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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2016 17:43:00 +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/07/t1481129159jbmo7qeiq6bq7s5.htm/, Retrieved Tue, 07 May 2024 12:53:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298253, Retrieved Tue, 07 May 2024 12:53:49 +0000

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F1 competition

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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] [Partial Autocorre...] [2016-12-07 16:43:00] [00d6a26c230b6c589ee3bbc701d55499] [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=298253&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=298253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298253&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	0.067637	0.7253	0.234863
2	0.136377	1.4625	0.073168
3	0.098496	1.0563	0.146534
4	-0.320766	-3.4398	0.000406
5	-0.236922	-2.5407	0.006198
6	-0.410349	-4.4005	1.2e-05
7	-0.311628	-3.3418	0.000562
8	-0.160694	-1.7233	0.043765
9	0.033661	0.361	0.359392
10	0.111384	1.1945	0.117378
11	0.319185	3.4229	0.00043
12	0.487176	5.2244	0
13	0.134253	1.4397	0.076334
14	0.180448	1.9351	0.027718
15	-0.019568	-0.2098	0.417081
16	-0.25428	-2.7268	0.003698
17	-0.167206	-1.7931	0.037794
18	-0.419927	-4.5032	8e-06
19	-0.214178	-2.2968	0.01172
20	-0.078982	-0.847	0.199381

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.067637 & 0.7253 & 0.234863 \tabularnewline
2 & 0.136377 & 1.4625 & 0.073168 \tabularnewline
3 & 0.098496 & 1.0563 & 0.146534 \tabularnewline
4 & -0.320766 & -3.4398 & 0.000406 \tabularnewline
5 & -0.236922 & -2.5407 & 0.006198 \tabularnewline
6 & -0.410349 & -4.4005 & 1.2e-05 \tabularnewline
7 & -0.311628 & -3.3418 & 0.000562 \tabularnewline
8 & -0.160694 & -1.7233 & 0.043765 \tabularnewline
9 & 0.033661 & 0.361 & 0.359392 \tabularnewline
10 & 0.111384 & 1.1945 & 0.117378 \tabularnewline
11 & 0.319185 & 3.4229 & 0.00043 \tabularnewline
12 & 0.487176 & 5.2244 & 0 \tabularnewline
13 & 0.134253 & 1.4397 & 0.076334 \tabularnewline
14 & 0.180448 & 1.9351 & 0.027718 \tabularnewline
15 & -0.019568 & -0.2098 & 0.417081 \tabularnewline
16 & -0.25428 & -2.7268 & 0.003698 \tabularnewline
