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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

Sun, 18 Dec 2016 21:58:34 +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/18/t1482095071b4yugos61m4vrld.htm/, Retrieved Wed, 08 May 2024 23:52:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301240, Retrieved Wed, 08 May 2024 23:52:38 +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] [] [2016-12-18 20:58:34] [8e62cbb8023b87d93040197279d31dd8] [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=301240&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=301240&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301240&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	0.818236	8.7746	0
2	0.585818	6.2822	0
3	0.398381	4.2722	2e-05
4	0.297896	3.1946	0.000904
5	0.262186	2.8116	0.002898
6	0.244611	2.6232	0.004946
7	0.245391	2.6315	0.004833
8	0.254906	2.7336	0.003628
9	0.29557	3.1696	0.000978
10	0.363366	3.8967	8.2e-05
11	0.407223	4.367	1.4e-05
12	0.403424	4.3262	1.6e-05
13	0.285622	3.063	0.001365
14	0.156532	1.6786	0.047971
15	0.071939	0.7715	0.221007
16	0.045001	0.4826	0.315154
17	0.05268	0.5649	0.286611
18	0.051202	0.5491	0.292009
19	0.055592	0.5962	0.276121
20	0.075954	0.8145	0.208516
21	0.127763	1.3701	0.086662

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.818236 & 8.7746 & 0 \tabularnewline
2 & 0.585818 & 6.2822 & 0 \tabularnewline
3 & 0.398381 & 4.2722 & 2e-05 \tabularnewline
4 & 0.297896 & 3.1946 & 0.000904 \tabularnewline
5 & 0.262186 & 2.8116 & 0.002898 \tabularnewline
6 & 0.244611 & 2.6232 & 0.004946 \tabularnewline
7 & 0.245391 & 2.6315 & 0.004833 \tabularnewline
8 & 0.254906 & 2.7336 & 0.003628 \tabularnewline
9 & 0.29557 & 3.1696 & 0.000978 \tabularnewline
10 & 0.363366 & 3.8967 & 8.2e-05 \tabularnewline
11 & 0.407223 & 4.367 & 1.4e-05 \tabularnewline
12 & 0.403424 & 4.3262 & 1.6e-05 \tabularnewline
13 & 0.285622 & 3.063 & 0.001365 \tabularnewline
14 & 0.156532 & 1.6786 & 0.047971 \tabularnewline
15 & 0.071939 & 0.7715 & 0.221007 \tabularnewline
16 & 0.045001 & 0.4826 & 0.315154 \tabularnewline
17 & 0.05268 & 0.5649 & 0.286611 \tabularnewline
18 & 0.051202 & 0.5491 & 0.292009 \tabularnewline
19 & 0.055592 & 0.5962 & 0.276121 \tabularnewline
20 & 0.075954 & 0.8145 & 0.208516 \tabularnewline
