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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 21:19:49 +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/21/t14823516128pjzzms70jocvwf.htm/, Retrieved Mon, 06 May 2024 10:42:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302489, Retrieved Mon, 06 May 2024 10:42:41 +0000

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-       [(Partial) Autocorrelation Function] [Default autocorre...] [2016-12-21 20:19:49] [e7c866b75ad2fc21ab540ba3a0a42299] [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=302489&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=302489&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302489&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	-0.449265	-2.7695	0.004318
2	0.070964	0.4375	0.33213
3	0.069245	0.4269	0.335948
4	-0.151268	-0.9325	0.178489
5	0.078741	0.4854	0.315093
6	-0.084192	-0.519	0.303387
7	0.016803	0.1036	0.459024
8	0.022136	0.1365	0.44609
9	0.072271	0.4455	0.329241
10	-0.141107	-0.8698	0.194924
11	0.155053	0.9558	0.172605
12	-0.282622	-1.7422	0.044782
13	0.185604	1.1441	0.12986
14	-0.12297	-0.758	0.226552
15	0.021219	0.1308	0.44831
16	0.242485	1.4948	0.071616
17	-0.218984	-1.3499	0.092516

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.449265 & -2.7695 & 0.004318 \tabularnewline
2 & 0.070964 & 0.4375 & 0.33213 \tabularnewline
3 & 0.069245 & 0.4269 & 0.335948 \tabularnewline
4 & -0.151268 & -0.9325 & 0.178489 \tabularnewline
5 & 0.078741 & 0.4854 & 0.315093 \tabularnewline
6 & -0.084192 & -0.519 & 0.303387 \tabularnewline
7 & 0.016803 & 0.1036 & 0.459024 \tabularnewline
8 & 0.022136 & 0.1365 & 0.44609 \tabularnewline
9 & 0.072271 & 0.4455 & 0.329241 \tabularnewline
10 & -0.141107 & -0.8698 & 0.194924 \tabularnewline
11 & 0.155053 & 0.9558 & 0.172605 \tabularnewline
12 & -0.282622 & -1.7422 & 0.044782 \tabularnewline
13 & 0.185604 & 1.1441 & 0.12986 \tabularnewline
14 & -0.12297 & -0.758 & 0.226552 \tabularnewline
15 & 0.021219 & 0.1308 & 0.44831 \tabularnewline
16 & 0.242485 & 1.4948 & 0.071616 \tabularnewline
17 & -0.218984 & -1.3499 & 0.092516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302489&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]-0.449265[/C][C]-2.7695[/C][C]0.004318[/C][/ROW]
[ROW][C]2[/C][C]0.070964[/C][C]0.4375[/C][C]0.33213[/C][/ROW]
[ROW][C]3[/C][C]0.069245[/C][C]0.4269[/C][C]0.335948[/C][/ROW]
[ROW][C]4[/C][C]-0.151268[/C][C]-0.9325[/C][C]0.178489[/C][/ROW]
[ROW][C]5[/C][C]0.078741[/C][C]0.4854[/C][C]0.315093[/C][/ROW]
[ROW][C]6[/C][C]-0.084192[/C][C]-0.519[/C][C]0.303387[/C][/ROW]
[ROW][C]7[/C][C]0.016803[/C][C]0.1036[/C][C]0.459024[/C][/ROW]
[ROW][C]8[/C][C]0.022136[/C][C]0.1365[/C][C]0.44609[/C][/ROW]
[ROW][C]9[/C][C]0.072271[/C][C]0.4455[/C][C]0.329241[/C][/ROW]
[ROW][C]10[/C][C]-0.141107[/C][C]-0.8698[/C][C]0.194924[/C][/ROW]
[ROW][C]11[/C][C]0.155053[/C][C]0.9558[/C][C]0.172605[/C][/ROW]
[ROW][C]12[/C][C]-0.282622[/C][C]-1.7422[/C][C]0.044782[/C][/ROW]
[ROW][C]13[/C][C]0.185604[/C][C]1.1441[/C][C]0.12986[/C][/ROW]
[ROW][C]14[/C][C]-0.12297[/C][C]-0.758[/C][C]0.226552[/C][/ROW]
[ROW][C]15[/C][C]0.021219[/C][C]0.1308[/C][C]0.44831[/C][/ROW]
[ROW][C]16[/C][C]0.242485[/C][C]1.4948[/C][C]0.071616[/C][/ROW]
[ROW][C]17[/C][C]-0.218984[/C][C]-1.3499[/C][C]0.092516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302489&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302489&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	-0.449265	-2.7695	0.004318
2	0.070964	0.4375	0.33213
3	0.069245	0.4269	0.335948
4	-0.151268	-0.9325	0.178489
5	0.078741	0.4854	0.315093
6	-0.084192	-0.519	0.303387
7	0.016803	0.1036	0.459024
8	0.022136	0.1365	0.44609
9	0.072271	0.4455	0.329241
10	-0.141107	-0.8698	0.194924
11	0.155053	0.9558	0.172605
12	-0.282622	-1.7422	0.044782
13	0.185604	1.1441	0.12986
14	-0.12297	-0.758	0.226552
15	0.021219	0.1308	0.44831
16	0.242485	1.4948	0.071616
17	-0.218984	-1.3499	0.092516

