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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 21:59:54 +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/18/t1482094805j0litjve45u54da.htm/, Retrieved Fri, 01 Nov 2024 03:44:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301238, Retrieved Fri, 01 Nov 2024 03:44:12 +0000

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User-defined keywords

Estimated Impact

102

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Spectral Analysis] [] [2016-12-16 13:29:44] [683f400e1b95307fc738e729f07c4fce]
- R P   [Spectral Analysis] [] [2016-12-18 18:43:40] [683f400e1b95307fc738e729f07c4fce]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-18 20:59:54] [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	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=301238&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=301238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301238&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	0.955299	10.3331	0
2	0.902648	9.7636	0
3	0.844238	9.1318	0
4	0.779934	8.4363	0
5	0.712595	7.7079	0
6	0.642014	6.9444	0
7	0.569749	6.1628	0
8	0.494061	5.3441	0
9	0.42095	4.5533	7e-06
10	0.35394	3.8284	0.000104
11	0.289617	3.1327	0.001095
12	0.227148	2.457	0.007739
13	0.168247	1.8199	0.035668
14	0.113763	1.2305	0.110482
15	0.060345	0.6527	0.257606
16	0.009299	0.1006	0.460027
17	-0.039447	-0.4267	0.335196
18	-0.085677	-0.9267	0.177985
19	-0.127167	-1.3755	0.085799
20	-0.164064	-1.7746	0.03928

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.955299 & 10.3331 & 0 \tabularnewline
2 & 0.902648 & 9.7636 & 0 \tabularnewline
3 & 0.844238 & 9.1318 & 0 \tabularnewline
4 & 0.779934 & 8.4363 & 0 \tabularnewline
5 & 0.712595 & 7.7079 & 0 \tabularnewline
6 & 0.642014 & 6.9444 & 0 \tabularnewline
7 & 0.569749 & 6.1628 & 0 \tabularnewline
8 & 0.494061 & 5.3441 & 0 \tabularnewline
9 & 0.42095 & 4.5533 & 7e-06 \tabularnewline
10 & 0.35394 & 3.8284 & 0.000104 \tabularnewline
11 & 0.289617 & 3.1327 & 0.001095 \tabularnewline
12 & 0.227148 & 2.457 & 0.007739 \tabularnewline
13 & 0.168247 & 1.8199 & 0.035668 \tabularnewline
14 & 0.113763 & 1.2305 & 0.110482 \tabularnewline
15 & 0.060345 & 0.6527 & 0.257606 \tabularnewline
16 & 0.009299 & 0.1006 & 0.460027 \tabularnewline
17 & -0.039447 & -0.4267 & 0.335196 \tabularnewline
18 & -0.085677 & -0.9267 & 0.177985 \tabularnewline
19 & -0.127167 & -1.3755 & 0.085799 \tabularnewline
20 & -0.164064 & -1.7746 & 0.03928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301238&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]0.955299[/C][C]10.3331[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.902648[/C][C]9.7636[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.844238[/C][C]9.1318[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.779934[/C][C]8.4363[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.712595[/C][C]7.7079[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.642014[/C][C]6.9444[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.569749[/C][C]6.1628[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.494061[/C][C]5.3441[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.42095[/C][C]4.5533[/C][C]7e-06[/C][/ROW]
[ROW][C]10[/C][C]0.35394[/C][C]3.8284[/C][C]0.000104[/C][/ROW]
[ROW][C]11[/C][C]0.289617[/C][C]3.1327[/C][C]0.001095[/C][/ROW]
[ROW][C]12[/C][C]0.227148[/C][C]2.457[/C][C]0.007739[/C][/ROW]
[ROW][C]13[/C][C]0.168247[/C][C]1.8199[/C][C]0.035668[/C][/ROW]
[ROW][C]14[/C][C]0.113763[/C][C]1.2305[/C][C]0.110482[/C][/ROW]
[ROW][C]15[/C][C]0.060345[/C][C]0.6527[/C][C]0.257606[/C][/ROW]
[ROW][C]16[/C][C]0.009299[/C][C]0.1006[/C][C]0.460027[/C][/ROW]
[ROW][C]17[/C][C]-0.039447[/C][C]-0.4267[/C][C]0.335196[/C][/ROW]
[ROW][C]18[/C][C]-0.085677[/C][C]-0.9267[/C][C]0.177985[/C][/ROW]
[ROW][C]19[/C][C]-0.127167[/C][C]-1.3755[/C][C]0.085799[/C][/ROW]
[ROW][C]20[/C][C]-0.164064[/C][C]-1.7746[/C][C]0.03928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301238&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	0.955299	10.3331	0
2	0.902648	9.7636	0
3	0.844238	9.1318	0
4	0.779934	8.4363	0
5	0.712595	7.7079	0
6	0.642014	6.9444	0
7	0.569749	6.1628	0
8	0.494061	5.3441	0
9	0.42095	4.5533	7e-06
10	0.35394	3.8284	0.000104
11	0.289617	3.1327	0.001095
12	0.227148	2.457	0.007739
13	0.168247	1.8199	0.035668
14	0.113763	1.2305	0.110482
15	0.060345	0.6527	0.257606
16	0.009299	0.1006	0.460027
17	-0.039447	-0.4267	0.335196
18	-0.085677	-0.9267	0.177985
19	-0.127167	-1.3755	0.085799
20	-0.164064	-1.7746	0.03928