17 & -0.167206 & -1.7931 & 0.037794 \tabularnewline
18 & -0.419927 & -4.5032 & 8e-06 \tabularnewline
19 & -0.214178 & -2.2968 & 0.01172 \tabularnewline
20 & -0.078982 & -0.847 & 0.199381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298253&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]0.067637[/C][C]0.7253[/C][C]0.234863[/C][/ROW]
[ROW][C]2[/C][C]0.136377[/C][C]1.4625[/C][C]0.073168[/C][/ROW]
[ROW][C]3[/C][C]0.098496[/C][C]1.0563[/C][C]0.146534[/C][/ROW]
[ROW][C]4[/C][C]-0.320766[/C][C]-3.4398[/C][C]0.000406[/C][/ROW]
[ROW][C]5[/C][C]-0.236922[/C][C]-2.5407[/C][C]0.006198[/C][/ROW]
[ROW][C]6[/C][C]-0.410349[/C][C]-4.4005[/C][C]1.2e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.311628[/C][C]-3.3418[/C][C]0.000562[/C][/ROW]
[ROW][C]8[/C][C]-0.160694[/C][C]-1.7233[/C][C]0.043765[/C][/ROW]
[ROW][C]9[/C][C]0.033661[/C][C]0.361[/C][C]0.359392[/C][/ROW]
[ROW][C]10[/C][C]0.111384[/C][C]1.1945[/C][C]0.117378[/C][/ROW]
[ROW][C]11[/C][C]0.319185[/C][C]3.4229[/C][C]0.00043[/C][/ROW]
[ROW][C]12[/C][C]0.487176[/C][C]5.2244[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.134253[/C][C]1.4397[/C][C]0.076334[/C][/ROW]
[ROW][C]14[/C][C]0.180448[/C][C]1.9351[/C][C]0.027718[/C][/ROW]
[ROW][C]15[/C][C]-0.019568[/C][C]-0.2098[/C][C]0.417081[/C][/ROW]
[ROW][C]16[/C][C]-0.25428[/C][C]-2.7268[/C][C]0.003698[/C][/ROW]
[ROW][C]17[/C][C]-0.167206[/C][C]-1.7931[/C][C]0.037794[/C][/ROW]
[ROW][C]18[/C][C]-0.419927[/C][C]-4.5032[/C][C]8e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.214178[/C][C]-2.2968[/C][C]0.01172[/C][/ROW]
[ROW][C]20[/C][C]-0.078982[/C][C]-0.847[/C][C]0.199381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298253&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	0.067637	0.7253	0.234863
2	0.136377	1.4625	0.073168
3	0.098496	1.0563	0.146534
4	-0.320766	-3.4398	0.000406
5	-0.236922	-2.5407	0.006198
6	-0.410349	-4.4005	1.2e-05
7	-0.311628	-3.3418	0.000562
8	-0.160694	-1.7233	0.043765
9	0.033661	0.361	0.359392
10	0.111384	1.1945	0.117378
11	0.319185	3.4229	0.00043
12	0.487176	5.2244	0
13	0.134253	1.4397	0.076334
14	0.180448	1.9351	0.027718
15	-0.019568	-0.2098	0.417081
16	-0.25428	-2.7268	0.003698
17	-0.167206	-1.7931	0.037794
18	-0.419927	-4.5032	8e-06
19	-0.214178	-2.2968	0.01172
20	-0.078982	-0.847	0.199381