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.449265	-2.7695	0.004318
2	-0.163971	-1.0108	0.159257
3	0.042085	0.2594	0.398352
4	-0.111635	-0.6882	0.247764
5	-0.047974	-0.2957	0.384522
6	-0.101824	-0.6277	0.266983
7	-0.060111	-0.3706	0.356514
8	-0.019173	-0.1182	0.45327
9	0.113175	0.6977	0.244818
10	-0.097173	-0.599	0.276359
11	0.058456	0.3603	0.360292
12	-0.271906	-1.6761	0.050961
13	-0.018916	-0.1166	0.453893
14	-0.143185	-0.8827	0.191487
15	-0.016981	-0.1047	0.45859
16	0.20687	1.2752	0.104984
17	0.018136	0.1118	0.455785

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.449265 & -2.7695 & 0.004318 \tabularnewline
2 & -0.163971 & -1.0108 & 0.159257 \tabularnewline
3 & 0.042085 & 0.2594 & 0.398352 \tabularnewline
4 & -0.111635 & -0.6882 & 0.247764 \tabularnewline
5 & -0.047974 & -0.2957 & 0.384522 \tabularnewline
6 & -0.101824 & -0.6277 & 0.266983 \tabularnewline
7 & -0.060111 & -0.3706 & 0.356514 \tabularnewline
8 & -0.019173 & -0.1182 & 0.45327 \tabularnewline
9 & 0.113175 & 0.6977 & 0.244818 \tabularnewline
10 & -0.097173 & -0.599 & 0.276359 \tabularnewline
11 & 0.058456 & 0.3603 & 0.360292 \tabularnewline
12 & -0.271906 & -1.6761 & 0.050961 \tabularnewline
13 & -0.018916 & -0.1166 & 0.453893 \tabularnewline
14 & -0.143185 & -0.8827 & 0.191487 \tabularnewline
15 & -0.016981 & -0.1047 & 0.45859 \tabularnewline
16 & 0.20687 & 1.2752 & 0.104984 \tabularnewline
17 & 0.018136 & 0.1118 & 0.455785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302489&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]-0.449265[/C][C]-2.7695[/C][C]0.004318[/C][/ROW]
[ROW][C]2[/C][C]-0.163971[/C][C]-1.0108[/C][C]0.159257[/C][/ROW]
[ROW][C]3[/C][C]0.042085[/C][C]0.2594[/C][C]0.398352[/C][/ROW]
[ROW][C]4[/C][C]-0.111635[/C][C]-0.6882[/C][C]0.247764[/C][/ROW]
[ROW][C]5[/C][C]-0.047974[/C][C]-0.2957[/C][C]0.384522[/C][/ROW]
[ROW][C]6[/C][C]-0.101824[/C][C]-0.6277[/C][C]0.266983[/C][/ROW]
[ROW][C]7[/C][C]-0.060111[/C][C]-0.3706[/C][C]0.356514[/C][/ROW]
[ROW][C]8[/C][C]-0.019173[/C][C]-0.1182[/C][C]0.45327[/C][/ROW]
[ROW][C]9[/C][C]0.113175[/C][C]0.6977[/C][C]0.244818[/C][/ROW]
[ROW][C]10[/C][C]-0.097173[/C][C]-0.599[/C][C]0.276359[/C][/ROW]
[ROW][C]11[/C][C]0.058456[/C][C]0.3603[/C][C]0.360292[/C][/ROW]
[ROW][C]12[/C][C]-0.271906[/C][C]-1.6761[/C][C]0.050961[/C][/ROW]
[ROW][C]13[/C][C]-0.018916[/C][C]-0.1166[/C][C]0.453893[/C][/ROW]
[ROW][C]14[/C][C]-0.143185[/C][C]-0.8827[/C][C]0.191487[/C][/ROW]
[ROW][C]15[/C][C]-0.016981[/C][C]-0.1047[/C][C]0.45859[/C][/ROW]
[ROW][C]16[/C][C]0.20687[/C][C]1.2752[/C][C]0.104984[/C][/ROW]
[ROW][C]17[/C][C]0.018136[/C][C]0.1118[/C][C]0.455785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302489&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302489&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	-0.449265	-2.7695	0.004318
2	-0.163971	-1.0108	0.159257
3	0.042085	0.2594	0.398352
4	-0.111635	-0.6882	0.247764
5	-0.047974	-0.2957	0.384522
6	-0.101824	-0.6277	0.266983
7	-0.060111	-0.3706	0.356514
8	-0.019173	-0.1182	0.45327
9	0.113175	0.6977	0.244818
10	-0.097173	-0.599	0.276359
11	0.058456	0.3603	0.360292
12	-0.271906	-1.6761	0.050961
13	-0.018916	-0.1166	0.453893
14	-0.143185	-0.8827	0.191487
15	-0.016981	-0.1047	0.45859
16	0.20687	1.2752	0.104984
17	0.018136	0.1118	0.455785

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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Parameters (Session):

par1 = TRUE ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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')

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Input Parameters & R Code