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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

Sun, 10 Dec 2017 11:57:14 +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/10/t15129035462mzsike1rraemsp.htm/, Retrieved Wed, 15 May 2024 05:13:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308895, Retrieved Wed, 15 May 2024 05:13:25 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

104

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

-       [(Partial) Autocorrelation Function] [] [2017-12-10 10:57:14] [834c75312b1a933b06457deba9c9b5e8] [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=308895&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=308895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308895&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	-0.545958	-7.7017	0
2	-0.107304	-1.5137	0.065843
3	0.35997	5.078	0
4	-0.274137	-3.8672	7.5e-05
5	0.030308	0.4276	0.33472
6	0.206709	2.916	0.001976
7	-0.272868	-3.8493	8e-05
8	0.054422	0.7677	0.221782
9	0.234348	3.3059	0.000562
10	-0.256239	-3.6147	0.00019
11	0.165261	2.3313	0.01037
12	-0.051596	-0.7278	0.233781
13	-0.176514	-2.49	0.006796
14	0.257376	3.6307	0.00018
15	-0.019861	-0.2802	0.389816
16	-0.279855	-3.9478	5.5e-05
17	0.236152	3.3313	0.000515
18	0.073491	1.0367	0.150561
19	-0.262272	-3.6998	0.00014
20	0.248055	3.4992	0.000288
21	-0.052303	-0.7378	0.230743
22	-0.281224	-3.9671	5.1e-05
23	0.459157	6.4772	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.545958 & -7.7017 & 0 \tabularnewline
2 & -0.107304 & -1.5137 & 0.065843 \tabularnewline
3 & 0.35997 & 5.078 & 0 \tabularnewline
4 & -0.274137 & -3.8672 & 7.5e-05 \tabularnewline
5 & 0.030308 & 0.4276 & 0.33472 \tabularnewline
6 & 0.206709 & 2.916 & 0.001976 \tabularnewline
7 & -0.272868 & -3.8493 & 8e-05 \tabularnewline
8 & 0.054422 & 0.7677 & 0.221782 \tabularnewline
9 & 0.234348 & 3.3059 & 0.000562 \tabularnewline
10 & -0.256239 & -3.6147 & 0.00019 \tabularnewline
11 & 0.165261 & 2.3313 & 0.01037 \tabularnewline
12 & -0.051596 & -0.7278 & 0.233781 \tabularnewline
13 & -0.176514 & -2.49 & 0.006796 \tabularnewline
14 & 0.257376 & 3.6307 & 0.00018 \tabularnewline
15 & -0.019861 & -0.2802 & 0.389816 \tabularnewline
16 & -0.279855 & -3.9478 & 5.5e-05 \tabularnewline
17 & 0.236152 & 3.3313 & 0.000515 \tabularnewline
18 & 0.073491 & 1.0367 & 0.150561 \tabularnewline
19 & -0.262272 & -3.6998 & 0.00014 \tabularnewline
20 & 0.248055 & 3.4992 & 0.000288 \tabularnewline
21 & -0.052303 & -0.7378 & 0.230743 \tabularnewline
22 & -0.281224 & -3.9671 & 5.1e-05 \tabularnewline
23 & 0.459157 & 6.4772 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308895&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]-0.545958[/C][C]-7.7017[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.107304[/C][C]-1.5137[/C][C]0.065843[/C][/ROW]
