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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

Tue, 20 Dec 2016 11:44:12 +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/20/t1482230667gwokv1e0mb9bk5j.htm/, Retrieved Thu, 03 Apr 2025 01:00:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301589, Retrieved Thu, 03 Apr 2025 01:00:23 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

149

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

-       [(Partial) Autocorrelation Function] [] [2016-12-20 10:44:12] [2e11ca31a00cf8de75c33c1af2d59434] [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=301589&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=301589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301589&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	-0.332152	-2.0743	0.02235
2	-0.014819	-0.0925	0.46337
3	-0.027463	-0.1715	0.432356
4	-0.319383	-1.9945	0.026558
5	0.100274	0.6262	0.267412
6	0.051847	0.3238	0.373916
7	0.237604	1.4838	0.072945
8	-0.171289	-1.0697	0.145666
9	0.117772	0.7355	0.233221
10	-0.045146	-0.2819	0.389741
11	-0.112832	-0.7046	0.242612
12	0.139864	0.8735	0.193882
13	-0.173745	-1.085	0.142283
14	0.09728	0.6075	0.273516
15	-0.007543	-0.0471	0.481334
16	-0.01585	-0.099	0.460829
17	-0.040697	-0.2542	0.400356
18	0.108738	0.6791	0.250553
19	-0.099419	-0.6209	0.269147
20	0.006644	0.0415	0.483557
21	0.162989	1.0179	0.157507
22	-0.232783	-1.4537	0.077011
23	0.100695	0.6288	0.26656
24	-0.058682	-0.3665	0.357998

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.332152 & -2.0743 & 0.02235 \tabularnewline
2 & -0.014819 & -0.0925 & 0.46337 \tabularnewline
3 & -0.027463 & -0.1715 & 0.432356 \tabularnewline
4 & -0.319383 & -1.9945 & 0.026558 \tabularnewline
5 & 0.100274 & 0.6262 & 0.267412 \tabularnewline
6 & 0.051847 & 0.3238 & 0.373916 \tabularnewline
7 & 0.237604 & 1.4838 & 0.072945 \tabularnewline
8 & -0.171289 & -1.0697 & 0.145666 \tabularnewline
9 & 0.117772 & 0.7355 & 0.233221 \tabularnewline
10 & -0.045146 & -0.2819 & 0.389741 \tabularnewline
11 & -0.112832 & -0.7046 & 0.242612 \tabularnewline
12 & 0.139864 & 0.8735 & 0.193882 \tabularnewline
13 & -0.173745 & -1.085 & 0.142283 \tabularnewline
14 & 0.09728 & 0.6075 & 0.273516 \tabularnewline
15 & -0.007543 & -0.0471 & 0.481334 \tabularnewline
16 & -0.01585 & -0.099 & 0.460829 \tabularnewline
17 & -0.040697 & -0.2542 & 0.400356 \tabularnewline
18 & 0.108738 & 0.6791 & 0.250553 \tabularnewline
19 & -0.099419 & -0.6209 & 0.269147 \tabularnewline
20 & 0.006644 & 0.0415 & 0.483557 \tabularnewline
21 & 0.162989 & 1.0179 & 0.157507 \tabularnewline
