-21 15:06:39] [361c8dad91b3f1ef2e651cd04783c23b] [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=302369&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=302369&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302369&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	0.270764	2.0262	0.023758
2	0.100587	0.7527	0.227383
3	0.164457	1.2307	0.111793
4	-0.151767	-1.1357	0.130456
5	-0.150895	-1.1292	0.131815
6	0.063975	0.4787	0.316991
7	0.077979	0.5835	0.280936
8	-0.157811	-1.1809	0.121308
9	0.003153	0.0236	0.49063
10	-0.032612	-0.244	0.404042
11	-0.017686	-0.1323	0.447591
12	0.031784	0.2378	0.406433
13	0.046173	0.3455	0.365496
14	0.037229	0.2786	0.39079
15	-0.137267	-1.0272	0.154369
16	-0.124982	-0.9353	0.17683
17	-0.055698	-0.4168	0.339208
18	-0.158171	-1.1836	0.120777
19	-0.065651	-0.4913	0.312573
20	0.029258	0.2189	0.413743
21	-0.019897	-0.1489	0.441084
22	-0.003029	-0.0227	0.490999
23	-0.003282	-0.0246	0.490245
24	-0.103916	-0.7776	0.220029

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.270764 & 2.0262 & 0.023758 \tabularnewline
2 & 0.100587 & 0.7527 & 0.227383 \tabularnewline
3 & 0.164457 & 1.2307 & 0.111793 \tabularnewline
4 & -0.151767 & -1.1357 & 0.130456 \tabularnewline
5 & -0.150895 & -1.1292 & 0.131815 \tabularnewline
6 & 0.063975 & 0.4787 & 0.316991 \tabularnewline
7 & 0.077979 & 0.5835 & 0.280936 \tabularnewline
8 & -0.157811 & -1.1809 & 0.121308 \tabularnewline
9 & 0.003153 & 0.0236 & 0.49063 \tabularnewline
10 & -0.032612 & -0.244 & 0.404042 \tabularnewline
11 & -0.017686 & -0.1323 & 0.447591 \tabularnewline
12 & 0.031784 & 0.2378 & 0.406433 \tabularnewline
13 & 0.046173 & 0.3455 & 0.365496 \tabularnewline
14 & 0.037229 & 0.2786 & 0.39079 \tabularnewline
15 & -0.137267 & -1.0272 & 0.154369 \tabularnewline
16 & -0.124982 & -0.9353 & 0.17683 \tabularnewline
17 & -0.055698 & -0.4168 & 0.339208 \tabularnewline
18 & -0.158171 & -1.1836 & 0.120777 \tabularnewline
19 & -0.065651 & -0.4913 & 0.312573 \tabularnewline
20 & 0.029258 & 0.2189 & 0.413743 \tabularnewline
21 & -0.019897 & -0.1489 & 0.441084 \tabularnewline
22 & -0.003029 & -0.0227 & 0.490999 \tabularnewline
23 & -0.003282 & -0.0246 & 0.490245 \tabularnewline
24 & -0.103916 & -0.7776 & 0.220029 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302369&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]0.270764[/C][C]2.0262[/C][C]0.023758[/C][/ROW]
[ROW][C]2[/C][C]0.100587[/C][C]0.7527[/C][C]0.227383[/C][/ROW]
[ROW][C]3[/C][C]0.164457[/C][C]1.2307[/C][C]0.111793[/C][/ROW]
[ROW][C]4[/C][C]-0.151767[/C][C]-1.1357[/C][C]0.130456[/C][/ROW]
[ROW][C]5[/C][C]-0.150895[/C][C]-1.1292[/C][C]0.131815[/C][/ROW]
[ROW][C]6[/C][C]0.063975[/C][C]0.4787[/C][C]0.316991[/C][/ROW]
[ROW][C]7[/C][C]0.077979[/C][C]0.5835[/C][C]0.280936[/C][/ROW]
[ROW][C]8[/C][C]-0.157811[/C][C]-1.1809[/C][C]0.121308[/C][/ROW]
[ROW][C]9[/C][C]0.003153[/C][C]0.0236[/C][C]0.49063[/C][/ROW]
[ROW][C]10[/C][C]-0.032612[/C][C]-0.244[/C][C]0.404042[/C][/ROW]
[ROW][C]11[/C][C]-0.017686[/C][C]-0.1323[/C][C]0.447591[/C][/ROW]
[ROW][C]12[/C][C]0.031784[/C][C]0.2378[/C][C]0.406433[/C][/ROW]
[ROW][C]13[/C][C]0.046173[/C][C]0.3455[/C][C]0.365496[/C][/ROW]