[ROW][C]3[/C][C]0.35997[/C][C]5.078[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.274137[/C][C]-3.8672[/C][C]7.5e-05[/C][/ROW]
[ROW][C]5[/C][C]0.030308[/C][C]0.4276[/C][C]0.33472[/C][/ROW]
[ROW][C]6[/C][C]0.206709[/C][C]2.916[/C][C]0.001976[/C][/ROW]
[ROW][C]7[/C][C]-0.272868[/C][C]-3.8493[/C][C]8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.054422[/C][C]0.7677[/C][C]0.221782[/C][/ROW]
[ROW][C]9[/C][C]0.234348[/C][C]3.3059[/C][C]0.000562[/C][/ROW]
[ROW][C]10[/C][C]-0.256239[/C][C]-3.6147[/C][C]0.00019[/C][/ROW]
[ROW][C]11[/C][C]0.165261[/C][C]2.3313[/C][C]0.01037[/C][/ROW]
[ROW][C]12[/C][C]-0.051596[/C][C]-0.7278[/C][C]0.233781[/C][/ROW]
[ROW][C]13[/C][C]-0.176514[/C][C]-2.49[/C][C]0.006796[/C][/ROW]
[ROW][C]14[/C][C]0.257376[/C][C]3.6307[/C][C]0.00018[/C][/ROW]
[ROW][C]15[/C][C]-0.019861[/C][C]-0.2802[/C][C]0.389816[/C][/ROW]
[ROW][C]16[/C][C]-0.279855[/C][C]-3.9478[/C][C]5.5e-05[/C][/ROW]
[ROW][C]17[/C][C]0.236152[/C][C]3.3313[/C][C]0.000515[/C][/ROW]
[ROW][C]18[/C][C]0.073491[/C][C]1.0367[/C][C]0.150561[/C][/ROW]
[ROW][C]19[/C][C]-0.262272[/C][C]-3.6998[/C][C]0.00014[/C][/ROW]
[ROW][C]20[/C][C]0.248055[/C][C]3.4992[/C][C]0.000288[/C][/ROW]
[ROW][C]21[/C][C]-0.052303[/C][C]-0.7378[/C][C]0.230743[/C][/ROW]
[ROW][C]22[/C][C]-0.281224[/C][C]-3.9671[/C][C]5.1e-05[/C][/ROW]
[ROW][C]23[/C][C]0.459157[/C][C]6.4772[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308895&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	-0.545958	-7.7017	0
2	-0.107304	-1.5137	0.065843
3	0.35997	5.078	0
4	-0.274137	-3.8672	7.5e-05
5	0.030308	0.4276	0.33472
6	0.206709	2.916	0.001976
7	-0.272868	-3.8493	8e-05
8	0.054422	0.7677	0.221782
9	0.234348	3.3059	0.000562
10	-0.256239	-3.6147	0.00019
11	0.165261	2.3313	0.01037
12	-0.051596	-0.7278	0.233781
13	-0.176514	-2.49	0.006796
14	0.257376	3.6307	0.00018
15	-0.019861	-0.2802	0.389816
16	-0.279855	-3.9478	5.5e-05
17	0.236152	3.3313	0.000515
18	0.073491	1.0367	0.150561
19	-0.262272	-3.6998	0.00014
20	0.248055	3.4992	0.000288
21	-0.052303	-0.7378	0.230743
22	-0.281224	-3.9671	5.1e-05
23	0.459157	6.4772	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.545958	-7.7017	0
2	-0.577514	-8.1468	0
3	-0.102057	-1.4397	0.075762
4	-0.151235	-2.1334	0.017057
5	-0.130164	-1.8362	0.033911
6	0.088647	1.2505	0.10629
7	-0.05252	-0.7409	0.229817
8	-0.193633	-2.7315	0.003435
9	0.053566	0.7556	0.22538
10	0.06788	0.9576	0.169722
11	0.267718	3.7766	0.000105
12	0.092263	1.3015	0.097292
13	-0.191713	-2.7044	0.003717
14	-0.14296	-2.0167	0.022536
15	0.123326	1.7397	0.041726
16	-0.069928	-0.9865	0.162552
17	-0.193395	-2.7282	0.003469
18	0.059818	0.8438	0.199886
19	-0.020143	-0.2842	0.388292
20	-0.02661	-0.3754	0.353891
21	0.14416	2.0336	0.021659
22	-0.151963	-2.1437	0.016635
23	0.153486	2.1652	0.015782