22 & -0.232783 & -1.4537 & 0.077011 \tabularnewline
23 & 0.100695 & 0.6288 & 0.26656 \tabularnewline
24 & -0.058682 & -0.3665 & 0.357998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301589&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]-0.332152[/C][C]-2.0743[/C][C]0.02235[/C][/ROW]
[ROW][C]2[/C][C]-0.014819[/C][C]-0.0925[/C][C]0.46337[/C][/ROW]
[ROW][C]3[/C][C]-0.027463[/C][C]-0.1715[/C][C]0.432356[/C][/ROW]
[ROW][C]4[/C][C]-0.319383[/C][C]-1.9945[/C][C]0.026558[/C][/ROW]
[ROW][C]5[/C][C]0.100274[/C][C]0.6262[/C][C]0.267412[/C][/ROW]
[ROW][C]6[/C][C]0.051847[/C][C]0.3238[/C][C]0.373916[/C][/ROW]
[ROW][C]7[/C][C]0.237604[/C][C]1.4838[/C][C]0.072945[/C][/ROW]
[ROW][C]8[/C][C]-0.171289[/C][C]-1.0697[/C][C]0.145666[/C][/ROW]
[ROW][C]9[/C][C]0.117772[/C][C]0.7355[/C][C]0.233221[/C][/ROW]
[ROW][C]10[/C][C]-0.045146[/C][C]-0.2819[/C][C]0.389741[/C][/ROW]
[ROW][C]11[/C][C]-0.112832[/C][C]-0.7046[/C][C]0.242612[/C][/ROW]
[ROW][C]12[/C][C]0.139864[/C][C]0.8735[/C][C]0.193882[/C][/ROW]
[ROW][C]13[/C][C]-0.173745[/C][C]-1.085[/C][C]0.142283[/C][/ROW]
[ROW][C]14[/C][C]0.09728[/C][C]0.6075[/C][C]0.273516[/C][/ROW]
[ROW][C]15[/C][C]-0.007543[/C][C]-0.0471[/C][C]0.481334[/C][/ROW]
[ROW][C]16[/C][C]-0.01585[/C][C]-0.099[/C][C]0.460829[/C][/ROW]
[ROW][C]17[/C][C]-0.040697[/C][C]-0.2542[/C][C]0.400356[/C][/ROW]
[ROW][C]18[/C][C]0.108738[/C][C]0.6791[/C][C]0.250553[/C][/ROW]
[ROW][C]19[/C][C]-0.099419[/C][C]-0.6209[/C][C]0.269147[/C][/ROW]
[ROW][C]20[/C][C]0.006644[/C][C]0.0415[/C][C]0.483557[/C][/ROW]
[ROW][C]21[/C][C]0.162989[/C][C]1.0179[/C][C]0.157507[/C][/ROW]
[ROW][C]22[/C][C]-0.232783[/C][C]-1.4537[/C][C]0.077011[/C][/ROW]
[ROW][C]23[/C][C]0.100695[/C][C]0.6288[/C][C]0.26656[/C][/ROW]
[ROW][C]24[/C][C]-0.058682[/C][C]-0.3665[/C][C]0.357998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301589&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	-0.332152	-2.0743	0.02235
2	-0.014819	-0.0925	0.46337
3	-0.027463	-0.1715	0.432356
4	-0.319383	-1.9945	0.026558
5	0.100274	0.6262	0.267412
6	0.051847	0.3238	0.373916
7	0.237604	1.4838	0.072945
8	-0.171289	-1.0697	0.145666
9	0.117772	0.7355	0.233221
10	-0.045146	-0.2819	0.389741
11	-0.112832	-0.7046	0.242612
12	0.139864	0.8735	0.193882
13	-0.173745	-1.085	0.142283
14	0.09728	0.6075	0.273516
15	-0.007543	-0.0471	0.481334
16	-0.01585	-0.099	0.460829
17	-0.040697	-0.2542	0.400356
18	0.108738	0.6791	0.250553
19	-0.099419	-0.6209	0.269147
20	0.006644	0.0415	0.483557
21	0.162989	1.0179	0.157507
22	-0.232783	-1.4537	0.077011
23	0.100695	0.6288	0.26656
24	-0.058682	-0.3665	0.357998

