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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

Mon, 18 Dec 2017 14:01:59 +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/18/t1513602142qdl0the6rzt3p08.htm/, Retrieved Tue, 14 May 2024 12:13:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310159, Retrieved Tue, 14 May 2024 12:13:14 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie (D...] [2017-12-18 13:01:59] [0687db01a969247b131332e81d79dad3] [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=310159&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=310159&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310159&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	-0.49819	-7.0278	0
2	-0.071765	-1.0124	0.156296
3	0.335034	4.7262	2e-06
4	-0.294738	-4.1578	2.4e-05
5	0.127908	1.8044	0.036344
6	0.149412	2.1077	0.018154
7	-0.226597	-3.1965	0.000809
8	0.092021	1.2981	0.097876
9	0.015829	0.2233	0.411766
10	-0.073555	-1.0376	0.150351
11	0.174062	2.4555	0.007464
12	-0.235716	-3.3252	0.000526
13	0.027601	0.3894	0.348715
14	0.053664	0.757	0.224964
15	-0.03813	-0.5379	0.295626
16	-0.038165	-0.5384	0.295458
17	0.033537	0.4731	0.318333
18	0.023564	0.3324	0.369965
19	-0.136364	-1.9236	0.027913
20	0.08437	1.1902	0.117697
21	0.055994	0.7899	0.215264
22	-0.242684	-3.4235	0.000375
23	0.290018	4.0912	3.1e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.49819 & -7.0278 & 0 \tabularnewline
2 & -0.071765 & -1.0124 & 0.156296 \tabularnewline
3 & 0.335034 & 4.7262 & 2e-06 \tabularnewline
4 & -0.294738 & -4.1578 & 2.4e-05 \tabularnewline
5 & 0.127908 & 1.8044 & 0.036344 \tabularnewline
6 & 0.149412 & 2.1077 & 0.018154 \tabularnewline
7 & -0.226597 & -3.1965 & 0.000809 \tabularnewline
8 & 0.092021 & 1.2981 & 0.097876 \tabularnewline
9 & 0.015829 & 0.2233 & 0.411766 \tabularnewline
10 & -0.073555 & -1.0376 & 0.150351 \tabularnewline
11 & 0.174062 & 2.4555 & 0.007464 \tabularnewline
12 & -0.235716 & -3.3252 & 0.000526 \tabularnewline
13 & 0.027601 & 0.3894 & 0.348715 \tabularnewline
14 & 0.053664 & 0.757 & 0.224964 \tabularnewline
15 & -0.03813 & -0.5379 & 0.295626 \tabularnewline
16 & -0.038165 & -0.5384 & 0.295458 \tabularnewline
17 & 0.033537 & 0.4731 & 0.318333 \tabularnewline
18 & 0.023564 & 0.3324 & 0.369965 \tabularnewline
19 & -0.136364 & -1.9236 & 0.027913 \tabularnewline
20 & 0.08437 & 1.1902 & 0.117697 \tabularnewline
21 & 0.055994 & 0.7899 & 0.215264 \tabularnewline
22 & -0.242684 & -3.4235 & 0.000375 \tabularnewline
23 & 0.290018 & 4.0912 & 3.1e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310159&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]-0.49819[/C][C]-7.0278[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.071765[/C][C]-1.0124[/C][C]0.156296[/C][/ROW]
[ROW][C]3[/C][C]0.335034[/C][C]4.7262[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.294738[/C][C]-4.1578[/C][C]2.4e-05[/C][/ROW]
[ROW][C]5[/C][C]0.127908[/C][C]1.8044[/C][C]0.036344[/C][/ROW]
[ROW][C]6[/C][C]0.149412[/C][C]2.1077[/C][C]0.018154[/C][/ROW]
[ROW][C]7[/C][C]-0.226597[/C][C]-3.1965[/C][C]0.000809[/C][/ROW]
[ROW][C]8[/C][C]0.092021[/C][C]1.2981[/C][C]0.097876[/C][/ROW]
