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Author

*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, 03 Dec 2017 15:19:05 +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/2017/Dec/03/t1512310826wr494myvciprk84.htm/, Retrieved Wed, 22 May 2024 16:45:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308458, Retrieved Wed, 22 May 2024 16:45:10 +0000

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No (this computation is public)

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Estimated Impact

100

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

-       [(Partial) Autocorrelation Function] [] [2017-12-03 14:19:05] [834c75312b1a933b06457deba9c9b5e8] [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=308458&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=308458&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308458&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	-0.54896	-7.744	0
2	-0.104296	-1.4713	0.071399
3	0.353437	4.9858	1e-06
4	-0.264052	-3.7249	0.000127
5	0.02535	0.3576	0.360511
6	0.209462	2.9548	0.001753
7	-0.272939	-3.8503	7.9e-05
8	0.04426	0.6244	0.26655
9	0.24436	3.4471	0.000346
10	-0.259578	-3.6618	0.00016
11	0.169722	2.3942	0.008792
12	-0.059837	-0.8441	0.199812
13	-0.169479	-2.3908	0.008872
14	0.25706	3.6263	0.000183
15	-0.024314	-0.343	0.365982
16	-0.277272	-3.9114	6.3e-05
17	0.235813	3.3265	0.000524
18	0.068438	0.9654	0.167749
19	-0.256862	-3.6235	0.000185
20	0.248943	3.5118	0.000275
21	-0.05764	-0.8131	0.208561
22	-0.274717	-3.8754	7.2e-05
23	0.453491	6.3973	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.54896 & -7.744 & 0 \tabularnewline
2 & -0.104296 & -1.4713 & 0.071399 \tabularnewline
3 & 0.353437 & 4.9858 & 1e-06 \tabularnewline
4 & -0.264052 & -3.7249 & 0.000127 \tabularnewline
5 & 0.02535 & 0.3576 & 0.360511 \tabularnewline
6 & 0.209462 & 2.9548 & 0.001753 \tabularnewline
7 & -0.272939 & -3.8503 & 7.9e-05 \tabularnewline
8 & 0.04426 & 0.6244 & 0.26655 \tabularnewline
9 & 0.24436 & 3.4471 & 0.000346 \tabularnewline
10 & -0.259578 & -3.6618 & 0.00016 \tabularnewline
11 & 0.169722 & 2.3942 & 0.008792 \tabularnewline
12 & -0.059837 & -0.8441 & 0.199812 \tabularnewline
13 & -0.169479 & -2.3908 & 0.008872 \tabularnewline
14 & 0.25706 & 3.6263 & 0.000183 \tabularnewline
15 & -0.024314 & -0.343 & 0.365982 \tabularnewline
16 & -0.277272 & -3.9114 & 6.3e-05 \tabularnewline
17 & 0.235813 & 3.3265 & 0.000524 \tabularnewline
18 & 0.068438 & 0.9654 & 0.167749 \tabularnewline
19 & -0.256862 & -3.6235 & 0.000185 \tabularnewline
20 & 0.248943 & 3.5118 & 0.000275 \tabularnewline
21 & -0.05764 & -0.8131 & 0.208561 \tabularnewline
22 & -0.274717 & -3.8754 & 7.2e-05 \tabularnewline
23 & 0.453491 & 6.3973 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308458&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]-0.54896[/C][C]-7.744[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.104296[/C][C]-1.4713[/C][C]0.071399[/C][/ROW]