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.545958 & -7.7017 & 0 \tabularnewline
2 & -0.577514 & -8.1468 & 0 \tabularnewline
3 & -0.102057 & -1.4397 & 0.075762 \tabularnewline
4 & -0.151235 & -2.1334 & 0.017057 \tabularnewline
5 & -0.130164 & -1.8362 & 0.033911 \tabularnewline
6 & 0.088647 & 1.2505 & 0.10629 \tabularnewline
7 & -0.05252 & -0.7409 & 0.229817 \tabularnewline
8 & -0.193633 & -2.7315 & 0.003435 \tabularnewline
9 & 0.053566 & 0.7556 & 0.22538 \tabularnewline
10 & 0.06788 & 0.9576 & 0.169722 \tabularnewline
11 & 0.267718 & 3.7766 & 0.000105 \tabularnewline
12 & 0.092263 & 1.3015 & 0.097292 \tabularnewline
13 & -0.191713 & -2.7044 & 0.003717 \tabularnewline
14 & -0.14296 & -2.0167 & 0.022536 \tabularnewline
15 & 0.123326 & 1.7397 & 0.041726 \tabularnewline
16 & -0.069928 & -0.9865 & 0.162552 \tabularnewline
17 & -0.193395 & -2.7282 & 0.003469 \tabularnewline
18 & 0.059818 & 0.8438 & 0.199886 \tabularnewline
19 & -0.020143 & -0.2842 & 0.388292 \tabularnewline
20 & -0.02661 & -0.3754 & 0.353891 \tabularnewline
21 & 0.14416 & 2.0336 & 0.021659 \tabularnewline
22 & -0.151963 & -2.1437 & 0.016635 \tabularnewline
23 & 0.153486 & 2.1652 & 0.015782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308895&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]-0.545958[/C][C]-7.7017[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.577514[/C][C]-8.1468[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.102057[/C][C]-1.4397[/C][C]0.075762[/C][/ROW]
[ROW][C]4[/C][C]-0.151235[/C][C]-2.1334[/C][C]0.017057[/C][/ROW]
[ROW][C]5[/C][C]-0.130164[/C][C]-1.8362[/C][C]0.033911[/C][/ROW]
[ROW][C]6[/C][C]0.088647[/C][C]1.2505[/C][C]0.10629[/C][/ROW]
[ROW][C]7[/C][C]-0.05252[/C][C]-0.7409[/C][C]0.229817[/C][/ROW]
[ROW][C]8[/C][C]-0.193633[/C][C]-2.7315[/C][C]0.003435[/C][/ROW]
[ROW][C]9[/C][C]0.053566[/C][C]0.7556[/C][C]0.22538[/C][/ROW]
[ROW][C]10[/C][C]0.06788[/C][C]0.9576[/C][C]0.169722[/C][/ROW]
[ROW][C]11[/C][C]0.267718[/C][C]3.7766[/C][C]0.000105[/C][/ROW]
[ROW][C]12[/C][C]0.092263[/C][C]1.3015[/C][C]0.097292[/C][/ROW]
[ROW][C]13[/C][C]-0.191713[/C][C]-2.7044[/C][C]0.003717[/C][/ROW]
[ROW][C]14[/C][C]-0.14296[/C][C]-2.0167[/C][C]0.022536[/C][/ROW]
[ROW][C]15[/C][C]0.123326[/C][C]1.7397[/C][C]0.041726[/C][/ROW]
[ROW][C]16[/C][C]-0.069928[/C][C]-0.9865[/C][C]0.162552[/C][/ROW]
[ROW][C]17[/C][C]-0.193395[/C][C]-2.7282[/C][C]0.003469[/C][/ROW]
[ROW][C]18[/C][C]0.059818[/C][C]0.8438[/C][C]0.199886[/C][/ROW]
[ROW][C]19[/C][C]-0.020143[/C][C]-0.2842[/C][C]0.388292[/C][/ROW]
[ROW][C]20[/C][C]-0.02661[/C][C]-0.3754[/C][C]0.353891[/C][/ROW]
[ROW][C]21[/C][C]0.14416[/C][C]2.0336[/C][C]0.021659[/C][/ROW]
[ROW][C]22[/C][C]-0.151963[/C][C]-2.1437[/C][C]0.016635[/C][/ROW]
[ROW][C]23[/C][C]0.153486[/C][C]2.1652[/C][C]0.015782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308895&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308895&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	-0.545958	-7.7017	0
2	-0.577514	-8.1468	0
3	-0.102057	-1.4397	0.075762
4	-0.151235	-2.1334	0.017057
5	-0.130164	-1.8362	0.033911
6	0.088647	1.2505	0.10629
7	-0.05252	-0.7409	0.229817
8	-0.193633	-2.7315	0.003435
9	0.053566	0.7556	0.22538
10	0.06788	0.9576	0.169722
11	0.267718	3.7766	0.000105
12	0.092263	1.3015	0.097292
13	-0.191713	-2.7044	0.003717
14	-0.14296	-2.0167	0.022536
15	0.123326	1.7397	0.041726
16	-0.069928	-0.9865	0.162552
17	-0.193395	-2.7282	0.003469
18	0.059818	0.8438	0.199886
19	-0.020143	-0.2842	0.388292
20	-0.02661	-0.3754	0.353891
21	0.14416	2.0336	0.021659
22	-0.151963	-2.1437	0.016635
23	0.153486	2.1652	0.015782

Figure 1

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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 = 0.6 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.6 ; par3 = 1 ; 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)
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