[ROW][C]14[/C][C]0.037229[/C][C]0.2786[/C][C]0.39079[/C][/ROW]
[ROW][C]15[/C][C]-0.137267[/C][C]-1.0272[/C][C]0.154369[/C][/ROW]
[ROW][C]16[/C][C]-0.124982[/C][C]-0.9353[/C][C]0.17683[/C][/ROW]
[ROW][C]17[/C][C]-0.055698[/C][C]-0.4168[/C][C]0.339208[/C][/ROW]
[ROW][C]18[/C][C]-0.158171[/C][C]-1.1836[/C][C]0.120777[/C][/ROW]
[ROW][C]19[/C][C]-0.065651[/C][C]-0.4913[/C][C]0.312573[/C][/ROW]
[ROW][C]20[/C][C]0.029258[/C][C]0.2189[/C][C]0.413743[/C][/ROW]
[ROW][C]21[/C][C]-0.019897[/C][C]-0.1489[/C][C]0.441084[/C][/ROW]
[ROW][C]22[/C][C]-0.003029[/C][C]-0.0227[/C][C]0.490999[/C][/ROW]
[ROW][C]23[/C][C]-0.003282[/C][C]-0.0246[/C][C]0.490245[/C][/ROW]
[ROW][C]24[/C][C]-0.103916[/C][C]-0.7776[/C][C]0.220029[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302369&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302369&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	0.270764	2.0262	0.023758
2	0.100587	0.7527	0.227383
3	0.164457	1.2307	0.111793
4	-0.151767	-1.1357	0.130456
5	-0.150895	-1.1292	0.131815
6	0.063975	0.4787	0.316991
7	0.077979	0.5835	0.280936
8	-0.157811	-1.1809	0.121308
9	0.003153	0.0236	0.49063
10	-0.032612	-0.244	0.404042
11	-0.017686	-0.1323	0.447591
12	0.031784	0.2378	0.406433
13	0.046173	0.3455	0.365496
14	0.037229	0.2786	0.39079
15	-0.137267	-1.0272	0.154369
16	-0.124982	-0.9353	0.17683
17	-0.055698	-0.4168	0.339208
18	-0.158171	-1.1836	0.120777
19	-0.065651	-0.4913	0.312573
20	0.029258	0.2189	0.413743
21	-0.019897	-0.1489	0.441084
22	-0.003029	-0.0227	0.490999
23	-0.003282	-0.0246	0.490245
24	-0.103916	-0.7776	0.220029

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.270764	2.0262	0.023758
2	0.029432	0.2203	0.413238
3	0.140464	1.0511	0.148855
4	-0.255157	-1.9094	0.030668
5	-0.066392	-0.4968	0.310626
6	0.135344	1.0128	0.157751
7	0.12634	0.9454	0.174247
8	-0.264939	-1.9826	0.026162
9	0.012531	0.0938	0.462812
10	-0.019092	-0.1429	0.443452
11	0.187978	1.4067	0.082521
12	-0.096688	-0.7235	0.236177
13	-0.024984	-0.187	0.426183
14	0.008745	0.0654	0.474028
15	-0.088813	-0.6646	0.254512
16	-0.11846	-0.8865	0.189577
17	0.041191	0.3082	0.37952
18	-0.133701	-1.0005	0.160679
19	0.041136	0.3078	0.379676
20	-0.05	-0.3742	0.354846
21	0.050858	0.3806	0.352475
22	0.00192	0.0144	0.494293
23	-0.093174	-0.6973	0.244265
24	-0.150636	-1.1273	0.132221

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.270764 & 2.0262 & 0.023758 \tabularnewline
2 & 0.029432 & 0.2203 & 0.413238 \tabularnewline
3 & 0.140464 & 1.0511 & 0.148855 \tabularnewline
4 & -0.255157 & -1.9094 & 0.030668 \tabularnewline
5 & -0.066392 & -0.4968 & 0.310626 \tabularnewline
6 & 0.135344 & 1.0128 & 0.157751 \tabularnewline
7 & 0.12634 & 0.9454 & 0.174247 \tabularnewline
8 & -0.264939 & -1.9826 & 0.026162 \tabularnewline
9 & 0.012531 & 0.0938 & 0.462812 \tabularnewline
10 & -0.019092 & -0.1429 & 0.443452 \tabularnewline
11 & 0.187978 & 1.4067 & 0.082521 \tabularnewline
12 & -0.096688 & -0.7235 & 0.236177 \tabularnewline
13 & -0.024984 & -0.187 & 0.426183 \tabularnewline
14 & 0.008745 & 0.0654 & 0.474028 \tabularnewline
15 & -0.088813 & -0.6646 & 0.254512 \tabularnewline
16 & -0.11846 & -0.8865 & 0.189577 \tabularnewline
