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

Mon, 21 Nov 2016 20:45:10 +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/21/t1479757527rmkook3mh9t7iso.htm/, Retrieved Mon, 06 May 2024 17:22:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296881, Retrieved Mon, 06 May 2024 17:22:02 +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 Autocor 1] [2016-11-21 19:45:10] [d42b2dfaed369a60e2334709a5cede2f] [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=296881&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=296881&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296881&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	0.956377	9.6589	0
2	0.929636	9.3889	0
3	0.913754	9.2285	0
4	0.873461	8.8215	0
5	0.851147	8.5962	0
6	0.837961	8.463	0
7	0.800442	8.0841	0
8	0.769859	7.7752	0
9	0.746399	7.5383	0
10	0.702564	7.0955	0
11	0.67856	6.8531	0
12	0.657661	6.642	0
13	0.610078	6.1615	0
14	0.573508	5.7921	0
15	0.549087	5.5455	0
16	0.509743	5.1481	1e-06
17	0.47849	4.8325	2e-06
18	0.459635	4.6421	5e-06
19	0.425364	4.296	2e-05
20	0.394575	3.985	6.3e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956377 & 9.6589 & 0 \tabularnewline
2 & 0.929636 & 9.3889 & 0 \tabularnewline
3 & 0.913754 & 9.2285 & 0 \tabularnewline
4 & 0.873461 & 8.8215 & 0 \tabularnewline
5 & 0.851147 & 8.5962 & 0 \tabularnewline
6 & 0.837961 & 8.463 & 0 \tabularnewline
7 & 0.800442 & 8.0841 & 0 \tabularnewline
8 & 0.769859 & 7.7752 & 0 \tabularnewline
9 & 0.746399 & 7.5383 & 0 \tabularnewline
10 & 0.702564 & 7.0955 & 0 \tabularnewline
11 & 0.67856 & 6.8531 & 0 \tabularnewline
12 & 0.657661 & 6.642 & 0 \tabularnewline
13 & 0.610078 & 6.1615 & 0 \tabularnewline
14 & 0.573508 & 5.7921 & 0 \tabularnewline
15 & 0.549087 & 5.5455 & 0 \tabularnewline
16 & 0.509743 & 5.1481 & 1e-06 \tabularnewline
17 & 0.47849 & 4.8325 & 2e-06 \tabularnewline
18 & 0.459635 & 4.6421 & 5e-06 \tabularnewline
19 & 0.425364 & 4.296 & 2e-05 \tabularnewline
20 & 0.394575 & 3.985 & 6.3e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296881&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]0.956377[/C][C]9.6589[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.929636[/C][C]9.3889[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.913754[/C][C]9.2285[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.873461[/C][C]8.8215[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.851147[/C][C]8.5962[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.837961[/C][C]8.463[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.800442[/C][C]8.0841[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.769859[/C][C]7.7752[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.746399[/C][C]7.5383[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.702564[/C][C]7.0955[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.67856[/C][C]6.8531[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.657661[/C][C]6.642[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.610078[/C][C]6.1615[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.573508[/C][C]5.7921[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.549087[/C][C]5.5455[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.509743[/C][C]5.1481[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]0.47849[/C][C]4.8325[/C][C]2e-06[/C][/ROW]
[ROW][C]18[/C][C]0.459635[/C][C]4.6421[/C][C]5e-06[/C][/ROW]
[ROW][C]19[/C][C]0.425364[/C][C]4.296[/C][C]2e-05[/C][/ROW]
[ROW][C]20[/C][C]0.394575[/C][C]3.985[/C][C]6.3e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296881&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296881&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	0.956377	9.6589	0
2	0.929636	9.3889	0
3	0.913754	9.2285	0
4	0.873461	8.8215	0
5	0.851147	8.5962	0
6	0.837961	8.463	0
7	0.800442	8.0841	0
8	0.769859	7.7752	0
9	0.746399	7.5383	0
10	0.702564	7.0955	0
11	0.67856	6.8531	0
12	0.657661	6.642	0
13	0.610078	6.1615	0
14	0.573508	5.7921	0
15	0.549087	5.5455	0
16	0.509743	5.1481	1e-06
17	0.47849	4.8325	2e-06
18	0.459635	4.6421	5e-06
19	0.425364	4.296	2e-05
20	0.394575	3.985	6.3e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.956377	9.6589	0
2	0.175523	1.7727	0.039632
3	0.155479	1.5703	0.059726
4	-0.247855	-2.5032	0.006947
5	0.123414	1.2464	0.107733
6	0.103832	1.0487	0.148407
7	-0.180177	-1.8197	0.035869
8	-0.073912	-0.7465	0.22855
9	0.018743	0.1893	0.425117
10	-0.125119	-1.2636	0.10462
11	0.125364	1.2661	0.104178
12	-0.009811	-0.0991	0.460633
13	-0.211547	-2.1365	0.017514
14	-0.072781	-0.7351	0.231997
15	0.136973	1.3834	0.084788
16	0.02567	0.2592	0.397983
17	-0.085925	-0.8678	0.19377
18	0.042729	0.4315	0.333493
19	0.021008	0.2122	0.416197
20	-0.043135	-0.4356	0.332007

