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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

Thu, 14 Dec 2017 18:01:28 +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/14/t1513271037o40i72reermi96s.htm/, Retrieved Tue, 14 May 2024 22:35:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309564, Retrieved Tue, 14 May 2024 22:35:36 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2017-12-14 17:01:28] [c34712453b62a314277c4dd71143a000] [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=309564&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=309564&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309564&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	-0.552368	-7.7921	0
2	-0.017685	-0.2495	0.401625
3	0.298708	4.2138	1.9e-05
4	-0.244675	-3.4516	0.00034
5	-0.009124	-0.1287	0.44886
6	0.283852	4.0042	4.4e-05
7	-0.325748	-4.5952	4e-06
8	0.161392	2.2767	0.011934
9	0.116436	1.6425	0.05103
10	-0.249599	-3.521	0.000266
11	0.215802	3.0443	0.001324
12	-0.106822	-1.5069	0.06671
13	-0.101535	-1.4323	0.076811
14	0.089032	1.2559	0.105304
15	0.095472	1.3468	0.089788
16	-0.238256	-3.361	0.000465
17	0.201339	2.8402	0.002488
18	-0.077224	-1.0894	0.138653
19	-0.051408	-0.7252	0.23459
20	0.078214	1.1034	0.135604
21	-0.042127	-0.5943	0.276502
22	-0.135624	-1.9132	0.028578
23	0.28209	3.9794	4.8e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.552368 & -7.7921 & 0 \tabularnewline
2 & -0.017685 & -0.2495 & 0.401625 \tabularnewline
3 & 0.298708 & 4.2138 & 1.9e-05 \tabularnewline
4 & -0.244675 & -3.4516 & 0.00034 \tabularnewline
5 & -0.009124 & -0.1287 & 0.44886 \tabularnewline
6 & 0.283852 & 4.0042 & 4.4e-05 \tabularnewline
7 & -0.325748 & -4.5952 & 4e-06 \tabularnewline
8 & 0.161392 & 2.2767 & 0.011934 \tabularnewline
9 & 0.116436 & 1.6425 & 0.05103 \tabularnewline
10 & -0.249599 & -3.521 & 0.000266 \tabularnewline
11 & 0.215802 & 3.0443 & 0.001324 \tabularnewline
12 & -0.106822 & -1.5069 & 0.06671 \tabularnewline
13 & -0.101535 & -1.4323 & 0.076811 \tabularnewline
14 & 0.089032 & 1.2559 & 0.105304 \tabularnewline
15 & 0.095472 & 1.3468 & 0.089788 \tabularnewline
16 & -0.238256 & -3.361 & 0.000465 \tabularnewline
17 & 0.201339 & 2.8402 & 0.002488 \tabularnewline
18 & -0.077224 & -1.0894 & 0.138653 \tabularnewline
19 & -0.051408 & -0.7252 & 0.23459 \tabularnewline
20 & 0.078214 & 1.1034 & 0.135604 \tabularnewline
21 & -0.042127 & -0.5943 & 0.276502 \tabularnewline
22 & -0.135624 & -1.9132 & 0.028578 \tabularnewline
23 & 0.28209 & 3.9794 & 4.8e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309564&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]-0.552368[/C][C]-7.7921[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.017685[/C][C]-0.2495[/C][C]0.401625[/C][/ROW]