17 & 0.041191 & 0.3082 & 0.37952 \tabularnewline
18 & -0.133701 & -1.0005 & 0.160679 \tabularnewline
19 & 0.041136 & 0.3078 & 0.379676 \tabularnewline
20 & -0.05 & -0.3742 & 0.354846 \tabularnewline
21 & 0.050858 & 0.3806 & 0.352475 \tabularnewline
22 & 0.00192 & 0.0144 & 0.494293 \tabularnewline
23 & -0.093174 & -0.6973 & 0.244265 \tabularnewline
24 & -0.150636 & -1.1273 & 0.132221 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302369&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]0.270764[/C][C]2.0262[/C][C]0.023758[/C][/ROW]
[ROW][C]2[/C][C]0.029432[/C][C]0.2203[/C][C]0.413238[/C][/ROW]
[ROW][C]3[/C][C]0.140464[/C][C]1.0511[/C][C]0.148855[/C][/ROW]
[ROW][C]4[/C][C]-0.255157[/C][C]-1.9094[/C][C]0.030668[/C][/ROW]
[ROW][C]5[/C][C]-0.066392[/C][C]-0.4968[/C][C]0.310626[/C][/ROW]
[ROW][C]6[/C][C]0.135344[/C][C]1.0128[/C][C]0.157751[/C][/ROW]
[ROW][C]7[/C][C]0.12634[/C][C]0.9454[/C][C]0.174247[/C][/ROW]
[ROW][C]8[/C][C]-0.264939[/C][C]-1.9826[/C][C]0.026162[/C][/ROW]
[ROW][C]9[/C][C]0.012531[/C][C]0.0938[/C][C]0.462812[/C][/ROW]
[ROW][C]10[/C][C]-0.019092[/C][C]-0.1429[/C][C]0.443452[/C][/ROW]
[ROW][C]11[/C][C]0.187978[/C][C]1.4067[/C][C]0.082521[/C][/ROW]
[ROW][C]12[/C][C]-0.096688[/C][C]-0.7235[/C][C]0.236177[/C][/ROW]
[ROW][C]13[/C][C]-0.024984[/C][C]-0.187[/C][C]0.426183[/C][/ROW]
[ROW][C]14[/C][C]0.008745[/C][C]0.0654[/C][C]0.474028[/C][/ROW]
[ROW][C]15[/C][C]-0.088813[/C][C]-0.6646[/C][C]0.254512[/C][/ROW]
[ROW][C]16[/C][C]-0.11846[/C][C]-0.8865[/C][C]0.189577[/C][/ROW]
[ROW][C]17[/C][C]0.041191[/C][C]0.3082[/C][C]0.37952[/C][/ROW]
[ROW][C]18[/C][C]-0.133701[/C][C]-1.0005[/C][C]0.160679[/C][/ROW]
[ROW][C]19[/C][C]0.041136[/C][C]0.3078[/C][C]0.379676[/C][/ROW]
[ROW][C]20[/C][C]-0.05[/C][C]-0.3742[/C][C]0.354846[/C][/ROW]
[ROW][C]21[/C][C]0.050858[/C][C]0.3806[/C][C]0.352475[/C][/ROW]
[ROW][C]22[/C][C]0.00192[/C][C]0.0144[/C][C]0.494293[/C][/ROW]
[ROW][C]23[/C][C]-0.093174[/C][C]-0.6973[/C][C]0.244265[/C][/ROW]
[ROW][C]24[/C][C]-0.150636[/C][C]-1.1273[/C][C]0.132221[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302369&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302369&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	0.270764	2.0262	0.023758
2	0.029432	0.2203	0.413238
3	0.140464	1.0511	0.148855
4	-0.255157	-1.9094	0.030668
5	-0.066392	-0.4968	0.310626
6	0.135344	1.0128	0.157751
7	0.12634	0.9454	0.174247
8	-0.264939	-1.9826	0.026162
9	0.012531	0.0938	0.462812
10	-0.019092	-0.1429	0.443452
11	0.187978	1.4067	0.082521
12	-0.096688	-0.7235	0.236177
13	-0.024984	-0.187	0.426183
14	0.008745	0.0654	0.474028
15	-0.088813	-0.6646	0.254512
16	-0.11846	-0.8865	0.189577
17	0.041191	0.3082	0.37952
18	-0.133701	-1.0005	0.160679
19	0.041136	0.3078	0.379676
20	-0.05	-0.3742	0.354846
21	0.050858	0.3806	0.352475
22	0.00192	0.0144	0.494293
23	-0.093174	-0.6973	0.244265
24	-0.150636	-1.1273	0.132221

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 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 4 ; 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 <- '4'
par4 <- '1'
par3 <- '0'
par2 <- '1'
par1 <- '24'
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