Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Mar 2017 18:30:16 +0000

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/2017/Mar/19/t148994825687p7cs4r9tr9hps.htm/, Retrieved Wed, 15 May 2024 23:39:13 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 23:39:13 +0200

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

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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.967568	8.2101	0
2	0.927895	7.8735	0
3	0.886428	7.5216	0
4	0.844226	7.1635	0
5	0.798582	6.7762	0
6	0.749699	6.3614	0
7	0.699106	5.9321	0
8	0.649097	5.5078	0
9	0.598952	5.0823	1e-06
10	0.551727	4.6816	7e-06
11	0.502995	4.2681	3e-05
12	0.456231	3.8713	0.000118
13	0.413868	3.5118	0.000386
14	0.372449	3.1603	0.001153
15	0.339566	2.8813	0.002607
16	0.306633	2.6019	0.005624
17	0.274568	2.3298	0.011313
18	0.243371	2.0651	0.021259

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.967568 & 8.2101 & 0 \tabularnewline
2 & 0.927895 & 7.8735 & 0 \tabularnewline
3 & 0.886428 & 7.5216 & 0 \tabularnewline
4 & 0.844226 & 7.1635 & 0 \tabularnewline
5 & 0.798582 & 6.7762 & 0 \tabularnewline
6 & 0.749699 & 6.3614 & 0 \tabularnewline
7 & 0.699106 & 5.9321 & 0 \tabularnewline
8 & 0.649097 & 5.5078 & 0 \tabularnewline
9 & 0.598952 & 5.0823 & 1e-06 \tabularnewline
10 & 0.551727 & 4.6816 & 7e-06 \tabularnewline
11 & 0.502995 & 4.2681 & 3e-05 \tabularnewline
12 & 0.456231 & 3.8713 & 0.000118 \tabularnewline
13 & 0.413868 & 3.5118 & 0.000386 \tabularnewline
14 & 0.372449 & 3.1603 & 0.001153 \tabularnewline
15 & 0.339566 & 2.8813 & 0.002607 \tabularnewline
16 & 0.306633 & 2.6019 & 0.005624 \tabularnewline
17 & 0.274568 & 2.3298 & 0.011313 \tabularnewline
18 & 0.243371 & 2.0651 & 0.021259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.967568[/C][C]8.2101[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.927895[/C][C]7.8735[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.886428[/C][C]7.5216[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.844226[/C][C]7.1635[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.798582[/C][C]6.7762[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.749699[/C][C]6.3614[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.699106[/C][C]5.9321[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.649097[/C][C]5.5078[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.598952[/C][C]5.0823[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.551727[/C][C]4.6816[/C][C]7e-06[/C][/ROW]
[ROW][C]11[/C][C]0.502995[/C][C]4.2681[/C][C]3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.456231[/C][C]3.8713[/C][C]0.000118[/C][/ROW]
[ROW][C]13[/C][C]0.413868[/C][C]3.5118[/C][C]0.000386[/C][/ROW]
[ROW][C]14[/C][C]0.372449[/C][C]3.1603[/C][C]0.001153[/C][/ROW]
[ROW][C]15[/C][C]0.339566[/C][C]2.8813[/C][C]0.002607[/C][/ROW]
[ROW][C]16[/C][C]0.306633[/C][C]2.6019[/C][C]0.005624[/C][/ROW]
[ROW][C]17[/C][C]0.274568[/C][C]2.3298[/C][C]0.011313[/C][/ROW]
[ROW][C]18[/C][C]0.243371[/C][C]2.0651[/C][C]0.021259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.967568	8.2101	0
2	0.927895	7.8735	0
3	0.886428	7.5216	0
4	0.844226	7.1635	0
5	0.798582	6.7762	0
6	0.749699	6.3614	0
7	0.699106	5.9321	0
8	0.649097	5.5078	0
9	0.598952	5.0823	1e-06
10	0.551727	4.6816	7e-06
11	0.502995	4.2681	3e-05
12	0.456231	3.8713	0.000118
13	0.413868	3.5118	0.000386
14	0.372449	3.1603	0.001153
15	0.339566	2.8813	0.002607
16	0.306633	2.6019	0.005624
17	0.274568	2.3298	0.011313
18	0.243371	2.0651	0.021259

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.967568	8.2101	0
2	-0.129942	-1.1026	0.136937
3	-0.036784	-0.3121	0.377926
4	-0.029014	-0.2462	0.403117
5	-0.075517	-0.6408	0.261849
6	-0.065981	-0.5599	0.288653
7	-0.044431	-0.377	0.353637
8	-0.014421	-0.1224	0.451474
9	-0.031971	-0.2713	0.393476
10	0.019872	0.1686	0.433284
11	-0.060695	-0.515	0.304059
12	0.004039	0.0343	0.486379
13	0.032846	0.2787	0.390633
14	-0.034122	-0.2895	0.386503
15	0.104268	0.8847	0.189621
16	-0.057612	-0.4889	0.313216
17	-0.018658	-0.1583	0.437324
18	-0.0223	-0.1892	0.425225

