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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 20:27:54 +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/21/t148234896910r8xnik1j1bm67.htm/, Retrieved Mon, 06 May 2024 11:54:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302474, Retrieved Mon, 06 May 2024 11:54:50 +0000

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

-       [(Partial) Autocorrelation Function] [PAF ] [2016-12-21 19:27:54] [bb262dce3bb40077245e847c94886178] [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=302474&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=302474&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302474&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	0.498807	5.5991	0
2	0.447213	5.02	1e-06
3	0.337735	3.7911	0.000116
4	0.194776	2.1864	0.015319
5	0.252975	2.8396	0.002634
6	-0.054403	-0.6107	0.271257
7	0.239357	2.6868	0.004094
8	0.210354	2.3612	0.009874
9	0.33291	3.7369	0.000141
10	0.387062	4.3448	1.4e-05
11	0.448607	5.0356	1e-06
12	0.803164	9.0155	0
13	0.389018	4.3667	1.3e-05
14	0.368485	4.1362	3.2e-05
15	0.217201	2.4381	0.00808
16	0.108364	1.2164	0.113056
17	0.162215	1.8209	0.035501
18	-0.129172	-1.4499	0.074779
19	0.145754	1.6361	0.052158
20	0.123334	1.3844	0.084339
21	0.19499	2.1888	0.015229

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.498807 & 5.5991 & 0 \tabularnewline
2 & 0.447213 & 5.02 & 1e-06 \tabularnewline
3 & 0.337735 & 3.7911 & 0.000116 \tabularnewline
4 & 0.194776 & 2.1864 & 0.015319 \tabularnewline
5 & 0.252975 & 2.8396 & 0.002634 \tabularnewline
6 & -0.054403 & -0.6107 & 0.271257 \tabularnewline
7 & 0.239357 & 2.6868 & 0.004094 \tabularnewline
8 & 0.210354 & 2.3612 & 0.009874 \tabularnewline
9 & 0.33291 & 3.7369 & 0.000141 \tabularnewline
10 & 0.387062 & 4.3448 & 1.4e-05 \tabularnewline
11 & 0.448607 & 5.0356 & 1e-06 \tabularnewline
12 & 0.803164 & 9.0155 & 0 \tabularnewline
13 & 0.389018 & 4.3667 & 1.3e-05 \tabularnewline
14 & 0.368485 & 4.1362 & 3.2e-05 \tabularnewline
15 & 0.217201 & 2.4381 & 0.00808 \tabularnewline
16 & 0.108364 & 1.2164 & 0.113056 \tabularnewline
17 & 0.162215 & 1.8209 & 0.035501 \tabularnewline
18 & -0.129172 & -1.4499 & 0.074779 \tabularnewline
19 & 0.145754 & 1.6361 & 0.052158 \tabularnewline