21 & 0.127763 & 1.3701 & 0.086662 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301240&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]0.818236[/C][C]8.7746[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.585818[/C][C]6.2822[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.398381[/C][C]4.2722[/C][C]2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.297896[/C][C]3.1946[/C][C]0.000904[/C][/ROW]
[ROW][C]5[/C][C]0.262186[/C][C]2.8116[/C][C]0.002898[/C][/ROW]
[ROW][C]6[/C][C]0.244611[/C][C]2.6232[/C][C]0.004946[/C][/ROW]
[ROW][C]7[/C][C]0.245391[/C][C]2.6315[/C][C]0.004833[/C][/ROW]
[ROW][C]8[/C][C]0.254906[/C][C]2.7336[/C][C]0.003628[/C][/ROW]
[ROW][C]9[/C][C]0.29557[/C][C]3.1696[/C][C]0.000978[/C][/ROW]
[ROW][C]10[/C][C]0.363366[/C][C]3.8967[/C][C]8.2e-05[/C][/ROW]
[ROW][C]11[/C][C]0.407223[/C][C]4.367[/C][C]1.4e-05[/C][/ROW]
[ROW][C]12[/C][C]0.403424[/C][C]4.3262[/C][C]1.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.285622[/C][C]3.063[/C][C]0.001365[/C][/ROW]
[ROW][C]14[/C][C]0.156532[/C][C]1.6786[/C][C]0.047971[/C][/ROW]
[ROW][C]15[/C][C]0.071939[/C][C]0.7715[/C][C]0.221007[/C][/ROW]
[ROW][C]16[/C][C]0.045001[/C][C]0.4826[/C][C]0.315154[/C][/ROW]
[ROW][C]17[/C][C]0.05268[/C][C]0.5649[/C][C]0.286611[/C][/ROW]
[ROW][C]18[/C][C]0.051202[/C][C]0.5491[/C][C]0.292009[/C][/ROW]
[ROW][C]19[/C][C]0.055592[/C][C]0.5962[/C][C]0.276121[/C][/ROW]
[ROW][C]20[/C][C]0.075954[/C][C]0.8145[/C][C]0.208516[/C][/ROW]
[ROW][C]21[/C][C]0.127763[/C][C]1.3701[/C][C]0.086662[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301240&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301240&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	0.818236	8.7746	0
2	0.585818	6.2822	0
3	0.398381	4.2722	2e-05
4	0.297896	3.1946	0.000904
5	0.262186	2.8116	0.002898
6	0.244611	2.6232	0.004946
7	0.245391	2.6315	0.004833
8	0.254906	2.7336	0.003628
9	0.29557	3.1696	0.000978
10	0.363366	3.8967	8.2e-05
11	0.407223	4.367	1.4e-05
12	0.403424	4.3262	1.6e-05
13	0.285622	3.063	0.001365
14	0.156532	1.6786	0.047971
15	0.071939	0.7715	0.221007
16	0.045001	0.4826	0.315154
17	0.05268	0.5649	0.286611
18	0.051202	0.5491	0.292009
19	0.055592	0.5962	0.276121
20	0.075954	0.8145	0.208516
21	0.127763	1.3701	0.086662

