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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2016 13:17:38 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/07/t1481113232o27g64sf6gzvmo6.htm/, Retrieved Wed, 08 May 2024 02:56:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298036, Retrieved Wed, 08 May 2024 02:56:27 +0000

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-       [(Partial) Autocorrelation Function] [autocorrelation N...] [2016-12-07 12:17:38] [9412b5b3b31fe4708efb1e5c8c74b28f] [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=298036&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=298036&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298036&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	-0.032549	-0.2563	0.399289
2	0.009851	0.0776	0.469212
3	-0.084962	-0.669	0.252991
4	-0.061193	-0.4818	0.31581
5	-0.101158	-0.7965	0.214386
6	-0.078111	-0.615	0.270388
7	0.111024	0.8742	0.19269
8	-0.17343	-1.3656	0.088501
9	0.108378	0.8534	0.198371
10	0.071563	0.5635	0.287569
11	-0.174435	-1.3735	0.087271
12	-0.080385	-0.633	0.264546
13	-0.026688	-0.2101	0.417124
14	0.08712	0.686	0.24764
15	0.114349	0.9004	0.185699
16	-0.01481	-0.1166	0.453771
17	-0.00614	-0.0483	0.480799

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.032549 & -0.2563 & 0.399289 \tabularnewline
2 & 0.009851 & 0.0776 & 0.469212 \tabularnewline
3 & -0.084962 & -0.669 & 0.252991 \tabularnewline
4 & -0.061193 & -0.4818 & 0.31581 \tabularnewline
5 & -0.101158 & -0.7965 & 0.214386 \tabularnewline
6 & -0.078111 & -0.615 & 0.270388 \tabularnewline
7 & 0.111024 & 0.8742 & 0.19269 \tabularnewline
8 & -0.17343 & -1.3656 & 0.088501 \tabularnewline
9 & 0.108378 & 0.8534 & 0.198371 \tabularnewline
10 & 0.071563 & 0.5635 & 0.287569 \tabularnewline
11 & -0.174435 & -1.3735 & 0.087271 \tabularnewline
12 & -0.080385 & -0.633 & 0.264546 \tabularnewline
13 & -0.026688 & -0.2101 & 0.417124 \tabularnewline
14 & 0.08712 & 0.686 & 0.24764 \tabularnewline
15 & 0.114349 & 0.9004 & 0.185699 \tabularnewline
16 & -0.01481 & -0.1166 & 0.453771 \tabularnewline
17 & -0.00614 & -0.0483 & 0.480799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298036&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]-0.032549[/C][C]-0.2563[/C][C]0.399289[/C][/ROW]
[ROW][C]2[/C][C]0.009851[/C][C]0.0776[/C][C]0.469212[/C][/ROW]
[ROW][C]3[/C][C]-0.084962[/C][C]-0.669[/C][C]0.252991[/C][/ROW]
[ROW][C]4[/C][C]-0.061193[/C][C]-0.4818[/C][C]0.31581[/C][/ROW]
[ROW][C]5[/C][C]-0.101158[/C][C]-0.7965[/C][C]0.214386[/C][/ROW]
[ROW][C]6[/C][C]-0.078111[/C][C]-0.615[/C][C]0.270388[/C][/ROW]
[ROW][C]7[/C][C]0.111024[/C][C]0.8742[/C][C]0.19269[/C][/ROW]
[ROW][C]8[/C][C]-0.17343[/C][C]-1.3656[/C][C]0.088501[/C][/ROW]
[ROW][C]9[/C][C]0.108378[/C][C]0.8534[/C][C]0.198371[/C][/ROW]
[ROW][C]10[/C][C]0.071563[/C][C]0.5635[/C][C]0.287569[/C][/ROW]
[ROW][C]11[/C][C]-0.174435[/C][C]-1.3735[/C][C]0.087271[/C][/ROW]
[ROW][C]12[/C][C]-0.080385[/C][C]-0.633[/C][C]0.264546[/C][/ROW]
[ROW][C]13[/C][C]-0.026688[/C][C]-0.2101[/C][C]0.417124[/C][/ROW]
[ROW][C]14[/C][C]0.08712[/C][C]0.686[/C][C]0.24764[/C][/ROW]
[ROW][C]15[/C][C]0.114349[/C][C]0.9004[/C][C]0.185699[/C][/ROW]
[ROW][C]16[/C][C]-0.01481[/C][C]-0.1166[/C][C]0.453771[/C][/ROW]
[ROW][C]17[/C][C]-0.00614[/C][C]-0.0483[/C][C]0.480799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298036&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298036&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	-0.032549	-0.2563	0.399289
2	0.009851	0.0776	0.469212
3	-0.084962	-0.669	0.252991
4	-0.061193	-0.4818	0.31581
5	-0.101158	-0.7965	0.214386
6	-0.078111	-0.615	0.270388
7	0.111024	0.8742	0.19269
8	-0.17343	-1.3656	0.088501
9	0.108378	0.8534	0.198371
10	0.071563	0.5635	0.287569
11	-0.174435	-1.3735	0.087271
12	-0.080385	-0.633	0.264546
13	-0.026688	-0.2101	0.417124
14	0.08712	0.686	0.24764
15	0.114349	0.9004	0.185699
16	-0.01481	-0.1166	0.453771
17	-0.00614	-0.0483	0.480799