20 & 0.123334 & 1.3844 & 0.084339 \tabularnewline
21 & 0.19499 & 2.1888 & 0.015229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302474&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]0.498807[/C][C]5.5991[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.447213[/C][C]5.02[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.337735[/C][C]3.7911[/C][C]0.000116[/C][/ROW]
[ROW][C]4[/C][C]0.194776[/C][C]2.1864[/C][C]0.015319[/C][/ROW]
[ROW][C]5[/C][C]0.252975[/C][C]2.8396[/C][C]0.002634[/C][/ROW]
[ROW][C]6[/C][C]-0.054403[/C][C]-0.6107[/C][C]0.271257[/C][/ROW]
[ROW][C]7[/C][C]0.239357[/C][C]2.6868[/C][C]0.004094[/C][/ROW]
[ROW][C]8[/C][C]0.210354[/C][C]2.3612[/C][C]0.009874[/C][/ROW]
[ROW][C]9[/C][C]0.33291[/C][C]3.7369[/C][C]0.000141[/C][/ROW]
[ROW][C]10[/C][C]0.387062[/C][C]4.3448[/C][C]1.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.448607[/C][C]5.0356[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.803164[/C][C]9.0155[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.389018[/C][C]4.3667[/C][C]1.3e-05[/C][/ROW]
[ROW][C]14[/C][C]0.368485[/C][C]4.1362[/C][C]3.2e-05[/C][/ROW]
[ROW][C]15[/C][C]0.217201[/C][C]2.4381[/C][C]0.00808[/C][/ROW]
[ROW][C]16[/C][C]0.108364[/C][C]1.2164[/C][C]0.113056[/C][/ROW]
[ROW][C]17[/C][C]0.162215[/C][C]1.8209[/C][C]0.035501[/C][/ROW]
[ROW][C]18[/C][C]-0.129172[/C][C]-1.4499[/C][C]0.074779[/C][/ROW]
[ROW][C]19[/C][C]0.145754[/C][C]1.6361[/C][C]0.052158[/C][/ROW]
[ROW][C]20[/C][C]0.123334[/C][C]1.3844[/C][C]0.084339[/C][/ROW]
[ROW][C]21[/C][C]0.19499[/C][C]2.1888[/C][C]0.015229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302474&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302474&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	0.498807	5.5991	0
2	0.447213	5.02	1e-06
3	0.337735	3.7911	0.000116
4	0.194776	2.1864	0.015319
5	0.252975	2.8396	0.002634
6	-0.054403	-0.6107	0.271257
7	0.239357	2.6868	0.004094
8	0.210354	2.3612	0.009874
9	0.33291	3.7369	0.000141
10	0.387062	4.3448	1.4e-05
11	0.448607	5.0356	1e-06
12	0.803164	9.0155	0
13	0.389018	4.3667	1.3e-05
14	0.368485	4.1362	3.2e-05
15	0.217201	2.4381	0.00808
16	0.108364	1.2164	0.113056
17	0.162215	1.8209	0.035501
18	-0.129172	-1.4499	0.074779
19	0.145754	1.6361	0.052158
20	0.123334	1.3844	0.084339
21	0.19499	2.1888	0.015229