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.818236	8.7746	0
2	-0.253233	-2.7156	0.003818
3	0.015725	0.1686	0.43319
4	0.10582	1.1348	0.129412
5	0.065382	0.7011	0.242315
6	0.005356	0.0574	0.47715
7	0.081973	0.8791	0.1906
8	0.058929	0.6319	0.26434
9	0.14417	1.5461	0.062419
10	0.147864	1.5857	0.05778
11	0.030724	0.3295	0.371197
12	0.003727	0.04	0.484094
13	-0.249348	-2.674	0.004294
14	0.000633	0.0068	0.497297
15	0.004906	0.0526	0.479068
16	-0.002383	-0.0255	0.48983
17	-0.012509	-0.1341	0.44676
18	-0.051413	-0.5513	0.291232
19	0.011338	0.1216	0.451718
20	0.036896	0.3957	0.346542
21	0.072151	0.7737	0.220338

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.818236 & 8.7746 & 0 \tabularnewline
2 & -0.253233 & -2.7156 & 0.003818 \tabularnewline
3 & 0.015725 & 0.1686 & 0.43319 \tabularnewline
4 & 0.10582 & 1.1348 & 0.129412 \tabularnewline
5 & 0.065382 & 0.7011 & 0.242315 \tabularnewline
6 & 0.005356 & 0.0574 & 0.47715 \tabularnewline
7 & 0.081973 & 0.8791 & 0.1906 \tabularnewline
8 & 0.058929 & 0.6319 & 0.26434 \tabularnewline
9 & 0.14417 & 1.5461 & 0.062419 \tabularnewline
10 & 0.147864 & 1.5857 & 0.05778 \tabularnewline
11 & 0.030724 & 0.3295 & 0.371197 \tabularnewline
12 & 0.003727 & 0.04 & 0.484094 \tabularnewline
13 & -0.249348 & -2.674 & 0.004294 \tabularnewline
14 & 0.000633 & 0.0068 & 0.497297 \tabularnewline
15 & 0.004906 & 0.0526 & 0.479068 \tabularnewline
16 & -0.002383 & -0.0255 & 0.48983 \tabularnewline
17 & -0.012509 & -0.1341 & 0.44676 \tabularnewline
18 & -0.051413 & -0.5513 & 0.291232 \tabularnewline
19 & 0.011338 & 0.1216 & 0.451718 \tabularnewline
20 & 0.036896 & 0.3957 & 0.346542 \tabularnewline
21 & 0.072151 & 0.7737 & 0.220338 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301240&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]0.818236[/C][C]8.7746[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.253233[/C][C]-2.7156[/C][C]0.003818[/C][/ROW]
[ROW][C]3[/C][C]0.015725[/C][C]0.1686[/C][C]0.43319[/C][/ROW]
[ROW][C]4[/C][C]0.10582[/C][C]1.1348[/C][C]0.129412[/C][/ROW]
[ROW][C]5[/C][C]0.065382[/C][C]0.7011[/C][C]0.242315[/C][/ROW]
[ROW][C]6[/C][C]0.005356[/C][C]0.0574[/C][C]0.47715[/C][/ROW]
[ROW][C]7[/C][C]0.081973[/C][C]0.8791[/C][C]0.1906[/C][/ROW]
[ROW][C]8[/C][C]0.058929[/C][C]0.6319[/C][C]0.26434[/C][/ROW]
[ROW][C]9[/C][C]0.14417[/C][C]1.5461[/C][C]0.062419[/C][/ROW]
[ROW][C]10[/C][C]0.147864[/C][C]1.5857[/C][C]0.05778[/C][/ROW]
[ROW][C]11[/C][C]0.030724[/C][C]0.3295[/C][C]0.371197[/C][/ROW]
[ROW][C]12[/C][C]0.003727[/C][C]0.04[/C][C]0.484094[/C][/ROW]
[ROW][C]13[/C][C]-0.249348[/C][C]-2.674[/C][C]0.004294[/C][/ROW]
[ROW][C]14[/C][C]0.000633[/C][C]0.0068[/C][C]0.497297[/C][/ROW]
[ROW][C]15[/C][C]0.004906[/C][C]0.0526[/C][C]0.479068[/C][/ROW]
[ROW][C]16[/C][C]-0.002383[/C][C]-0.0255[/C][C]0.48983[/C][/ROW]
[ROW][C]17[/C][C]-0.012509[/C][C]-0.1341[/C][C]0.44676[/C][/ROW]
[ROW][C]18[/C][C]-0.051413[/C][C]-0.5513[/C][C]0.291232[/C][/ROW]
[ROW][C]19[/C][C]0.011338[/C][C]0.1216[/C][C]0.451718[/C][/ROW]
[ROW][C]20[/C][C]0.036896[/C][C]0.3957[/C][C]0.346542[/C][/ROW]
[ROW][C]21[/C][C]0.072151[/C][C]0.7737[/C][C]0.220338[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301240&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301240&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	0.818236	8.7746	0
2	-0.253233	-2.7156	0.003818
3	0.015725	0.1686	0.43319
4	0.10582	1.1348	0.129412
5	0.065382	0.7011	0.242315
6	0.005356	0.0574	0.47715
7	0.081973	0.8791	0.1906
8	0.058929	0.6319	0.26434
9	0.14417	1.5461	0.062419
10	0.147864	1.5857	0.05778
11	0.030724	0.3295	0.371197
12	0.003727	0.04	0.484094
13	-0.249348	-2.674	0.004294
14	0.000633	0.0068	0.497297
15	0.004906	0.0526	0.479068
16	-0.002383	-0.0255	0.48983
17	-0.012509	-0.1341	0.44676
18	-0.051413	-0.5513	0.291232
19	0.011338	0.1216	0.451718
20	0.036896	0.3957	0.346542
21	0.072151	0.7737	0.220338

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