[ROW][C]9[/C][C]0.015829[/C][C]0.2233[/C][C]0.411766[/C][/ROW]
[ROW][C]10[/C][C]-0.073555[/C][C]-1.0376[/C][C]0.150351[/C][/ROW]
[ROW][C]11[/C][C]0.174062[/C][C]2.4555[/C][C]0.007464[/C][/ROW]
[ROW][C]12[/C][C]-0.235716[/C][C]-3.3252[/C][C]0.000526[/C][/ROW]
[ROW][C]13[/C][C]0.027601[/C][C]0.3894[/C][C]0.348715[/C][/ROW]
[ROW][C]14[/C][C]0.053664[/C][C]0.757[/C][C]0.224964[/C][/ROW]
[ROW][C]15[/C][C]-0.03813[/C][C]-0.5379[/C][C]0.295626[/C][/ROW]
[ROW][C]16[/C][C]-0.038165[/C][C]-0.5384[/C][C]0.295458[/C][/ROW]
[ROW][C]17[/C][C]0.033537[/C][C]0.4731[/C][C]0.318333[/C][/ROW]
[ROW][C]18[/C][C]0.023564[/C][C]0.3324[/C][C]0.369965[/C][/ROW]
[ROW][C]19[/C][C]-0.136364[/C][C]-1.9236[/C][C]0.027913[/C][/ROW]
[ROW][C]20[/C][C]0.08437[/C][C]1.1902[/C][C]0.117697[/C][/ROW]
[ROW][C]21[/C][C]0.055994[/C][C]0.7899[/C][C]0.215264[/C][/ROW]
[ROW][C]22[/C][C]-0.242684[/C][C]-3.4235[/C][C]0.000375[/C][/ROW]
[ROW][C]23[/C][C]0.290018[/C][C]4.0912[/C][C]3.1e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310159&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310159&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	-0.49819	-7.0278	0
2	-0.071765	-1.0124	0.156296
3	0.335034	4.7262	2e-06
4	-0.294738	-4.1578	2.4e-05
5	0.127908	1.8044	0.036344
6	0.149412	2.1077	0.018154
7	-0.226597	-3.1965	0.000809
8	0.092021	1.2981	0.097876
9	0.015829	0.2233	0.411766
10	-0.073555	-1.0376	0.150351
11	0.174062	2.4555	0.007464
12	-0.235716	-3.3252	0.000526
13	0.027601	0.3894	0.348715
14	0.053664	0.757	0.224964
15	-0.03813	-0.5379	0.295626
16	-0.038165	-0.5384	0.295458
17	0.033537	0.4731	0.318333
18	0.023564	0.3324	0.369965
19	-0.136364	-1.9236	0.027913
20	0.08437	1.1902	0.117697
21	0.055994	0.7899	0.215264
22	-0.242684	-3.4235	0.000375
23	0.290018	4.0912	3.1e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.49819	-7.0278	0
2	-0.425585	-6.0036	0
3	0.117024	1.6508	0.050176
4	-0.065474	-0.9236	0.1784
5	0.05036	0.7104	0.23914
6	0.191868	2.7066	0.003694
7	0.061206	0.8634	0.194474
8	-0.038849	-0.548	0.292143
9	-0.09064	-1.2786	0.101258
10	-0.048448	-0.6834	0.247561
11	0.144716	2.0415	0.021262
12	-0.143362	-2.0224	0.022238
13	-0.174835	-2.4664	0.007248
14	-0.204057	-2.8786	0.002216
15	0.011296	0.1594	0.436775
16	-0.109601	-1.5461	0.061834
17	-0.053438	-0.7538	0.225918
18	0.153345	2.1632	0.015859
19	-0.037668	-0.5314	0.297879
20	-0.122834	-1.7328	0.042341
21	-0.005324	-0.0751	0.470103
22	-0.2116	-2.985	0.001596
23	0.154241	2.1758	0.015373

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.49819 & -7.0278 & 0 \tabularnewline
2 & -0.425585 & -6.0036 & 0 \tabularnewline
3 & 0.117024 & 1.6508 & 0.050176 \tabularnewline
4 & -0.065474 & -0.9236 & 0.1784 \tabularnewline
5 & 0.05036 & 0.7104 & 0.23914 \tabularnewline
6 & 0.191868 & 2.7066 & 0.003694 \tabularnewline
7 & 0.061206 & 0.8634 & 0.194474 \tabularnewline
8 & -0.038849 & -0.548 & 0.292143 \tabularnewline
9 & -0.09064 & -1.2786 & 0.101258 \tabularnewline
10 & -0.048448 & -0.6834 & 0.247561 \tabularnewline
11 & 0.144716 & 2.0415 & 0.021262 \tabularnewline
12 & -0.143362 & -2.0224 & 0.022238 \tabularnewline
13 & -0.174835 & -2.4664 & 0.007248 \tabularnewline