[ROW][C]3[/C][C]0.353437[/C][C]4.9858[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.264052[/C][C]-3.7249[/C][C]0.000127[/C][/ROW]
[ROW][C]5[/C][C]0.02535[/C][C]0.3576[/C][C]0.360511[/C][/ROW]
[ROW][C]6[/C][C]0.209462[/C][C]2.9548[/C][C]0.001753[/C][/ROW]
[ROW][C]7[/C][C]-0.272939[/C][C]-3.8503[/C][C]7.9e-05[/C][/ROW]
[ROW][C]8[/C][C]0.04426[/C][C]0.6244[/C][C]0.26655[/C][/ROW]
[ROW][C]9[/C][C]0.24436[/C][C]3.4471[/C][C]0.000346[/C][/ROW]
[ROW][C]10[/C][C]-0.259578[/C][C]-3.6618[/C][C]0.00016[/C][/ROW]
[ROW][C]11[/C][C]0.169722[/C][C]2.3942[/C][C]0.008792[/C][/ROW]
[ROW][C]12[/C][C]-0.059837[/C][C]-0.8441[/C][C]0.199812[/C][/ROW]
[ROW][C]13[/C][C]-0.169479[/C][C]-2.3908[/C][C]0.008872[/C][/ROW]
[ROW][C]14[/C][C]0.25706[/C][C]3.6263[/C][C]0.000183[/C][/ROW]
[ROW][C]15[/C][C]-0.024314[/C][C]-0.343[/C][C]0.365982[/C][/ROW]
[ROW][C]16[/C][C]-0.277272[/C][C]-3.9114[/C][C]6.3e-05[/C][/ROW]
[ROW][C]17[/C][C]0.235813[/C][C]3.3265[/C][C]0.000524[/C][/ROW]
[ROW][C]18[/C][C]0.068438[/C][C]0.9654[/C][C]0.167749[/C][/ROW]
[ROW][C]19[/C][C]-0.256862[/C][C]-3.6235[/C][C]0.000185[/C][/ROW]
[ROW][C]20[/C][C]0.248943[/C][C]3.5118[/C][C]0.000275[/C][/ROW]
[ROW][C]21[/C][C]-0.05764[/C][C]-0.8131[/C][C]0.208561[/C][/ROW]
[ROW][C]22[/C][C]-0.274717[/C][C]-3.8754[/C][C]7.2e-05[/C][/ROW]
[ROW][C]23[/C][C]0.453491[/C][C]6.3973[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308458&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308458&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	-0.54896	-7.744	0
2	-0.104296	-1.4713	0.071399
3	0.353437	4.9858	1e-06
4	-0.264052	-3.7249	0.000127
5	0.02535	0.3576	0.360511
6	0.209462	2.9548	0.001753
7	-0.272939	-3.8503	7.9e-05
8	0.04426	0.6244	0.26655
9	0.24436	3.4471	0.000346
10	-0.259578	-3.6618	0.00016
11	0.169722	2.3942	0.008792
12	-0.059837	-0.8441	0.199812
13	-0.169479	-2.3908	0.008872
14	0.25706	3.6263	0.000183
15	-0.024314	-0.343	0.365982
16	-0.277272	-3.9114	6.3e-05
17	0.235813	3.3265	0.000524
18	0.068438	0.9654	0.167749
19	-0.256862	-3.6235	0.000185
20	0.248943	3.5118	0.000275
21	-0.05764	-0.8131	0.208561
22	-0.274717	-3.8754	7.2e-05
23	0.453491	6.3973	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.54896	-7.744	0
2	-0.58063	-8.1908	0
3	-0.120498	-1.6998	0.045362
4	-0.153942	-2.1716	0.015533
5	-0.13426	-1.894	0.02984
6	0.100645	1.4198	0.078619
7	-0.039559	-0.558	0.288721
8	-0.205678	-2.9015	0.002066
9	0.037428	0.528	0.299049
10	0.053257	0.7513	0.226685
11	0.283577	4.0004	4.5e-05
12	0.105863	1.4934	0.068461
13	-0.187853	-2.65	0.004348
14	-0.15204	-2.1448	0.016591
15	0.108232	1.5268	0.064199
16	-0.075555	-1.0658	0.143895
17	-0.192854	-2.7205	0.003547
18	0.055096	0.7772	0.218973
19	-0.025854	-0.3647	0.357856
20	-0.043098	-0.608	0.271949
21	0.135775	1.9153	0.028441
22	-0.14668	-2.0692	0.019911
23	0.158432	2.235	0.013266