[ROW][C]3[/C][C]0.298708[/C][C]4.2138[/C][C]1.9e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.244675[/C][C]-3.4516[/C][C]0.00034[/C][/ROW]
[ROW][C]5[/C][C]-0.009124[/C][C]-0.1287[/C][C]0.44886[/C][/ROW]
[ROW][C]6[/C][C]0.283852[/C][C]4.0042[/C][C]4.4e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.325748[/C][C]-4.5952[/C][C]4e-06[/C][/ROW]
[ROW][C]8[/C][C]0.161392[/C][C]2.2767[/C][C]0.011934[/C][/ROW]
[ROW][C]9[/C][C]0.116436[/C][C]1.6425[/C][C]0.05103[/C][/ROW]
[ROW][C]10[/C][C]-0.249599[/C][C]-3.521[/C][C]0.000266[/C][/ROW]
[ROW][C]11[/C][C]0.215802[/C][C]3.0443[/C][C]0.001324[/C][/ROW]
[ROW][C]12[/C][C]-0.106822[/C][C]-1.5069[/C][C]0.06671[/C][/ROW]
[ROW][C]13[/C][C]-0.101535[/C][C]-1.4323[/C][C]0.076811[/C][/ROW]
[ROW][C]14[/C][C]0.089032[/C][C]1.2559[/C][C]0.105304[/C][/ROW]
[ROW][C]15[/C][C]0.095472[/C][C]1.3468[/C][C]0.089788[/C][/ROW]
[ROW][C]16[/C][C]-0.238256[/C][C]-3.361[/C][C]0.000465[/C][/ROW]
[ROW][C]17[/C][C]0.201339[/C][C]2.8402[/C][C]0.002488[/C][/ROW]
[ROW][C]18[/C][C]-0.077224[/C][C]-1.0894[/C][C]0.138653[/C][/ROW]
[ROW][C]19[/C][C]-0.051408[/C][C]-0.7252[/C][C]0.23459[/C][/ROW]
[ROW][C]20[/C][C]0.078214[/C][C]1.1034[/C][C]0.135604[/C][/ROW]
[ROW][C]21[/C][C]-0.042127[/C][C]-0.5943[/C][C]0.276502[/C][/ROW]
[ROW][C]22[/C][C]-0.135624[/C][C]-1.9132[/C][C]0.028578[/C][/ROW]
[ROW][C]23[/C][C]0.28209[/C][C]3.9794[/C][C]4.8e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309564&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309564&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	-0.552368	-7.7921	0
2	-0.017685	-0.2495	0.401625
3	0.298708	4.2138	1.9e-05
4	-0.244675	-3.4516	0.00034
5	-0.009124	-0.1287	0.44886
6	0.283852	4.0042	4.4e-05
7	-0.325748	-4.5952	4e-06
8	0.161392	2.2767	0.011934
9	0.116436	1.6425	0.05103
10	-0.249599	-3.521	0.000266
11	0.215802	3.0443	0.001324
12	-0.106822	-1.5069	0.06671
13	-0.101535	-1.4323	0.076811
14	0.089032	1.2559	0.105304
15	0.095472	1.3468	0.089788
16	-0.238256	-3.361	0.000465
17	0.201339	2.8402	0.002488
18	-0.077224	-1.0894	0.138653
19	-0.051408	-0.7252	0.23459
20	0.078214	1.1034	0.135604
21	-0.042127	-0.5943	0.276502
22	-0.135624	-1.9132	0.028578
23	0.28209	3.9794	4.8e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.552368	-7.7921	0
2	-0.464527	-6.553	0
3	0.051035	0.7199	0.236204
4	0.019485	0.2749	0.391853
5	-0.12074	-1.7033	0.045041
6	0.194708	2.7467	0.003286
7	-0.006431	-0.0907	0.463903
8	0.033982	0.4794	0.316097
9	0.138401	1.9524	0.026148
10	0.010146	0.1431	0.443167
11	0.101615	1.4335	0.076648
12	-0.113021	-1.5944	0.056222
13	-0.15759	-2.2231	0.013668
14	-0.282517	-3.9854	4.7e-05
15	0.042626	0.6013	0.274156
16	-0.068191	-0.962	0.16862
17	-0.04612	-0.6506	0.258027
18	-0.00606	-0.0855	0.465982
19	0.033066	0.4665	0.320699
20	0.035583	0.502	0.308126
21	0.010054	0.1418	0.443678
22	-0.150536	-2.1236	0.017471
23	0.128098	1.807	0.036133