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.955299	10.3331	0
2	-0.113807	-1.231	0.110393
3	-0.086659	-0.9374	0.175251
4	-0.090415	-0.978	0.16505
5	-0.059086	-0.6391	0.261999
6	-0.067202	-0.7269	0.234369
7	-0.052783	-0.5709	0.284569
8	-0.079534	-0.8603	0.195694
9	-0.010998	-0.119	0.452756
10	0.022287	0.2411	0.404963
11	-0.024769	-0.2679	0.394615
12	-0.039024	-0.4221	0.33686
13	-0.019407	-0.2099	0.41705
14	-0.010582	-0.1145	0.454533
15	-0.052311	-0.5658	0.286298
16	-0.038156	-0.4127	0.340282
17	-0.040254	-0.4354	0.332033
18	-0.030333	-0.3281	0.371709
19	-0.002914	-0.0315	0.487455
20	-0.009183	-0.0993	0.460525

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.955299 & 10.3331 & 0 \tabularnewline
2 & -0.113807 & -1.231 & 0.110393 \tabularnewline
3 & -0.086659 & -0.9374 & 0.175251 \tabularnewline
4 & -0.090415 & -0.978 & 0.16505 \tabularnewline
5 & -0.059086 & -0.6391 & 0.261999 \tabularnewline
6 & -0.067202 & -0.7269 & 0.234369 \tabularnewline
7 & -0.052783 & -0.5709 & 0.284569 \tabularnewline
8 & -0.079534 & -0.8603 & 0.195694 \tabularnewline
9 & -0.010998 & -0.119 & 0.452756 \tabularnewline
10 & 0.022287 & 0.2411 & 0.404963 \tabularnewline
11 & -0.024769 & -0.2679 & 0.394615 \tabularnewline
12 & -0.039024 & -0.4221 & 0.33686 \tabularnewline
13 & -0.019407 & -0.2099 & 0.41705 \tabularnewline
14 & -0.010582 & -0.1145 & 0.454533 \tabularnewline
15 & -0.052311 & -0.5658 & 0.286298 \tabularnewline
16 & -0.038156 & -0.4127 & 0.340282 \tabularnewline
17 & -0.040254 & -0.4354 & 0.332033 \tabularnewline
18 & -0.030333 & -0.3281 & 0.371709 \tabularnewline
19 & -0.002914 & -0.0315 & 0.487455 \tabularnewline
20 & -0.009183 & -0.0993 & 0.460525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301238&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]0.955299[/C][C]10.3331[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.113807[/C][C]-1.231[/C][C]0.110393[/C][/ROW]
[ROW][C]3[/C][C]-0.086659[/C][C]-0.9374[/C][C]0.175251[/C][/ROW]
[ROW][C]4[/C][C]-0.090415[/C][C]-0.978[/C][C]0.16505[/C][/ROW]
[ROW][C]5[/C][C]-0.059086[/C][C]-0.6391[/C][C]0.261999[/C][/ROW]
[ROW][C]6[/C][C]-0.067202[/C][C]-0.7269[/C][C]0.234369[/C][/ROW]
[ROW][C]7[/C][C]-0.052783[/C][C]-0.5709[/C][C]0.284569[/C][/ROW]
[ROW][C]8[/C][C]-0.079534[/C][C]-0.8603[/C][C]0.195694[/C][/ROW]
[ROW][C]9[/C][C]-0.010998[/C][C]-0.119[/C][C]0.452756[/C][/ROW]
[ROW][C]10[/C][C]0.022287[/C][C]0.2411[/C][C]0.404963[/C][/ROW]
[ROW][C]11[/C][C]-0.024769[/C][C]-0.2679[/C][C]0.394615[/C][/ROW]
[ROW][C]12[/C][C]-0.039024[/C][C]-0.4221[/C][C]0.33686[/C][/ROW]
[ROW][C]13[/C][C]-0.019407[/C][C]-0.2099[/C][C]0.41705[/C][/ROW]
[ROW][C]14[/C][C]-0.010582[/C][C]-0.1145[/C][C]0.454533[/C][/ROW]
[ROW][C]15[/C][C]-0.052311[/C][C]-0.5658[/C][C]0.286298[/C][/ROW]
[ROW][C]16[/C][C]-0.038156[/C][C]-0.4127[/C][C]0.340282[/C][/ROW]
[ROW][C]17[/C][C]-0.040254[/C][C]-0.4354[/C][C]0.332033[/C][/ROW]
[ROW][C]18[/C][C]-0.030333[/C][C]-0.3281[/C][C]0.371709[/C][/ROW]
[ROW][C]19[/C][C]-0.002914[/C][C]-0.0315[/C][C]0.487455[/C][/ROW]
[ROW][C]20[/C][C]-0.009183[/C][C]-0.0993[/C][C]0.460525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301238&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	0.955299	10.3331	0
2	-0.113807	-1.231	0.110393
3	-0.086659	-0.9374	0.175251
4	-0.090415	-0.978	0.16505
5	-0.059086	-0.6391	0.261999
6	-0.067202	-0.7269	0.234369
7	-0.052783	-0.5709	0.284569
8	-0.079534	-0.8603	0.195694
9	-0.010998	-0.119	0.452756
10	0.022287	0.2411	0.404963
11	-0.024769	-0.2679	0.394615
12	-0.039024	-0.4221	0.33686
13	-0.019407	-0.2099	0.41705
14	-0.010582	-0.1145	0.454533
15	-0.052311	-0.5658	0.286298
16	-0.038156	-0.4127	0.340282
17	-0.040254	-0.4354	0.332033
18	-0.030333	-0.3281	0.371709
19	-0.002914	-0.0315	0.487455
20	-0.009183	-0.0993	0.460525

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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 <- '60'
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