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.332152	-2.0743	0.02235
2	-0.140662	-0.8784	0.192544
3	-0.091505	-0.5714	0.285488
4	-0.419918	-2.6224	0.006196
5	-0.262847	-1.6415	0.05437
6	-0.149282	-0.9323	0.178467
7	0.18318	1.144	0.129807
8	-0.171276	-1.0696	0.145684
9	0.043291	0.2704	0.394157
10	0.124812	0.7794	0.22021
11	0.140922	0.8801	0.19211
12	0.116952	0.7304	0.234766
13	-0.069559	-0.4344	0.333199
14	0.013035	0.0814	0.467768
15	0.042294	0.2641	0.396537
16	-0.082011	-0.5122	0.305715
17	-0.272584	-1.7023	0.048331
18	0.00938	0.0586	0.476793
19	-0.1326	-0.8281	0.20633
20	-0.073854	-0.4612	0.323603
21	0.05605	0.35	0.3641
22	-0.045012	-0.2811	0.390061
23	0.047224	0.2949	0.384811
24	-0.019	-0.1187	0.453078

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.332152 & -2.0743 & 0.02235 \tabularnewline
2 & -0.140662 & -0.8784 & 0.192544 \tabularnewline
3 & -0.091505 & -0.5714 & 0.285488 \tabularnewline
4 & -0.419918 & -2.6224 & 0.006196 \tabularnewline
5 & -0.262847 & -1.6415 & 0.05437 \tabularnewline
6 & -0.149282 & -0.9323 & 0.178467 \tabularnewline
7 & 0.18318 & 1.144 & 0.129807 \tabularnewline
8 & -0.171276 & -1.0696 & 0.145684 \tabularnewline
9 & 0.043291 & 0.2704 & 0.394157 \tabularnewline
10 & 0.124812 & 0.7794 & 0.22021 \tabularnewline
11 & 0.140922 & 0.8801 & 0.19211 \tabularnewline
12 & 0.116952 & 0.7304 & 0.234766 \tabularnewline
13 & -0.069559 & -0.4344 & 0.333199 \tabularnewline
14 & 0.013035 & 0.0814 & 0.467768 \tabularnewline
15 & 0.042294 & 0.2641 & 0.396537 \tabularnewline
16 & -0.082011 & -0.5122 & 0.305715 \tabularnewline
17 & -0.272584 & -1.7023 & 0.048331 \tabularnewline
18 & 0.00938 & 0.0586 & 0.476793 \tabularnewline
19 & -0.1326 & -0.8281 & 0.20633 \tabularnewline
20 & -0.073854 & -0.4612 & 0.323603 \tabularnewline
21 & 0.05605 & 0.35 & 0.3641 \tabularnewline
22 & -0.045012 & -0.2811 & 0.390061 \tabularnewline
23 & 0.047224 & 0.2949 & 0.384811 \tabularnewline
24 & -0.019 & -0.1187 & 0.453078 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301589&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]-0.332152[/C][C]-2.0743[/C][C]0.02235[/C][/ROW]
[ROW][C]2[/C][C]-0.140662[/C][C]-0.8784[/C][C]0.192544[/C][/ROW]
[ROW][C]3[/C][C]-0.091505[/C][C]-0.5714[/C][C]0.285488[/C][/ROW]
[ROW][C]4[/C][C]-0.419918[/C][C]-2.6224[/C][C]0.006196[/C][/ROW]
[ROW][C]5[/C][C]-0.262847[/C][C]-1.6415[/C][C]0.05437[/C][/ROW]
[ROW][C]6[/C][C]-0.149282[/C][C]-0.9323[/C][C]0.178467[/C][/ROW]
[ROW][C]7[/C][C]0.18318[/C][C]1.144[/C][C]0.129807[/C][/ROW]
[ROW][C]8[/C][C]-0.171276[/C][C]-1.0696[/C][C]0.145684[/C][/ROW]
[ROW][C]9[/C][C]0.043291[/C][C]0.2704[/C][C]0.394157[/C][/ROW]
[ROW][C]10[/C][C]0.124812[/C][C]0.7794[/C][C]0.22021[/C][/ROW]
[ROW][C]11[/C][C]0.140922[/C][C]0.8801[/C][C]0.19211[/C][/ROW]
[ROW][C]12[/C][C]0.116952[/C][C]0.7304[/C][C]0.234766[/C][/ROW]
[ROW][C]13[/C][C]-0.069559[/C][C]-0.4344[/C][C]0.333199[/C][/ROW]
[ROW][C]14[/C][C]0.013035[/C][C]0.0814[/C][C]0.467768[/C][/ROW]
[ROW][C]15[/C][C]0.042294[/C][C]0.2641[/C][C]0.396537[/C][/ROW]
[ROW][C]16[/C][C]-0.082011[/C][C]-0.5122[/C][C]0.305715[/C][/ROW]
[ROW][C]17[/C][C]-0.272584[/C][C]-1.7023[/C][C]0.048331[/C][/ROW]
[ROW][C]18[/C][C]0.00938[/C][C]0.0586[/C][C]0.476793[/C][/ROW]
[ROW][C]19[/C][C]-0.1326[/C][C]-0.8281[/C][C]0.20633[/C][/ROW]
[ROW][C]20[/C][C]-0.073854[/C][C]-0.4612[/C][C]0.323603[/C][/ROW]
[ROW][C]21[/C][C]0.05605[/C][C]0.35[/C][C]0.3641[/C][/ROW]
[ROW][C]22[/C][C]-0.045012[/C][C]-0.2811[/C][C]0.390061[/C][/ROW]
[ROW][C]23[/C][C]0.047224[/C][C]0.2949[/C][C]0.384811[/C][/ROW]
[ROW][C]24[/C][C]-0.019[/C][C]-0.1187[/C][C]0.453078[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301589&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	-0.332152	-2.0743	0.02235
2	-0.140662	-0.8784	0.192544
3	-0.091505	-0.5714	0.285488
4	-0.419918	-2.6224	0.006196
5	-0.262847	-1.6415	0.05437
6	-0.149282	-0.9323	0.178467
7	0.18318	1.144	0.129807
8	-0.171276	-1.0696	0.145684
9	0.043291	0.2704	0.394157
10	0.124812	0.7794	0.22021
11	0.140922	0.8801	0.19211
12	0.116952	0.7304	0.234766
13	-0.069559	-0.4344	0.333199
14	0.013035	0.0814	0.467768
15	0.042294	0.2641	0.396537
16	-0.082011	-0.5122	0.305715
17	-0.272584	-1.7023	0.048331
18	0.00938	0.0586	0.476793
19	-0.1326	-0.8281	0.20633
20	-0.073854	-0.4612	0.323603
21	0.05605	0.35	0.3641
22	-0.045012	-0.2811	0.390061
23	0.047224	0.2949	0.384811
24	-0.019	-0.1187	0.453078

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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 <- '4'
par4 <- '1'
par3 <- '1'
par2 <- '0.0'
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