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.967568 & 8.2101 & 0 \tabularnewline
2 & -0.129942 & -1.1026 & 0.136937 \tabularnewline
3 & -0.036784 & -0.3121 & 0.377926 \tabularnewline
4 & -0.029014 & -0.2462 & 0.403117 \tabularnewline
5 & -0.075517 & -0.6408 & 0.261849 \tabularnewline
6 & -0.065981 & -0.5599 & 0.288653 \tabularnewline
7 & -0.044431 & -0.377 & 0.353637 \tabularnewline
8 & -0.014421 & -0.1224 & 0.451474 \tabularnewline
9 & -0.031971 & -0.2713 & 0.393476 \tabularnewline
10 & 0.019872 & 0.1686 & 0.433284 \tabularnewline
11 & -0.060695 & -0.515 & 0.304059 \tabularnewline
12 & 0.004039 & 0.0343 & 0.486379 \tabularnewline
13 & 0.032846 & 0.2787 & 0.390633 \tabularnewline
14 & -0.034122 & -0.2895 & 0.386503 \tabularnewline
15 & 0.104268 & 0.8847 & 0.189621 \tabularnewline
16 & -0.057612 & -0.4889 & 0.313216 \tabularnewline
17 & -0.018658 & -0.1583 & 0.437324 \tabularnewline
18 & -0.0223 & -0.1892 & 0.425225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.967568[/C][C]8.2101[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.129942[/C][C]-1.1026[/C][C]0.136937[/C][/ROW]
[ROW][C]3[/C][C]-0.036784[/C][C]-0.3121[/C][C]0.377926[/C][/ROW]
[ROW][C]4[/C][C]-0.029014[/C][C]-0.2462[/C][C]0.403117[/C][/ROW]
[ROW][C]5[/C][C]-0.075517[/C][C]-0.6408[/C][C]0.261849[/C][/ROW]
[ROW][C]6[/C][C]-0.065981[/C][C]-0.5599[/C][C]0.288653[/C][/ROW]
[ROW][C]7[/C][C]-0.044431[/C][C]-0.377[/C][C]0.353637[/C][/ROW]
[ROW][C]8[/C][C]-0.014421[/C][C]-0.1224[/C][C]0.451474[/C][/ROW]
[ROW][C]9[/C][C]-0.031971[/C][C]-0.2713[/C][C]0.393476[/C][/ROW]
[ROW][C]10[/C][C]0.019872[/C][C]0.1686[/C][C]0.433284[/C][/ROW]
[ROW][C]11[/C][C]-0.060695[/C][C]-0.515[/C][C]0.304059[/C][/ROW]
[ROW][C]12[/C][C]0.004039[/C][C]0.0343[/C][C]0.486379[/C][/ROW]
[ROW][C]13[/C][C]0.032846[/C][C]0.2787[/C][C]0.390633[/C][/ROW]
[ROW][C]14[/C][C]-0.034122[/C][C]-0.2895[/C][C]0.386503[/C][/ROW]
[ROW][C]15[/C][C]0.104268[/C][C]0.8847[/C][C]0.189621[/C][/ROW]
[ROW][C]16[/C][C]-0.057612[/C][C]-0.4889[/C][C]0.313216[/C][/ROW]
[ROW][C]17[/C][C]-0.018658[/C][C]-0.1583[/C][C]0.437324[/C][/ROW]
[ROW][C]18[/C][C]-0.0223[/C][C]-0.1892[/C][C]0.425225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.967568	8.2101	0
2	-0.129942	-1.1026	0.136937
3	-0.036784	-0.3121	0.377926
4	-0.029014	-0.2462	0.403117
5	-0.075517	-0.6408	0.261849
6	-0.065981	-0.5599	0.288653
7	-0.044431	-0.377	0.353637
8	-0.014421	-0.1224	0.451474
9	-0.031971	-0.2713	0.393476
10	0.019872	0.1686	0.433284
11	-0.060695	-0.515	0.304059
12	0.004039	0.0343	0.486379
13	0.032846	0.2787	0.390633
14	-0.034122	-0.2895	0.386503
15	0.104268	0.8847	0.189621
16	-0.057612	-0.4889	0.313216
17	-0.018658	-0.1583	0.437324
18	-0.0223	-0.1892	0.425225

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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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