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.067637	0.7253	0.234863
2	0.132408	1.4199	0.079168
3	0.083374	0.8941	0.186572
4	-0.358831	-3.848	9.8e-05
5	-0.258286	-2.7698	0.003271
6	-0.380733	-4.0829	4.1e-05
7	-0.280754	-3.0107	0.001602
8	-0.26996	-2.895	0.002269
9	-0.085161	-0.9132	0.181512
10	-0.198694	-2.1308	0.01762
11	-0.046681	-0.5006	0.308806
12	0.237617	2.5482	0.006074
13	-0.026144	-0.2804	0.389851
14	-0.044141	-0.4734	0.318427
15	-0.065699	-0.7045	0.241261
16	-0.080766	-0.8661	0.194114
17	0.054396	0.5833	0.280406
18	-0.095427	-1.0233	0.154148
19	-0.028015	-0.3004	0.382195
20	-0.020195	-0.2166	0.414464

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.067637 & 0.7253 & 0.234863 \tabularnewline
2 & 0.132408 & 1.4199 & 0.079168 \tabularnewline
3 & 0.083374 & 0.8941 & 0.186572 \tabularnewline
4 & -0.358831 & -3.848 & 9.8e-05 \tabularnewline
5 & -0.258286 & -2.7698 & 0.003271 \tabularnewline
6 & -0.380733 & -4.0829 & 4.1e-05 \tabularnewline
7 & -0.280754 & -3.0107 & 0.001602 \tabularnewline
8 & -0.26996 & -2.895 & 0.002269 \tabularnewline
9 & -0.085161 & -0.9132 & 0.181512 \tabularnewline
10 & -0.198694 & -2.1308 & 0.01762 \tabularnewline
11 & -0.046681 & -0.5006 & 0.308806 \tabularnewline
12 & 0.237617 & 2.5482 & 0.006074 \tabularnewline
13 & -0.026144 & -0.2804 & 0.389851 \tabularnewline
14 & -0.044141 & -0.4734 & 0.318427 \tabularnewline
15 & -0.065699 & -0.7045 & 0.241261 \tabularnewline
16 & -0.080766 & -0.8661 & 0.194114 \tabularnewline
17 & 0.054396 & 0.5833 & 0.280406 \tabularnewline
18 & -0.095427 & -1.0233 & 0.154148 \tabularnewline
19 & -0.028015 & -0.3004 & 0.382195 \tabularnewline
20 & -0.020195 & -0.2166 & 0.414464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298253&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]0.067637[/C][C]0.7253[/C][C]0.234863[/C][/ROW]
[ROW][C]2[/C][C]0.132408[/C][C]1.4199[/C][C]0.079168[/C][/ROW]
[ROW][C]3[/C][C]0.083374[/C][C]0.8941[/C][C]0.186572[/C][/ROW]
[ROW][C]4[/C][C]-0.358831[/C][C]-3.848[/C][C]9.8e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.258286[/C][C]-2.7698[/C][C]0.003271[/C][/ROW]
[ROW][C]6[/C][C]-0.380733[/C][C]-4.0829[/C][C]4.1e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.280754[/C][C]-3.0107[/C][C]0.001602[/C][/ROW]
[ROW][C]8[/C][C]-0.26996[/C][C]-2.895[/C][C]0.002269[/C][/ROW]
[ROW][C]9[/C][C]-0.085161[/C][C]-0.9132[/C][C]0.181512[/C][/ROW]
[ROW][C]10[/C][C]-0.198694[/C][C]-2.1308[/C][C]0.01762[/C][/ROW]
[ROW][C]11[/C][C]-0.046681[/C][C]-0.5006[/C][C]0.308806[/C][/ROW]
[ROW][C]12[/C][C]0.237617[/C][C]2.5482[/C][C]0.006074[/C][/ROW]
[ROW][C]13[/C][C]-0.026144[/C][C]-0.2804[/C][C]0.389851[/C][/ROW]
[ROW][C]14[/C][C]-0.044141[/C][C]-0.4734[/C][C]0.318427[/C][/ROW]
[ROW][C]15[/C][C]-0.065699[/C][C]-0.7045[/C][C]0.241261[/C][/ROW]
[ROW][C]16[/C][C]-0.080766[/C][C]-0.8661[/C][C]0.194114[/C][/ROW]
[ROW][C]17[/C][C]0.054396[/C][C]0.5833[/C][C]0.280406[/C][/ROW]
[ROW][C]18[/C][C]-0.095427[/C][C]-1.0233[/C][C]0.154148[/C][/ROW]
[ROW][C]19[/C][C]-0.028015[/C][C]-0.3004[/C][C]0.382195[/C][/ROW]
[ROW][C]20[/C][C]-0.020195[/C][C]-0.2166[/C][C]0.414464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298253&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298253&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	0.067637	0.7253	0.234863
2	0.132408	1.4199	0.079168
3	0.083374	0.8941	0.186572
4	-0.358831	-3.848	9.8e-05
5	-0.258286	-2.7698	0.003271
6	-0.380733	-4.0829	4.1e-05
7	-0.280754	-3.0107	0.001602
8	-0.26996	-2.895	0.002269
9	-0.085161	-0.9132	0.181512
10	-0.198694	-2.1308	0.01762
11	-0.046681	-0.5006	0.308806
12	0.237617	2.5482	0.006074
13	-0.026144	-0.2804	0.389851
14	-0.044141	-0.4734	0.318427
15	-0.065699	-0.7045	0.241261
16	-0.080766	-0.8661	0.194114
17	0.054396	0.5833	0.280406
18	-0.095427	-1.0233	0.154148
19	-0.028015	-0.3004	0.382195
20	-0.020195	-0.2166	0.414464

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

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Parameters (Session):

par4 = No season ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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 <- '0'
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