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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 15:26:32 +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/16/t14818984305e539eghyvdf33p.htm/, Retrieved Thu, 02 May 2024 15:38:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300306, Retrieved Thu, 02 May 2024 15:38:00 +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)

-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- RM D      [(Partial) Autocorrelation Function] [] [2016-12-16 14:26:32] [404ac5ee4f7301873f6a96ef36861981] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300306&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300306&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300306&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.072223	-0.7745	0.220111
2	0.064251	0.689	0.246101
3	0.113179	1.2137	0.113672
4	0.023896	0.2563	0.399107
5	0.067823	0.7273	0.234253
6	-0.042511	-0.4559	0.324669
7	-0.030168	-0.3235	0.373446
8	0.039005	0.4183	0.338262
9	0.055669	0.597	0.275847
10	-0.082411	-0.8838	0.189334
11	-0.011212	-0.1202	0.452255
12	-0.045635	-0.4894	0.312752
13	0.074857	0.8028	0.211886
14	-0.120231	-1.2893	0.099934
15	-0.045916	-0.4924	0.31169
16	-0.070701	-0.7582	0.224947
17	-0.072106	-0.7732	0.220481
18	0.025625	0.2748	0.391982
19	-0.111061	-1.191	0.118054
20	0.090704	0.9727	0.166373

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.072223 & -0.7745 & 0.220111 \tabularnewline
2 & 0.064251 & 0.689 & 0.246101 \tabularnewline
3 & 0.113179 & 1.2137 & 0.113672 \tabularnewline
4 & 0.023896 & 0.2563 & 0.399107 \tabularnewline
5 & 0.067823 & 0.7273 & 0.234253 \tabularnewline
6 & -0.042511 & -0.4559 & 0.324669 \tabularnewline
7 & -0.030168 & -0.3235 & 0.373446 \tabularnewline
8 & 0.039005 & 0.4183 & 0.338262 \tabularnewline
9 & 0.055669 & 0.597 & 0.275847 \tabularnewline
10 & -0.082411 & -0.8838 & 0.189334 \tabularnewline
11 & -0.011212 & -0.1202 & 0.452255 \tabularnewline
12 & -0.045635 & -0.4894 & 0.312752 \tabularnewline
13 & 0.074857 & 0.8028 & 0.211886 \tabularnewline
14 & -0.120231 & -1.2893 & 0.099934 \tabularnewline
15 & -0.045916 & -0.4924 & 0.31169 \tabularnewline
16 & -0.070701 & -0.7582 & 0.224947 \tabularnewline
17 & -0.072106 & -0.7732 & 0.220481 \tabularnewline