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.032549	-0.2563	0.399289
2	0.008801	0.0693	0.472489
3	-0.084454	-0.665	0.254261
4	-0.067235	-0.5294	0.299206
5	-0.105564	-0.8312	0.204522
6	-0.095043	-0.7484	0.228533
7	0.095089	0.7487	0.228424
8	-0.194268	-1.5297	0.065593
9	0.072676	0.5723	0.28461
10	0.075964	0.5981	0.275964
11	-0.229718	-1.8088	0.037665
12	-0.083114	-0.6544	0.257624
13	-0.029538	-0.2326	0.408425
14	0.030795	0.2425	0.404604
15	0.168175	1.3242	0.095147
16	-0.132266	-1.0415	0.150852
17	-0.039261	-0.3091	0.379126

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.032549 & -0.2563 & 0.399289 \tabularnewline
2 & 0.008801 & 0.0693 & 0.472489 \tabularnewline
3 & -0.084454 & -0.665 & 0.254261 \tabularnewline
4 & -0.067235 & -0.5294 & 0.299206 \tabularnewline
5 & -0.105564 & -0.8312 & 0.204522 \tabularnewline
6 & -0.095043 & -0.7484 & 0.228533 \tabularnewline
7 & 0.095089 & 0.7487 & 0.228424 \tabularnewline
8 & -0.194268 & -1.5297 & 0.065593 \tabularnewline
9 & 0.072676 & 0.5723 & 0.28461 \tabularnewline
10 & 0.075964 & 0.5981 & 0.275964 \tabularnewline
11 & -0.229718 & -1.8088 & 0.037665 \tabularnewline
12 & -0.083114 & -0.6544 & 0.257624 \tabularnewline
13 & -0.029538 & -0.2326 & 0.408425 \tabularnewline
14 & 0.030795 & 0.2425 & 0.404604 \tabularnewline
15 & 0.168175 & 1.3242 & 0.095147 \tabularnewline
16 & -0.132266 & -1.0415 & 0.150852 \tabularnewline
17 & -0.039261 & -0.3091 & 0.379126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298036&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]-0.032549[/C][C]-0.2563[/C][C]0.399289[/C][/ROW]
[ROW][C]2[/C][C]0.008801[/C][C]0.0693[/C][C]0.472489[/C][/ROW]
[ROW][C]3[/C][C]-0.084454[/C][C]-0.665[/C][C]0.254261[/C][/ROW]
[ROW][C]4[/C][C]-0.067235[/C][C]-0.5294[/C][C]0.299206[/C][/ROW]
[ROW][C]5[/C][C]-0.105564[/C][C]-0.8312[/C][C]0.204522[/C][/ROW]
[ROW][C]6[/C][C]-0.095043[/C][C]-0.7484[/C][C]0.228533[/C][/ROW]
[ROW][C]7[/C][C]0.095089[/C][C]0.7487[/C][C]0.228424[/C][/ROW]
[ROW][C]8[/C][C]-0.194268[/C][C]-1.5297[/C][C]0.065593[/C][/ROW]
[ROW][C]9[/C][C]0.072676[/C][C]0.5723[/C][C]0.28461[/C][/ROW]
[ROW][C]10[/C][C]0.075964[/C][C]0.5981[/C][C]0.275964[/C][/ROW]
[ROW][C]11[/C][C]-0.229718[/C][C]-1.8088[/C][C]0.037665[/C][/ROW]
[ROW][C]12[/C][C]-0.083114[/C][C]-0.6544[/C][C]0.257624[/C][/ROW]
[ROW][C]13[/C][C]-0.029538[/C][C]-0.2326[/C][C]0.408425[/C][/ROW]
[ROW][C]14[/C][C]0.030795[/C][C]0.2425[/C][C]0.404604[/C][/ROW]
[ROW][C]15[/C][C]0.168175[/C][C]1.3242[/C][C]0.095147[/C][/ROW]
[ROW][C]16[/C][C]-0.132266[/C][C]-1.0415[/C][C]0.150852[/C][/ROW]
[ROW][C]17[/C][C]-0.039261[/C][C]-0.3091[/C][C]0.379126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298036&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298036&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	-0.032549	-0.2563	0.399289
2	0.008801	0.0693	0.472489
3	-0.084454	-0.665	0.254261
4	-0.067235	-0.5294	0.299206
5	-0.105564	-0.8312	0.204522
6	-0.095043	-0.7484	0.228533
7	0.095089	0.7487	0.228424
8	-0.194268	-1.5297	0.065593
9	0.072676	0.5723	0.28461
10	0.075964	0.5981	0.275964
11	-0.229718	-1.8088	0.037665
12	-0.083114	-0.6544	0.257624
13	-0.029538	-0.2326	0.408425
14	0.030795	0.2425	0.404604
15	0.168175	1.3242	0.095147
16	-0.132266	-1.0415	0.150852
17	-0.039261	-0.3091	0.379126

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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):

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code