14 & -0.204057 & -2.8786 & 0.002216 \tabularnewline
15 & 0.011296 & 0.1594 & 0.436775 \tabularnewline
16 & -0.109601 & -1.5461 & 0.061834 \tabularnewline
17 & -0.053438 & -0.7538 & 0.225918 \tabularnewline
18 & 0.153345 & 2.1632 & 0.015859 \tabularnewline
19 & -0.037668 & -0.5314 & 0.297879 \tabularnewline
20 & -0.122834 & -1.7328 & 0.042341 \tabularnewline
21 & -0.005324 & -0.0751 & 0.470103 \tabularnewline
22 & -0.2116 & -2.985 & 0.001596 \tabularnewline
23 & 0.154241 & 2.1758 & 0.015373 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310159&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]-0.49819[/C][C]-7.0278[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.425585[/C][C]-6.0036[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.117024[/C][C]1.6508[/C][C]0.050176[/C][/ROW]
[ROW][C]4[/C][C]-0.065474[/C][C]-0.9236[/C][C]0.1784[/C][/ROW]
[ROW][C]5[/C][C]0.05036[/C][C]0.7104[/C][C]0.23914[/C][/ROW]
[ROW][C]6[/C][C]0.191868[/C][C]2.7066[/C][C]0.003694[/C][/ROW]
[ROW][C]7[/C][C]0.061206[/C][C]0.8634[/C][C]0.194474[/C][/ROW]
[ROW][C]8[/C][C]-0.038849[/C][C]-0.548[/C][C]0.292143[/C][/ROW]
[ROW][C]9[/C][C]-0.09064[/C][C]-1.2786[/C][C]0.101258[/C][/ROW]
[ROW][C]10[/C][C]-0.048448[/C][C]-0.6834[/C][C]0.247561[/C][/ROW]
[ROW][C]11[/C][C]0.144716[/C][C]2.0415[/C][C]0.021262[/C][/ROW]
[ROW][C]12[/C][C]-0.143362[/C][C]-2.0224[/C][C]0.022238[/C][/ROW]
[ROW][C]13[/C][C]-0.174835[/C][C]-2.4664[/C][C]0.007248[/C][/ROW]
[ROW][C]14[/C][C]-0.204057[/C][C]-2.8786[/C][C]0.002216[/C][/ROW]
[ROW][C]15[/C][C]0.011296[/C][C]0.1594[/C][C]0.436775[/C][/ROW]
[ROW][C]16[/C][C]-0.109601[/C][C]-1.5461[/C][C]0.061834[/C][/ROW]
[ROW][C]17[/C][C]-0.053438[/C][C]-0.7538[/C][C]0.225918[/C][/ROW]
[ROW][C]18[/C][C]0.153345[/C][C]2.1632[/C][C]0.015859[/C][/ROW]
[ROW][C]19[/C][C]-0.037668[/C][C]-0.5314[/C][C]0.297879[/C][/ROW]
[ROW][C]20[/C][C]-0.122834[/C][C]-1.7328[/C][C]0.042341[/C][/ROW]
[ROW][C]21[/C][C]-0.005324[/C][C]-0.0751[/C][C]0.470103[/C][/ROW]
[ROW][C]22[/C][C]-0.2116[/C][C]-2.985[/C][C]0.001596[/C][/ROW]
[ROW][C]23[/C][C]0.154241[/C][C]2.1758[/C][C]0.015373[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310159&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310159&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	-0.49819	-7.0278	0
2	-0.425585	-6.0036	0
3	0.117024	1.6508	0.050176
4	-0.065474	-0.9236	0.1784
5	0.05036	0.7104	0.23914
6	0.191868	2.7066	0.003694
7	0.061206	0.8634	0.194474
8	-0.038849	-0.548	0.292143
9	-0.09064	-1.2786	0.101258
10	-0.048448	-0.6834	0.247561
11	0.144716	2.0415	0.021262
12	-0.143362	-2.0224	0.022238
13	-0.174835	-2.4664	0.007248
14	-0.204057	-2.8786	0.002216
15	0.011296	0.1594	0.436775
16	-0.109601	-1.5461	0.061834
17	-0.053438	-0.7538	0.225918
18	0.153345	2.1632	0.015859
19	-0.037668	-0.5314	0.297879
20	-0.122834	-1.7328	0.042341
21	-0.005324	-0.0751	0.470103
22	-0.2116	-2.985	0.001596
23	0.154241	2.1758	0.015373

Figure 1

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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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
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