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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 11 Dec 2016 16:22:31 +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/11/t1481470559bxsqb9ptvomwk9p.htm/, Retrieved Thu, 02 May 2024 02:21:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298815, Retrieved Thu, 02 May 2024 02:21:42 +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)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMPD    [Standard Deviation-Mean Plot] [F1:N1809] [2016-12-11 14:01:05] [a4c5732063e280fade3b47e7f5057d96]
- RM D        [(Partial) Autocorrelation Function] [F1:N224] [2016-12-11 15:22:31] [8d7b5e4c30a3b8052caee801f90adcea] [Current]
- RMP           [ARIMA Forecasting] [F1:N224] [2016-12-17 13:58:05] [a4c5732063e280fade3b47e7f5057d96] 

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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=298815&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=298815&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298815&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	0.273209	1.7279	0.045858
2	-0.093339	-0.5903	0.279145
3	-0.173503	-1.0973	0.139529
4	-0.229916	-1.4541	0.076858
5	-0.322226	-2.0379	0.024103
6	0.107025	0.6769	0.251187
7	0.092586	0.5856	0.280729
8	0.151692	0.9594	0.171564
9	0.011702	0.074	0.470686
10	0.066527	0.4208	0.338093
11	0.093559	0.5917	0.278684
12	0.056659	0.3583	0.360986
13	-0.139396	-0.8816	0.191625
14	-0.057757	-0.3653	0.35841
15	-0.081591	-0.516	0.304338
16	-0.113438	-0.7174	0.238635

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.273209 & 1.7279 & 0.045858 \tabularnewline
2 & -0.093339 & -0.5903 & 0.279145 \tabularnewline
3 & -0.173503 & -1.0973 & 0.139529 \tabularnewline
4 & -0.229916 & -1.4541 & 0.076858 \tabularnewline
5 & -0.322226 & -2.0379 & 0.024103 \tabularnewline
6 & 0.107025 & 0.6769 & 0.251187 \tabularnewline
7 & 0.092586 & 0.5856 & 0.280729 \tabularnewline
8 & 0.151692 & 0.9594 & 0.171564 \tabularnewline
9 & 0.011702 & 0.074 & 0.470686 \tabularnewline
10 & 0.066527 & 0.4208 & 0.338093 \tabularnewline
11 & 0.093559 & 0.5917 & 0.278684 \tabularnewline
12 & 0.056659 & 0.3583 & 0.360986 \tabularnewline
13 & -0.139396 & -0.8816 & 0.191625 \tabularnewline
14 & -0.057757 & -0.3653 & 0.35841 \tabularnewline
15 & -0.081591 & -0.516 & 0.304338 \tabularnewline
16 & -0.113438 & -0.7174 & 0.238635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298815&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]0.273209[/C][C]1.7279[/C][C]0.045858[/C][/ROW]
[ROW][C]2[/C][C]-0.093339[/C][C]-0.5903[/C][C]0.279145[/C][/ROW]
[ROW][C]3[/C][C]-0.173503[/C][C]-1.0973[/C][C]0.139529[/C][/ROW]
[ROW][C]4[/C][C]-0.229916[/C][C]-1.4541[/C][C]0.076858[/C][/ROW]
[ROW][C]5[/C][C]-0.322226[/C][C]-2.0379[/C][C]0.024103[/C][/ROW]
[ROW][C]6[/C][C]0.107025[/C][C]0.6769[/C][C]0.251187[/C][/ROW]
[ROW][C]7[/C][C]0.092586[/C][C]0.5856[/C][C]0.280729[/C][/ROW]
[ROW][C]8[/C][C]0.151692[/C][C]0.9594[/C][C]0.171564[/C][/ROW]
[ROW][C]9[/C][C]0.011702[/C][C]0.074[/C][C]0.470686[/C][/ROW]
[ROW][C]10[/C][C]0.066527[/C][C]0.4208[/C][C]0.338093[/C][/ROW]
[ROW][C]11[/C][C]0.093559[/C][C]0.5917[/C][C]0.278684[/C][/ROW]
[ROW][C]12[/C][C]0.056659[/C][C]0.3583[/C][C]0.360986[/C][/ROW]
[ROW][C]13[/C][C]-0.139396[/C][C]-0.8816[/C][C]0.191625[/C][/ROW]
[ROW][C]14[/C][C]-0.057757[/C][C]-0.3653[/C][C]0.35841[/C][/ROW]
[ROW][C]15[/C][C]-0.081591[/C][C]-0.516[/C][C]0.304338[/C][/ROW]
[ROW][C]16[/C][C]-0.113438[/C][C]-0.7174[/C][C]0.238635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298815&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298815&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	0.273209	1.7279	0.045858
2	-0.093339	-0.5903	0.279145
3	-0.173503	-1.0973	0.139529
4	-0.229916	-1.4541	0.076858
5	-0.322226	-2.0379	0.024103
6	0.107025	0.6769	0.251187
7	0.092586	0.5856	0.280729
8	0.151692	0.9594	0.171564
9	0.011702	0.074	0.470686
10	0.066527	0.4208	0.338093
11	0.093559	0.5917	0.278684
12	0.056659	0.3583	0.360986
13	-0.139396	-0.8816	0.191625
14	-0.057757	-0.3653	0.35841
15	-0.081591	-0.516	0.304338
16	-0.113438	-0.7174	0.238635

