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, 20 Dec 2016 12:37:14 +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/t14822344299z6v8fgwto9d3lk.htm/, Retrieved Sat, 27 Apr 2024 23:51:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301619, Retrieved Sat, 27 Apr 2024 23:51:58 +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] [P Autocorrelation...] [2016-12-20 11:37:14] [86c9a777e8dbb7ef3face68c75fc8376] [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=301619&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=301619&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301619&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	0.81622	8.7148	0
2	0.761121	8.1265	0
3	0.765853	8.1771	0
4	0.704939	7.5267	0
5	0.678401	7.2433	0
6	0.664336	7.0932	0
7	0.614704	6.5632	0
8	0.601635	6.4237	0
9	0.589829	6.2977	0
10	0.530272	5.6618	0
11	0.571348	6.1003	0
12	0.608431	6.4963	0
13	0.50141	5.3536	0
14	0.474668	5.0681	1e-06
15	0.47766	5.1	1e-06
16	0.428286	4.5728	6e-06
17	0.399453	4.265	2.1e-05
18	0.372691	3.9792	6.1e-05
19	0.352801	3.7669	0.000132
20	0.326957	3.4909	0.000343

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.81622 & 8.7148 & 0 \tabularnewline
2 & 0.761121 & 8.1265 & 0 \tabularnewline
3 & 0.765853 & 8.1771 & 0 \tabularnewline
4 & 0.704939 & 7.5267 & 0 \tabularnewline
5 & 0.678401 & 7.2433 & 0 \tabularnewline
6 & 0.664336 & 7.0932 & 0 \tabularnewline
7 & 0.614704 & 6.5632 & 0 \tabularnewline
8 & 0.601635 & 6.4237 & 0 \tabularnewline
9 & 0.589829 & 6.2977 & 0 \tabularnewline
10 & 0.530272 & 5.6618 & 0 \tabularnewline
11 & 0.571348 & 6.1003 & 0 \tabularnewline
12 & 0.608431 & 6.4963 & 0 \tabularnewline
13 & 0.50141 & 5.3536 & 0 \tabularnewline
14 & 0.474668 & 5.0681 & 1e-06 \tabularnewline
15 & 0.47766 & 5.1 & 1e-06 \tabularnewline
16 & 0.428286 & 4.5728 & 6e-06 \tabularnewline
17 & 0.399453 & 4.265 & 2.1e-05 \tabularnewline
18 & 0.372691 & 3.9792 & 6.1e-05 \tabularnewline
19 & 0.352801 & 3.7669 & 0.000132 \tabularnewline
20 & 0.326957 & 3.4909 & 0.000343 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301619&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]0.81622[/C][C]8.7148[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.761121[/C][C]8.1265[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.765853[/C][C]8.1771[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.704939[/C][C]7.5267[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.678401[/C][C]7.2433[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.664336[/C][C]7.0932[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.614704[/C][C]6.5632[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.601635[/C][C]6.4237[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.589829[/C][C]6.2977[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.530272[/C][C]5.6618[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.571348[/C][C]6.1003[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.608431[/C][C]6.4963[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.50141[/C][C]5.3536[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.474668[/C][C]5.0681[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.47766[/C][C]5.1[/C][C]1e-06[/C][/ROW]
[ROW][C]16[/C][C]0.428286[/C][C]4.5728[/C][C]6e-06[/C][/ROW]
[ROW][C]17[/C][C]0.399453[/C][C]4.265[/C][C]2.1e-05[/C][/ROW]
[ROW][C]18[/C][C]0.372691[/C][C]3.9792[/C][C]6.1e-05[/C][/ROW]
[ROW][C]19[/C][C]0.352801[/C][C]3.7669[/C][C]0.000132[/C][/ROW]
[ROW][C]20[/C][C]0.326957[/C][C]3.4909[/C][C]0.000343[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301619&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301619&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	0.81622	8.7148	0
2	0.761121	8.1265	0
3	0.765853	8.1771	0
4	0.704939	7.5267	0
5	0.678401	7.2433	0
6	0.664336	7.0932	0
7	0.614704	6.5632	0
8	0.601635	6.4237	0
9	0.589829	6.2977	0
10	0.530272	5.6618	0
11	0.571348	6.1003	0
12	0.608431	6.4963	0
13	0.50141	5.3536	0
14	0.474668	5.0681	1e-06
15	0.47766	5.1	1e-06
16	0.428286	4.5728	6e-06
17	0.399453	4.265	2.1e-05
18	0.372691	3.9792	6.1e-05
19	0.352801	3.7669	0.000132
20	0.326957	3.4909	0.000343

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.81622	8.7148	0
2	0.284332	3.0358	0.001486
3	0.290653	3.1033	0.001207
4	-0.012672	-0.1353	0.446309
5	0.063103	0.6738	0.250915
6	0.046686	0.4985	0.309557
7	-0.043391	-0.4633	0.322022
8	0.050344	0.5375	0.295975
9	0.034343	0.3667	0.357269
10	-0.096631	-1.0317	0.15219
11	0.218686	2.3349	0.010648
12	0.196119	2.094	0.019239
13	-0.281101	-3.0013	0.001651
14	-0.117757	-1.2573	0.105607
15	0.019128	0.2042	0.419267
16	-0.01244	-0.1328	0.447285
17	-0.073099	-0.7805	0.218362
18	-0.044025	-0.4701	0.319604
19	0.091897	0.9812	0.164289
20	-0.068564	-0.7321	0.232817