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.498807	5.5991	0
2	0.26412	2.9647	0.001812
3	0.059868	0.672	0.251401
4	-0.089053	-0.9996	0.159705
5	0.14204	1.5944	0.056677
6	-0.329714	-3.701	0.00016
7	0.434413	4.8763	2e-06
8	0.054649	0.6134	0.270348
9	0.309332	3.4722	0.000354
10	-0.052006	-0.5838	0.280212
11	0.496622	5.5746	0
12	0.446489	5.0118	1e-06
13	-0.29033	-3.2589	0.000719
14	-0.178235	-2.0007	0.023788
15	-0.083378	-0.9359	0.175554
16	-0.123168	-1.3826	0.084622
17	-0.012472	-0.14	0.444442
18	-0.115148	-1.2925	0.099269
19	-0.042281	-0.4746	0.317947
20	-0.110153	-1.2365	0.109292
21	-0.160332	-1.7997	0.037149

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.498807 & 5.5991 & 0 \tabularnewline
2 & 0.26412 & 2.9647 & 0.001812 \tabularnewline
3 & 0.059868 & 0.672 & 0.251401 \tabularnewline
4 & -0.089053 & -0.9996 & 0.159705 \tabularnewline
5 & 0.14204 & 1.5944 & 0.056677 \tabularnewline
6 & -0.329714 & -3.701 & 0.00016 \tabularnewline
7 & 0.434413 & 4.8763 & 2e-06 \tabularnewline
8 & 0.054649 & 0.6134 & 0.270348 \tabularnewline
9 & 0.309332 & 3.4722 & 0.000354 \tabularnewline
10 & -0.052006 & -0.5838 & 0.280212 \tabularnewline
11 & 0.496622 & 5.5746 & 0 \tabularnewline
12 & 0.446489 & 5.0118 & 1e-06 \tabularnewline
13 & -0.29033 & -3.2589 & 0.000719 \tabularnewline
14 & -0.178235 & -2.0007 & 0.023788 \tabularnewline
15 & -0.083378 & -0.9359 & 0.175554 \tabularnewline
16 & -0.123168 & -1.3826 & 0.084622 \tabularnewline
17 & -0.012472 & -0.14 & 0.444442 \tabularnewline
18 & -0.115148 & -1.2925 & 0.099269 \tabularnewline
19 & -0.042281 & -0.4746 & 0.317947 \tabularnewline
20 & -0.110153 & -1.2365 & 0.109292 \tabularnewline
21 & -0.160332 & -1.7997 & 0.037149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302474&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]0.498807[/C][C]5.5991[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.26412[/C][C]2.9647[/C][C]0.001812[/C][/ROW]
[ROW][C]3[/C][C]0.059868[/C][C]0.672[/C][C]0.251401[/C][/ROW]
[ROW][C]4[/C][C]-0.089053[/C][C]-0.9996[/C][C]0.159705[/C][/ROW]
[ROW][C]5[/C][C]0.14204[/C][C]1.5944[/C][C]0.056677[/C][/ROW]
[ROW][C]6[/C][C]-0.329714[/C][C]-3.701[/C][C]0.00016[/C][/ROW]
[ROW][C]7[/C][C]0.434413[/C][C]4.8763[/C][C]2e-06[/C][/ROW]
[ROW][C]8[/C][C]0.054649[/C][C]0.6134[/C][C]0.270348[/C][/ROW]
[ROW][C]9[/C][C]0.309332[/C][C]3.4722[/C][C]0.000354[/C][/ROW]
[ROW][C]10[/C][C]-0.052006[/C][C]-0.5838[/C][C]0.280212[/C][/ROW]
[ROW][C]11[/C][C]0.496622[/C][C]5.5746[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.446489[/C][C]5.0118[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.29033[/C][C]-3.2589[/C][C]0.000719[/C][/ROW]
[ROW][C]14[/C][C]-0.178235[/C][C]-2.0007[/C][C]0.023788[/C][/ROW]
[ROW][C]15[/C][C]-0.083378[/C][C]-0.9359[/C][C]0.175554[/C][/ROW]
[ROW][C]16[/C][C]-0.123168[/C][C]-1.3826[/C][C]0.084622[/C][/ROW]
[ROW][C]17[/C][C]-0.012472[/C][C]-0.14[/C][C]0.444442[/C][/ROW]
[ROW][C]18[/C][C]-0.115148[/C][C]-1.2925[/C][C]0.099269[/C][/ROW]
[ROW][C]19[/C][C]-0.042281[/C][C]-0.4746[/C][C]0.317947[/C][/ROW]
[ROW][C]20[/C][C]-0.110153[/C][C]-1.2365[/C][C]0.109292[/C][/ROW]
[ROW][C]21[/C][C]-0.160332[/C][C]-1.7997[/C][C]0.037149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302474&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302474&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	0.498807	5.5991	0
2	0.26412	2.9647	0.001812
3	0.059868	0.672	0.251401
4	-0.089053	-0.9996	0.159705
5	0.14204	1.5944	0.056677
6	-0.329714	-3.701	0.00016
7	0.434413	4.8763	2e-06
8	0.054649	0.6134	0.270348
9	0.309332	3.4722	0.000354
10	-0.052006	-0.5838	0.280212
11	0.496622	5.5746	0
12	0.446489	5.0118	1e-06
13	-0.29033	-3.2589	0.000719
14	-0.178235	-2.0007	0.023788
15	-0.083378	-0.9359	0.175554
16	-0.123168	-1.3826	0.084622
17	-0.012472	-0.14	0.444442
18	-0.115148	-1.2925	0.099269
19	-0.042281	-0.4746	0.317947
20	-0.110153	-1.2365	0.109292
21	-0.160332	-1.7997	0.037149

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; 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):

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