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.273209	1.7279	0.045858
2	-0.181532	-1.1481	0.128871
3	-0.104795	-0.6628	0.255637
4	-0.183456	-1.1603	0.126407
5	-0.282478	-1.7865	0.040796
6	0.240299	1.5198	0.068216
7	-0.157571	-0.9966	0.162482
8	0.148369	0.9384	0.176844
9	-0.170127	-1.076	0.144192
10	0.138889	0.8784	0.192483
11	0.211063	1.3349	0.094733
12	-0.073836	-0.467	0.321523
13	-0.001223	-0.0077	0.496933
14	-0.07768	-0.4913	0.312954
15	0.060755	0.3842	0.351415
16	-0.104296	-0.6596	0.256637

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.273209 & 1.7279 & 0.045858 \tabularnewline
2 & -0.181532 & -1.1481 & 0.128871 \tabularnewline
3 & -0.104795 & -0.6628 & 0.255637 \tabularnewline
4 & -0.183456 & -1.1603 & 0.126407 \tabularnewline
5 & -0.282478 & -1.7865 & 0.040796 \tabularnewline
6 & 0.240299 & 1.5198 & 0.068216 \tabularnewline
7 & -0.157571 & -0.9966 & 0.162482 \tabularnewline
8 & 0.148369 & 0.9384 & 0.176844 \tabularnewline
9 & -0.170127 & -1.076 & 0.144192 \tabularnewline
10 & 0.138889 & 0.8784 & 0.192483 \tabularnewline
11 & 0.211063 & 1.3349 & 0.094733 \tabularnewline
12 & -0.073836 & -0.467 & 0.321523 \tabularnewline
13 & -0.001223 & -0.0077 & 0.496933 \tabularnewline
14 & -0.07768 & -0.4913 & 0.312954 \tabularnewline
15 & 0.060755 & 0.3842 & 0.351415 \tabularnewline
16 & -0.104296 & -0.6596 & 0.256637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298815&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]0.273209[/C][C]1.7279[/C][C]0.045858[/C][/ROW]
[ROW][C]2[/C][C]-0.181532[/C][C]-1.1481[/C][C]0.128871[/C][/ROW]
[ROW][C]3[/C][C]-0.104795[/C][C]-0.6628[/C][C]0.255637[/C][/ROW]
[ROW][C]4[/C][C]-0.183456[/C][C]-1.1603[/C][C]0.126407[/C][/ROW]
[ROW][C]5[/C][C]-0.282478[/C][C]-1.7865[/C][C]0.040796[/C][/ROW]
[ROW][C]6[/C][C]0.240299[/C][C]1.5198[/C][C]0.068216[/C][/ROW]
[ROW][C]7[/C][C]-0.157571[/C][C]-0.9966[/C][C]0.162482[/C][/ROW]
[ROW][C]8[/C][C]0.148369[/C][C]0.9384[/C][C]0.176844[/C][/ROW]
[ROW][C]9[/C][C]-0.170127[/C][C]-1.076[/C][C]0.144192[/C][/ROW]
[ROW][C]10[/C][C]0.138889[/C][C]0.8784[/C][C]0.192483[/C][/ROW]
[ROW][C]11[/C][C]0.211063[/C][C]1.3349[/C][C]0.094733[/C][/ROW]
[ROW][C]12[/C][C]-0.073836[/C][C]-0.467[/C][C]0.321523[/C][/ROW]
[ROW][C]13[/C][C]-0.001223[/C][C]-0.0077[/C][C]0.496933[/C][/ROW]
[ROW][C]14[/C][C]-0.07768[/C][C]-0.4913[/C][C]0.312954[/C][/ROW]
[ROW][C]15[/C][C]0.060755[/C][C]0.3842[/C][C]0.351415[/C][/ROW]
[ROW][C]16[/C][C]-0.104296[/C][C]-0.6596[/C][C]0.256637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298815&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298815&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	0.273209	1.7279	0.045858
2	-0.181532	-1.1481	0.128871
3	-0.104795	-0.6628	0.255637
4	-0.183456	-1.1603	0.126407
5	-0.282478	-1.7865	0.040796
6	0.240299	1.5198	0.068216
7	-0.157571	-0.9966	0.162482
8	0.148369	0.9384	0.176844
9	-0.170127	-1.076	0.144192
10	0.138889	0.8784	0.192483
11	0.211063	1.3349	0.094733
12	-0.073836	-0.467	0.321523
13	-0.001223	-0.0077	0.496933
14	-0.07768	-0.4913	0.312954
15	0.060755	0.3842	0.351415
16	-0.104296	-0.6596	0.256637

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 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code