18 & 0.025625 & 0.2748 & 0.391982 \tabularnewline
19 & -0.111061 & -1.191 & 0.118054 \tabularnewline
20 & 0.090704 & 0.9727 & 0.166373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300306&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]-0.072223[/C][C]-0.7745[/C][C]0.220111[/C][/ROW]
[ROW][C]2[/C][C]0.064251[/C][C]0.689[/C][C]0.246101[/C][/ROW]
[ROW][C]3[/C][C]0.113179[/C][C]1.2137[/C][C]0.113672[/C][/ROW]
[ROW][C]4[/C][C]0.023896[/C][C]0.2563[/C][C]0.399107[/C][/ROW]
[ROW][C]5[/C][C]0.067823[/C][C]0.7273[/C][C]0.234253[/C][/ROW]
[ROW][C]6[/C][C]-0.042511[/C][C]-0.4559[/C][C]0.324669[/C][/ROW]
[ROW][C]7[/C][C]-0.030168[/C][C]-0.3235[/C][C]0.373446[/C][/ROW]
[ROW][C]8[/C][C]0.039005[/C][C]0.4183[/C][C]0.338262[/C][/ROW]
[ROW][C]9[/C][C]0.055669[/C][C]0.597[/C][C]0.275847[/C][/ROW]
[ROW][C]10[/C][C]-0.082411[/C][C]-0.8838[/C][C]0.189334[/C][/ROW]
[ROW][C]11[/C][C]-0.011212[/C][C]-0.1202[/C][C]0.452255[/C][/ROW]
[ROW][C]12[/C][C]-0.045635[/C][C]-0.4894[/C][C]0.312752[/C][/ROW]
[ROW][C]13[/C][C]0.074857[/C][C]0.8028[/C][C]0.211886[/C][/ROW]
[ROW][C]14[/C][C]-0.120231[/C][C]-1.2893[/C][C]0.099934[/C][/ROW]
[ROW][C]15[/C][C]-0.045916[/C][C]-0.4924[/C][C]0.31169[/C][/ROW]
[ROW][C]16[/C][C]-0.070701[/C][C]-0.7582[/C][C]0.224947[/C][/ROW]
[ROW][C]17[/C][C]-0.072106[/C][C]-0.7732[/C][C]0.220481[/C][/ROW]
[ROW][C]18[/C][C]0.025625[/C][C]0.2748[/C][C]0.391982[/C][/ROW]
[ROW][C]19[/C][C]-0.111061[/C][C]-1.191[/C][C]0.118054[/C][/ROW]
[ROW][C]20[/C][C]0.090704[/C][C]0.9727[/C][C]0.166373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300306&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300306&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	-0.072223	-0.7745	0.220111
2	0.064251	0.689	0.246101
3	0.113179	1.2137	0.113672
4	0.023896	0.2563	0.399107
5	0.067823	0.7273	0.234253
6	-0.042511	-0.4559	0.324669
7	-0.030168	-0.3235	0.373446
8	0.039005	0.4183	0.338262
9	0.055669	0.597	0.275847
10	-0.082411	-0.8838	0.189334
11	-0.011212	-0.1202	0.452255
12	-0.045635	-0.4894	0.312752
13	0.074857	0.8028	0.211886
14	-0.120231	-1.2893	0.099934
15	-0.045916	-0.4924	0.31169
16	-0.070701	-0.7582	0.224947
17	-0.072106	-0.7732	0.220481
18	0.025625	0.2748	0.391982
19	-0.111061	-1.191	0.118054
20	0.090704	0.9727	0.166373

