Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

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

Tue, 29 Nov 2016 16:32:36 +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/Nov/29/t1480433660u0xstqm935nm3ro.htm/, Retrieved Tue, 07 May 2024 09:09:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297275, Retrieved Tue, 07 May 2024 09:09:29 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

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] [Partial auto corr...] [2016-11-22 11:20:14] [6645d1b9dc3eb52796fd44b1f711efc9]
-   PD    [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-11-29 15:32:36] [8b2c6464bd93a4843579a2d15e9e0aeb] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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=297275&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=297275&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297275&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	0.931142	10.0287	0
2	0.870221	9.3726	0
3	0.803186	8.6506	0
4	0.741281	7.9838	0
5	0.682329	7.3489	0
6	0.62745	6.7578	0
7	0.563967	6.0741	0
8	0.504665	5.4354	0
9	0.447154	4.816	2e-06
10	0.39165	4.2182	2.5e-05
11	0.345347	3.7195	0.000155
12	0.309928	3.338	0.000567
13	0.274787	2.9596	0.001868
14	0.248183	2.673	0.0043
15	0.226244	2.4367	0.00817
16	0.204604	2.2037	0.014762
17	0.184553	1.9877	0.024601
18	0.166859	1.7971	0.037459
19	0.147992	1.5939	0.056837
20	0.129396	1.3936	0.083046

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931142 & 10.0287 & 0 \tabularnewline
2 & 0.870221 & 9.3726 & 0 \tabularnewline
3 & 0.803186 & 8.6506 & 0 \tabularnewline
4 & 0.741281 & 7.9838 & 0 \tabularnewline
5 & 0.682329 & 7.3489 & 0 \tabularnewline
6 & 0.62745 & 6.7578 & 0 \tabularnewline
7 & 0.563967 & 6.0741 & 0 \tabularnewline
8 & 0.504665 & 5.4354 & 0 \tabularnewline
9 & 0.447154 & 4.816 & 2e-06 \tabularnewline
10 & 0.39165 & 4.2182 & 2.5e-05 \tabularnewline
11 & 0.345347 & 3.7195 & 0.000155 \tabularnewline
12 & 0.309928 & 3.338 & 0.000567 \tabularnewline
13 & 0.274787 & 2.9596 & 0.001868 \tabularnewline
14 & 0.248183 & 2.673 & 0.0043 \tabularnewline
15 & 0.226244 & 2.4367 & 0.00817 \tabularnewline
16 & 0.204604 & 2.2037 & 0.014762 \tabularnewline
17 & 0.184553 & 1.9877 & 0.024601 \tabularnewline
18 & 0.166859 & 1.7971 & 0.037459 \tabularnewline
19 & 0.147992 & 1.5939 & 0.056837 \tabularnewline
20 & 0.129396 & 1.3936 & 0.083046 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297275&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]0.931142[/C][C]10.0287[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.870221[/C][C]9.3726[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.803186[/C][C]8.6506[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.741281[/C][C]7.9838[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.682329[/C][C]7.3489[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.62745[/C][C]6.7578[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.563967[/C][C]6.0741[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.504665[/C][C]5.4354[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.447154[/C][C]4.816[/C][C]2e-06[/C][/ROW]
[ROW][C]10[/C][C]0.39165[/C][C]4.2182[/C][C]2.5e-05[/C][/ROW]
[ROW][C]11[/C][C]0.345347[/C][C]3.7195[/C][C]0.000155[/C][/ROW]
[ROW][C]12[/C][C]0.309928[/C][C]3.338[/C][C]0.000567[/C][/ROW]
[ROW][C]13[/C][C]0.274787[/C][C]2.9596[/C][C]0.001868[/C][/ROW]
[ROW][C]14[/C][C]0.248183[/C][C]2.673[/C][C]0.0043[/C][/ROW]
[ROW][C]15[/C][C]0.226244[/C][C]2.4367[/C][C]0.00817[/C][/ROW]
[ROW][C]16[/C][C]0.204604[/C][C]2.2037[/C][C]0.014762[/C][/ROW]
[ROW][C]17[/C][C]0.184553[/C][C]1.9877[/C][C]0.024601[/C][/ROW]
[ROW][C]18[/C][C]0.166859[/C][C]1.7971[/C][C]0.037459[/C][/ROW]
[ROW][C]19[/C][C]0.147992[/C][C]1.5939[/C][C]0.056837[/C][/ROW]
[ROW][C]20[/C][C]0.129396[/C][C]1.3936[/C][C]0.083046[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297275&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297275&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	0.931142	10.0287	0
2	0.870221	9.3726	0
3	0.803186	8.6506	0
4	0.741281	7.9838	0
5	0.682329	7.3489	0
6	0.62745	6.7578	0
7	0.563967	6.0741	0
8	0.504665	5.4354	0
9	0.447154	4.816	2e-06
10	0.39165	4.2182	2.5e-05
11	0.345347	3.7195	0.000155
12	0.309928	3.338	0.000567
13	0.274787	2.9596	0.001868
14	0.248183	2.673	0.0043
15	0.226244	2.4367	0.00817
16	0.204604	2.2037	0.014762
17	0.184553	1.9877	0.024601
18	0.166859	1.7971	0.037459
19	0.147992	1.5939	0.056837
20	0.129396	1.3936	0.083046