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.956377 & 9.6589 & 0 \tabularnewline
2 & 0.175523 & 1.7727 & 0.039632 \tabularnewline
3 & 0.155479 & 1.5703 & 0.059726 \tabularnewline
4 & -0.247855 & -2.5032 & 0.006947 \tabularnewline
5 & 0.123414 & 1.2464 & 0.107733 \tabularnewline
6 & 0.103832 & 1.0487 & 0.148407 \tabularnewline
7 & -0.180177 & -1.8197 & 0.035869 \tabularnewline
8 & -0.073912 & -0.7465 & 0.22855 \tabularnewline
9 & 0.018743 & 0.1893 & 0.425117 \tabularnewline
10 & -0.125119 & -1.2636 & 0.10462 \tabularnewline
11 & 0.125364 & 1.2661 & 0.104178 \tabularnewline
12 & -0.009811 & -0.0991 & 0.460633 \tabularnewline
13 & -0.211547 & -2.1365 & 0.017514 \tabularnewline
14 & -0.072781 & -0.7351 & 0.231997 \tabularnewline
15 & 0.136973 & 1.3834 & 0.084788 \tabularnewline
16 & 0.02567 & 0.2592 & 0.397983 \tabularnewline
17 & -0.085925 & -0.8678 & 0.19377 \tabularnewline
18 & 0.042729 & 0.4315 & 0.333493 \tabularnewline
19 & 0.021008 & 0.2122 & 0.416197 \tabularnewline
20 & -0.043135 & -0.4356 & 0.332007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296881&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]0.956377[/C][C]9.6589[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.175523[/C][C]1.7727[/C][C]0.039632[/C][/ROW]
[ROW][C]3[/C][C]0.155479[/C][C]1.5703[/C][C]0.059726[/C][/ROW]
[ROW][C]4[/C][C]-0.247855[/C][C]-2.5032[/C][C]0.006947[/C][/ROW]
[ROW][C]5[/C][C]0.123414[/C][C]1.2464[/C][C]0.107733[/C][/ROW]
[ROW][C]6[/C][C]0.103832[/C][C]1.0487[/C][C]0.148407[/C][/ROW]
[ROW][C]7[/C][C]-0.180177[/C][C]-1.8197[/C][C]0.035869[/C][/ROW]
[ROW][C]8[/C][C]-0.073912[/C][C]-0.7465[/C][C]0.22855[/C][/ROW]
[ROW][C]9[/C][C]0.018743[/C][C]0.1893[/C][C]0.425117[/C][/ROW]
[ROW][C]10[/C][C]-0.125119[/C][C]-1.2636[/C][C]0.10462[/C][/ROW]
[ROW][C]11[/C][C]0.125364[/C][C]1.2661[/C][C]0.104178[/C][/ROW]
[ROW][C]12[/C][C]-0.009811[/C][C]-0.0991[/C][C]0.460633[/C][/ROW]
[ROW][C]13[/C][C]-0.211547[/C][C]-2.1365[/C][C]0.017514[/C][/ROW]
[ROW][C]14[/C][C]-0.072781[/C][C]-0.7351[/C][C]0.231997[/C][/ROW]
[ROW][C]15[/C][C]0.136973[/C][C]1.3834[/C][C]0.084788[/C][/ROW]
[ROW][C]16[/C][C]0.02567[/C][C]0.2592[/C][C]0.397983[/C][/ROW]
[ROW][C]17[/C][C]-0.085925[/C][C]-0.8678[/C][C]0.19377[/C][/ROW]
[ROW][C]18[/C][C]0.042729[/C][C]0.4315[/C][C]0.333493[/C][/ROW]
[ROW][C]19[/C][C]0.021008[/C][C]0.2122[/C][C]0.416197[/C][/ROW]
[ROW][C]20[/C][C]-0.043135[/C][C]-0.4356[/C][C]0.332007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296881&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296881&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	0.956377	9.6589	0
2	0.175523	1.7727	0.039632
3	0.155479	1.5703	0.059726
4	-0.247855	-2.5032	0.006947
5	0.123414	1.2464	0.107733
6	0.103832	1.0487	0.148407
7	-0.180177	-1.8197	0.035869
8	-0.073912	-0.7465	0.22855
9	0.018743	0.1893	0.425117
10	-0.125119	-1.2636	0.10462
11	0.125364	1.2661	0.104178
12	-0.009811	-0.0991	0.460633
13	-0.211547	-2.1365	0.017514
14	-0.072781	-0.7351	0.231997
15	0.136973	1.3834	0.084788
16	0.02567	0.2592	0.397983
17	-0.085925	-0.8678	0.19377
18	0.042729	0.4315	0.333493
19	0.021008	0.2122	0.416197
20	-0.043135	-0.4356	0.332007

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