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.81622 & 8.7148 & 0 \tabularnewline
2 & 0.284332 & 3.0358 & 0.001486 \tabularnewline
3 & 0.290653 & 3.1033 & 0.001207 \tabularnewline
4 & -0.012672 & -0.1353 & 0.446309 \tabularnewline
5 & 0.063103 & 0.6738 & 0.250915 \tabularnewline
6 & 0.046686 & 0.4985 & 0.309557 \tabularnewline
7 & -0.043391 & -0.4633 & 0.322022 \tabularnewline
8 & 0.050344 & 0.5375 & 0.295975 \tabularnewline
9 & 0.034343 & 0.3667 & 0.357269 \tabularnewline
10 & -0.096631 & -1.0317 & 0.15219 \tabularnewline
11 & 0.218686 & 2.3349 & 0.010648 \tabularnewline
12 & 0.196119 & 2.094 & 0.019239 \tabularnewline
13 & -0.281101 & -3.0013 & 0.001651 \tabularnewline
14 & -0.117757 & -1.2573 & 0.105607 \tabularnewline
15 & 0.019128 & 0.2042 & 0.419267 \tabularnewline
16 & -0.01244 & -0.1328 & 0.447285 \tabularnewline
17 & -0.073099 & -0.7805 & 0.218362 \tabularnewline
18 & -0.044025 & -0.4701 & 0.319604 \tabularnewline
19 & 0.091897 & 0.9812 & 0.164289 \tabularnewline
20 & -0.068564 & -0.7321 & 0.232817 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301619&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]0.81622[/C][C]8.7148[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.284332[/C][C]3.0358[/C][C]0.001486[/C][/ROW]
[ROW][C]3[/C][C]0.290653[/C][C]3.1033[/C][C]0.001207[/C][/ROW]
[ROW][C]4[/C][C]-0.012672[/C][C]-0.1353[/C][C]0.446309[/C][/ROW]
[ROW][C]5[/C][C]0.063103[/C][C]0.6738[/C][C]0.250915[/C][/ROW]
[ROW][C]6[/C][C]0.046686[/C][C]0.4985[/C][C]0.309557[/C][/ROW]
[ROW][C]7[/C][C]-0.043391[/C][C]-0.4633[/C][C]0.322022[/C][/ROW]
[ROW][C]8[/C][C]0.050344[/C][C]0.5375[/C][C]0.295975[/C][/ROW]
[ROW][C]9[/C][C]0.034343[/C][C]0.3667[/C][C]0.357269[/C][/ROW]
[ROW][C]10[/C][C]-0.096631[/C][C]-1.0317[/C][C]0.15219[/C][/ROW]
[ROW][C]11[/C][C]0.218686[/C][C]2.3349[/C][C]0.010648[/C][/ROW]
[ROW][C]12[/C][C]0.196119[/C][C]2.094[/C][C]0.019239[/C][/ROW]
[ROW][C]13[/C][C]-0.281101[/C][C]-3.0013[/C][C]0.001651[/C][/ROW]
[ROW][C]14[/C][C]-0.117757[/C][C]-1.2573[/C][C]0.105607[/C][/ROW]
[ROW][C]15[/C][C]0.019128[/C][C]0.2042[/C][C]0.419267[/C][/ROW]
[ROW][C]16[/C][C]-0.01244[/C][C]-0.1328[/C][C]0.447285[/C][/ROW]
[ROW][C]17[/C][C]-0.073099[/C][C]-0.7805[/C][C]0.218362[/C][/ROW]
[ROW][C]18[/C][C]-0.044025[/C][C]-0.4701[/C][C]0.319604[/C][/ROW]
[ROW][C]19[/C][C]0.091897[/C][C]0.9812[/C][C]0.164289[/C][/ROW]
[ROW][C]20[/C][C]-0.068564[/C][C]-0.7321[/C][C]0.232817[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301619&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301619&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	0.81622	8.7148	0
2	0.284332	3.0358	0.001486
3	0.290653	3.1033	0.001207
4	-0.012672	-0.1353	0.446309
5	0.063103	0.6738	0.250915
6	0.046686	0.4985	0.309557
7	-0.043391	-0.4633	0.322022
8	0.050344	0.5375	0.295975
9	0.034343	0.3667	0.357269
10	-0.096631	-1.0317	0.15219
11	0.218686	2.3349	0.010648
12	0.196119	2.094	0.019239
13	-0.281101	-3.0013	0.001651
14	-0.117757	-1.2573	0.105607
15	0.019128	0.2042	0.419267
16	-0.01244	-0.1328	0.447285
17	-0.073099	-0.7805	0.218362
18	-0.044025	-0.4701	0.319604
19	0.091897	0.9812	0.164289
20	-0.068564	-0.7321	0.232817

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 = 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