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.552368 & -7.7921 & 0 \tabularnewline
2 & -0.464527 & -6.553 & 0 \tabularnewline
3 & 0.051035 & 0.7199 & 0.236204 \tabularnewline
4 & 0.019485 & 0.2749 & 0.391853 \tabularnewline
5 & -0.12074 & -1.7033 & 0.045041 \tabularnewline
6 & 0.194708 & 2.7467 & 0.003286 \tabularnewline
7 & -0.006431 & -0.0907 & 0.463903 \tabularnewline
8 & 0.033982 & 0.4794 & 0.316097 \tabularnewline
9 & 0.138401 & 1.9524 & 0.026148 \tabularnewline
10 & 0.010146 & 0.1431 & 0.443167 \tabularnewline
11 & 0.101615 & 1.4335 & 0.076648 \tabularnewline
12 & -0.113021 & -1.5944 & 0.056222 \tabularnewline
13 & -0.15759 & -2.2231 & 0.013668 \tabularnewline
14 & -0.282517 & -3.9854 & 4.7e-05 \tabularnewline
15 & 0.042626 & 0.6013 & 0.274156 \tabularnewline
16 & -0.068191 & -0.962 & 0.16862 \tabularnewline
17 & -0.04612 & -0.6506 & 0.258027 \tabularnewline
18 & -0.00606 & -0.0855 & 0.465982 \tabularnewline
19 & 0.033066 & 0.4665 & 0.320699 \tabularnewline
20 & 0.035583 & 0.502 & 0.308126 \tabularnewline
21 & 0.010054 & 0.1418 & 0.443678 \tabularnewline
22 & -0.150536 & -2.1236 & 0.017471 \tabularnewline
23 & 0.128098 & 1.807 & 0.036133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309564&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]-0.552368[/C][C]-7.7921[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.464527[/C][C]-6.553[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.051035[/C][C]0.7199[/C][C]0.236204[/C][/ROW]
[ROW][C]4[/C][C]0.019485[/C][C]0.2749[/C][C]0.391853[/C][/ROW]
[ROW][C]5[/C][C]-0.12074[/C][C]-1.7033[/C][C]0.045041[/C][/ROW]
[ROW][C]6[/C][C]0.194708[/C][C]2.7467[/C][C]0.003286[/C][/ROW]
[ROW][C]7[/C][C]-0.006431[/C][C]-0.0907[/C][C]0.463903[/C][/ROW]
[ROW][C]8[/C][C]0.033982[/C][C]0.4794[/C][C]0.316097[/C][/ROW]
[ROW][C]9[/C][C]0.138401[/C][C]1.9524[/C][C]0.026148[/C][/ROW]
[ROW][C]10[/C][C]0.010146[/C][C]0.1431[/C][C]0.443167[/C][/ROW]
[ROW][C]11[/C][C]0.101615[/C][C]1.4335[/C][C]0.076648[/C][/ROW]
[ROW][C]12[/C][C]-0.113021[/C][C]-1.5944[/C][C]0.056222[/C][/ROW]
[ROW][C]13[/C][C]-0.15759[/C][C]-2.2231[/C][C]0.013668[/C][/ROW]
[ROW][C]14[/C][C]-0.282517[/C][C]-3.9854[/C][C]4.7e-05[/C][/ROW]
[ROW][C]15[/C][C]0.042626[/C][C]0.6013[/C][C]0.274156[/C][/ROW]
[ROW][C]16[/C][C]-0.068191[/C][C]-0.962[/C][C]0.16862[/C][/ROW]
[ROW][C]17[/C][C]-0.04612[/C][C]-0.6506[/C][C]0.258027[/C][/ROW]
[ROW][C]18[/C][C]-0.00606[/C][C]-0.0855[/C][C]0.465982[/C][/ROW]
[ROW][C]19[/C][C]0.033066[/C][C]0.4665[/C][C]0.320699[/C][/ROW]
[ROW][C]20[/C][C]0.035583[/C][C]0.502[/C][C]0.308126[/C][/ROW]
[ROW][C]21[/C][C]0.010054[/C][C]0.1418[/C][C]0.443678[/C][/ROW]
[ROW][C]22[/C][C]-0.150536[/C][C]-2.1236[/C][C]0.017471[/C][/ROW]
[ROW][C]23[/C][C]0.128098[/C][C]1.807[/C][C]0.036133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309564&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309564&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	-0.552368	-7.7921	0
2	-0.464527	-6.553	0
3	0.051035	0.7199	0.236204
4	0.019485	0.2749	0.391853
5	-0.12074	-1.7033	0.045041
6	0.194708	2.7467	0.003286
7	-0.006431	-0.0907	0.463903
8	0.033982	0.4794	0.316097
9	0.138401	1.9524	0.026148
10	0.010146	0.1431	0.443167
11	0.101615	1.4335	0.076648
12	-0.113021	-1.5944	0.056222
13	-0.15759	-2.2231	0.013668
14	-0.282517	-3.9854	4.7e-05
15	0.042626	0.6013	0.274156
16	-0.068191	-0.962	0.16862
17	-0.04612	-0.6506	0.258027
18	-0.00606	-0.0855	0.465982
19	0.033066	0.4665	0.320699
20	0.035583	0.502	0.308126
21	0.010054	0.1418	0.443678
22	-0.150536	-2.1236	0.017471
23	0.128098	1.807	0.036133

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

Postscript link

PDF link

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