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.072223	-0.7745	0.220111
2	0.059344	0.6364	0.262891
3	0.122902	1.318	0.095065
4	0.037833	0.4057	0.342852
5	0.058481	0.6271	0.265907
6	-0.052113	-0.5589	0.288674
7	-0.054762	-0.5873	0.279092
8	0.023032	0.247	0.402678
9	0.075696	0.8117	0.209306
10	-0.068883	-0.7387	0.230801
11	-0.032174	-0.345	0.365353
12	-0.056749	-0.6086	0.272008
13	0.079963	0.8575	0.196474
14	-0.101458	-1.088	0.139431
15	-0.043006	-0.4612	0.322768
16	-0.085864	-0.9208	0.179545
17	-0.065271	-0.6999	0.242686
18	0.031149	0.334	0.369482
19	-0.050562	-0.5422	0.294358
20	0.102316	1.0972	0.137419

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.072223 & -0.7745 & 0.220111 \tabularnewline
2 & 0.059344 & 0.6364 & 0.262891 \tabularnewline
3 & 0.122902 & 1.318 & 0.095065 \tabularnewline
4 & 0.037833 & 0.4057 & 0.342852 \tabularnewline
5 & 0.058481 & 0.6271 & 0.265907 \tabularnewline
6 & -0.052113 & -0.5589 & 0.288674 \tabularnewline
7 & -0.054762 & -0.5873 & 0.279092 \tabularnewline
8 & 0.023032 & 0.247 & 0.402678 \tabularnewline
9 & 0.075696 & 0.8117 & 0.209306 \tabularnewline
10 & -0.068883 & -0.7387 & 0.230801 \tabularnewline
11 & -0.032174 & -0.345 & 0.365353 \tabularnewline
12 & -0.056749 & -0.6086 & 0.272008 \tabularnewline
13 & 0.079963 & 0.8575 & 0.196474 \tabularnewline
14 & -0.101458 & -1.088 & 0.139431 \tabularnewline
15 & -0.043006 & -0.4612 & 0.322768 \tabularnewline
16 & -0.085864 & -0.9208 & 0.179545 \tabularnewline
17 & -0.065271 & -0.6999 & 0.242686 \tabularnewline
18 & 0.031149 & 0.334 & 0.369482 \tabularnewline
19 & -0.050562 & -0.5422 & 0.294358 \tabularnewline
20 & 0.102316 & 1.0972 & 0.137419 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300306&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]-0.072223[/C][C]-0.7745[/C][C]0.220111[/C][/ROW]
[ROW][C]2[/C][C]0.059344[/C][C]0.6364[/C][C]0.262891[/C][/ROW]
[ROW][C]3[/C][C]0.122902[/C][C]1.318[/C][C]0.095065[/C][/ROW]
[ROW][C]4[/C][C]0.037833[/C][C]0.4057[/C][C]0.342852[/C][/ROW]
[ROW][C]5[/C][C]0.058481[/C][C]0.6271[/C][C]0.265907[/C][/ROW]
[ROW][C]6[/C][C]-0.052113[/C][C]-0.5589[/C][C]0.288674[/C][/ROW]
[ROW][C]7[/C][C]-0.054762[/C][C]-0.5873[/C][C]0.279092[/C][/ROW]
[ROW][C]8[/C][C]0.023032[/C][C]0.247[/C][C]0.402678[/C][/ROW]
[ROW][C]9[/C][C]0.075696[/C][C]0.8117[/C][C]0.209306[/C][/ROW]
[ROW][C]10[/C][C]-0.068883[/C][C]-0.7387[/C][C]0.230801[/C][/ROW]
[ROW][C]11[/C][C]-0.032174[/C][C]-0.345[/C][C]0.365353[/C][/ROW]
[ROW][C]12[/C][C]-0.056749[/C][C]-0.6086[/C][C]0.272008[/C][/ROW]
[ROW][C]13[/C][C]0.079963[/C][C]0.8575[/C][C]0.196474[/C][/ROW]
[ROW][C]14[/C][C]-0.101458[/C][C]-1.088[/C][C]0.139431[/C][/ROW]
[ROW][C]15[/C][C]-0.043006[/C][C]-0.4612[/C][C]0.322768[/C][/ROW]
[ROW][C]16[/C][C]-0.085864[/C][C]-0.9208[/C][C]0.179545[/C][/ROW]
[ROW][C]17[/C][C]-0.065271[/C][C]-0.6999[/C][C]0.242686[/C][/ROW]
[ROW][C]18[/C][C]0.031149[/C][C]0.334[/C][C]0.369482[/C][/ROW]
[ROW][C]19[/C][C]-0.050562[/C][C]-0.5422[/C][C]0.294358[/C][/ROW]
[ROW][C]20[/C][C]0.102316[/C][C]1.0972[/C][C]0.137419[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300306&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300306&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	-0.072223	-0.7745	0.220111
2	0.059344	0.6364	0.262891
3	0.122902	1.318	0.095065
4	0.037833	0.4057	0.342852
5	0.058481	0.6271	0.265907
6	-0.052113	-0.5589	0.288674
7	-0.054762	-0.5873	0.279092
8	0.023032	0.247	0.402678
9	0.075696	0.8117	0.209306
10	-0.068883	-0.7387	0.230801
11	-0.032174	-0.345	0.365353
12	-0.056749	-0.6086	0.272008
13	0.079963	0.8575	0.196474
14	-0.101458	-1.088	0.139431
15	-0.043006	-0.4612	0.322768
16	-0.085864	-0.9208	0.179545
17	-0.065271	-0.6999	0.242686
18	0.031149	0.334	0.369482
19	-0.050562	-0.5422	0.294358
20	0.102316	1.0972	0.137419

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 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;

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