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.54896 & -7.744 & 0 \tabularnewline
2 & -0.58063 & -8.1908 & 0 \tabularnewline
3 & -0.120498 & -1.6998 & 0.045362 \tabularnewline
4 & -0.153942 & -2.1716 & 0.015533 \tabularnewline
5 & -0.13426 & -1.894 & 0.02984 \tabularnewline
6 & 0.100645 & 1.4198 & 0.078619 \tabularnewline
7 & -0.039559 & -0.558 & 0.288721 \tabularnewline
8 & -0.205678 & -2.9015 & 0.002066 \tabularnewline
9 & 0.037428 & 0.528 & 0.299049 \tabularnewline
10 & 0.053257 & 0.7513 & 0.226685 \tabularnewline
11 & 0.283577 & 4.0004 & 4.5e-05 \tabularnewline
12 & 0.105863 & 1.4934 & 0.068461 \tabularnewline
13 & -0.187853 & -2.65 & 0.004348 \tabularnewline
14 & -0.15204 & -2.1448 & 0.016591 \tabularnewline
15 & 0.108232 & 1.5268 & 0.064199 \tabularnewline
16 & -0.075555 & -1.0658 & 0.143895 \tabularnewline
17 & -0.192854 & -2.7205 & 0.003547 \tabularnewline
18 & 0.055096 & 0.7772 & 0.218973 \tabularnewline
19 & -0.025854 & -0.3647 & 0.357856 \tabularnewline
20 & -0.043098 & -0.608 & 0.271949 \tabularnewline
21 & 0.135775 & 1.9153 & 0.028441 \tabularnewline
22 & -0.14668 & -2.0692 & 0.019911 \tabularnewline
23 & 0.158432 & 2.235 & 0.013266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308458&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]-0.54896[/C][C]-7.744[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.58063[/C][C]-8.1908[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.120498[/C][C]-1.6998[/C][C]0.045362[/C][/ROW]
[ROW][C]4[/C][C]-0.153942[/C][C]-2.1716[/C][C]0.015533[/C][/ROW]
[ROW][C]5[/C][C]-0.13426[/C][C]-1.894[/C][C]0.02984[/C][/ROW]
[ROW][C]6[/C][C]0.100645[/C][C]1.4198[/C][C]0.078619[/C][/ROW]
[ROW][C]7[/C][C]-0.039559[/C][C]-0.558[/C][C]0.288721[/C][/ROW]
[ROW][C]8[/C][C]-0.205678[/C][C]-2.9015[/C][C]0.002066[/C][/ROW]
[ROW][C]9[/C][C]0.037428[/C][C]0.528[/C][C]0.299049[/C][/ROW]
[ROW][C]10[/C][C]0.053257[/C][C]0.7513[/C][C]0.226685[/C][/ROW]
[ROW][C]11[/C][C]0.283577[/C][C]4.0004[/C][C]4.5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.105863[/C][C]1.4934[/C][C]0.068461[/C][/ROW]
[ROW][C]13[/C][C]-0.187853[/C][C]-2.65[/C][C]0.004348[/C][/ROW]
[ROW][C]14[/C][C]-0.15204[/C][C]-2.1448[/C][C]0.016591[/C][/ROW]
[ROW][C]15[/C][C]0.108232[/C][C]1.5268[/C][C]0.064199[/C][/ROW]
[ROW][C]16[/C][C]-0.075555[/C][C]-1.0658[/C][C]0.143895[/C][/ROW]
[ROW][C]17[/C][C]-0.192854[/C][C]-2.7205[/C][C]0.003547[/C][/ROW]
[ROW][C]18[/C][C]0.055096[/C][C]0.7772[/C][C]0.218973[/C][/ROW]
[ROW][C]19[/C][C]-0.025854[/C][C]-0.3647[/C][C]0.357856[/C][/ROW]
[ROW][C]20[/C][C]-0.043098[/C][C]-0.608[/C][C]0.271949[/C][/ROW]
[ROW][C]21[/C][C]0.135775[/C][C]1.9153[/C][C]0.028441[/C][/ROW]
[ROW][C]22[/C][C]-0.14668[/C][C]-2.0692[/C][C]0.019911[/C][/ROW]
[ROW][C]23[/C][C]0.158432[/C][C]2.235[/C][C]0.013266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308458&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308458&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	-0.54896	-7.744	0
2	-0.58063	-8.1908	0
3	-0.120498	-1.6998	0.045362
4	-0.153942	-2.1716	0.015533
5	-0.13426	-1.894	0.02984
6	0.100645	1.4198	0.078619
7	-0.039559	-0.558	0.288721
8	-0.205678	-2.9015	0.002066
9	0.037428	0.528	0.299049
10	0.053257	0.7513	0.226685
11	0.283577	4.0004	4.5e-05
12	0.105863	1.4934	0.068461
13	-0.187853	-2.65	0.004348
14	-0.15204	-2.1448	0.016591
15	0.108232	1.5268	0.064199
16	-0.075555	-1.0658	0.143895
17	-0.192854	-2.7205	0.003547
18	0.055096	0.7772	0.218973
19	-0.025854	-0.3647	0.357856
20	-0.043098	-0.608	0.271949
21	0.135775	1.9153	0.028441
22	-0.14668	-2.0692	0.019911
23	0.158432	2.235	0.013266

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code