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.931142	10.0287	0
2	0.024033	0.2588	0.398108
3	-0.075376	-0.8118	0.209279
4	-0.003155	-0.034	0.486476
5	-0.00765	-0.0824	0.467239
6	-0.004609	-0.0496	0.480246
7	-0.096838	-1.043	0.149565
8	-0.016098	-0.1734	0.431329
9	-0.015051	-0.1621	0.435755
10	-0.027434	-0.2955	0.38408
11	0.029205	0.3145	0.376835
12	0.052554	0.566	0.286235
13	-0.018135	-0.1953	0.422741
14	0.03085	0.3323	0.370145
15	0.023471	0.2528	0.40044
16	-0.015128	-0.1629	0.435426
17	-0.014167	-0.1526	0.439497
18	-0.005088	-0.0548	0.478196
19	-0.020157	-0.2171	0.414255
20	-0.023961	-0.2581	0.398407

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931142 & 10.0287 & 0 \tabularnewline
2 & 0.024033 & 0.2588 & 0.398108 \tabularnewline
3 & -0.075376 & -0.8118 & 0.209279 \tabularnewline
4 & -0.003155 & -0.034 & 0.486476 \tabularnewline
5 & -0.00765 & -0.0824 & 0.467239 \tabularnewline
6 & -0.004609 & -0.0496 & 0.480246 \tabularnewline
7 & -0.096838 & -1.043 & 0.149565 \tabularnewline
8 & -0.016098 & -0.1734 & 0.431329 \tabularnewline
9 & -0.015051 & -0.1621 & 0.435755 \tabularnewline
10 & -0.027434 & -0.2955 & 0.38408 \tabularnewline
11 & 0.029205 & 0.3145 & 0.376835 \tabularnewline
12 & 0.052554 & 0.566 & 0.286235 \tabularnewline
13 & -0.018135 & -0.1953 & 0.422741 \tabularnewline
14 & 0.03085 & 0.3323 & 0.370145 \tabularnewline
15 & 0.023471 & 0.2528 & 0.40044 \tabularnewline
16 & -0.015128 & -0.1629 & 0.435426 \tabularnewline
17 & -0.014167 & -0.1526 & 0.439497 \tabularnewline
18 & -0.005088 & -0.0548 & 0.478196 \tabularnewline
19 & -0.020157 & -0.2171 & 0.414255 \tabularnewline
20 & -0.023961 & -0.2581 & 0.398407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297275&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]0.931142[/C][C]10.0287[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.024033[/C][C]0.2588[/C][C]0.398108[/C][/ROW]
[ROW][C]3[/C][C]-0.075376[/C][C]-0.8118[/C][C]0.209279[/C][/ROW]
[ROW][C]4[/C][C]-0.003155[/C][C]-0.034[/C][C]0.486476[/C][/ROW]
[ROW][C]5[/C][C]-0.00765[/C][C]-0.0824[/C][C]0.467239[/C][/ROW]
[ROW][C]6[/C][C]-0.004609[/C][C]-0.0496[/C][C]0.480246[/C][/ROW]
[ROW][C]7[/C][C]-0.096838[/C][C]-1.043[/C][C]0.149565[/C][/ROW]
[ROW][C]8[/C][C]-0.016098[/C][C]-0.1734[/C][C]0.431329[/C][/ROW]
[ROW][C]9[/C][C]-0.015051[/C][C]-0.1621[/C][C]0.435755[/C][/ROW]
[ROW][C]10[/C][C]-0.027434[/C][C]-0.2955[/C][C]0.38408[/C][/ROW]
[ROW][C]11[/C][C]0.029205[/C][C]0.3145[/C][C]0.376835[/C][/ROW]
[ROW][C]12[/C][C]0.052554[/C][C]0.566[/C][C]0.286235[/C][/ROW]
[ROW][C]13[/C][C]-0.018135[/C][C]-0.1953[/C][C]0.422741[/C][/ROW]
[ROW][C]14[/C][C]0.03085[/C][C]0.3323[/C][C]0.370145[/C][/ROW]
[ROW][C]15[/C][C]0.023471[/C][C]0.2528[/C][C]0.40044[/C][/ROW]
[ROW][C]16[/C][C]-0.015128[/C][C]-0.1629[/C][C]0.435426[/C][/ROW]
[ROW][C]17[/C][C]-0.014167[/C][C]-0.1526[/C][C]0.439497[/C][/ROW]
[ROW][C]18[/C][C]-0.005088[/C][C]-0.0548[/C][C]0.478196[/C][/ROW]
[ROW][C]19[/C][C]-0.020157[/C][C]-0.2171[/C][C]0.414255[/C][/ROW]
[ROW][C]20[/C][C]-0.023961[/C][C]-0.2581[/C][C]0.398407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297275&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297275&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	0.931142	10.0287	0
2	0.024033	0.2588	0.398108
3	-0.075376	-0.8118	0.209279
4	-0.003155	-0.034	0.486476
5	-0.00765	-0.0824	0.467239
6	-0.004609	-0.0496	0.480246
7	-0.096838	-1.043	0.149565
8	-0.016098	-0.1734	0.431329
9	-0.015051	-0.1621	0.435755
10	-0.027434	-0.2955	0.38408
11	0.029205	0.3145	0.376835
12	0.052554	0.566	0.286235
13	-0.018135	-0.1953	0.422741
14	0.03085	0.3323	0.370145
15	0.023471	0.2528	0.40044
16	-0.015128	-0.1629	0.435426
17	-0.014167	-0.1526	0.439497
18	-0.005088	-0.0548	0.478196
19	-0.020157	-0.2171	0.414255
20	-0.023961	-0.2581	0.398407

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 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ;

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