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

Wed, 04 Apr 2012 15:36:32 -0400

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/2012/Apr/04/t13335682652l1bqbjb73x2kig.htm/, Retrieved Sun, 28 Apr 2024 22:03:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164311, Retrieved Sun, 28 Apr 2024 22:03:07 +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

KDGP2W12

Estimated Impact

167

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Opgave6bis persoo...] [2012-04-04 19:36:32] [217ce5420aea0c151a6b1492c55ab0fd] [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	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164311&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164311&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.922888	7.1487	0
2	0.857935	6.6455	0
3	0.79104	6.1274	0
4	0.726338	5.6262	0
5	0.668287	5.1765	1e-06
6	0.612833	4.747	7e-06
7	0.555141	4.3001	3.2e-05
8	0.499281	3.8674	0.000137
9	0.455245	3.5263	0.000407
10	0.411555	3.1879	0.001139
11	0.383261	2.9687	0.002146
12	0.353111	2.7352	0.004093
13	0.323113	2.5028	0.007531
14	0.287337	2.2257	0.014902
15	0.266839	2.0669	0.021532
16	0.235901	1.8273	0.036316
17	0.20438	1.5831	0.059326

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.922888 & 7.1487 & 0 \tabularnewline
2 & 0.857935 & 6.6455 & 0 \tabularnewline
3 & 0.79104 & 6.1274 & 0 \tabularnewline
4 & 0.726338 & 5.6262 & 0 \tabularnewline
5 & 0.668287 & 5.1765 & 1e-06 \tabularnewline
6 & 0.612833 & 4.747 & 7e-06 \tabularnewline
7 & 0.555141 & 4.3001 & 3.2e-05 \tabularnewline
8 & 0.499281 & 3.8674 & 0.000137 \tabularnewline
9 & 0.455245 & 3.5263 & 0.000407 \tabularnewline
10 & 0.411555 & 3.1879 & 0.001139 \tabularnewline
11 & 0.383261 & 2.9687 & 0.002146 \tabularnewline
12 & 0.353111 & 2.7352 & 0.004093 \tabularnewline
13 & 0.323113 & 2.5028 & 0.007531 \tabularnewline
14 & 0.287337 & 2.2257 & 0.014902 \tabularnewline
15 & 0.266839 & 2.0669 & 0.021532 \tabularnewline
16 & 0.235901 & 1.8273 & 0.036316 \tabularnewline
17 & 0.20438 & 1.5831 & 0.059326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164311&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]0.922888[/C][C]7.1487[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.857935[/C][C]6.6455[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.79104[/C][C]6.1274[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.726338[/C][C]5.6262[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.668287[/C][C]5.1765[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.612833[/C][C]4.747[/C][C]7e-06[/C][/ROW]
[ROW][C]7[/C][C]0.555141[/C][C]4.3001[/C][C]3.2e-05[/C][/ROW]
[ROW][C]8[/C][C]0.499281[/C][C]3.8674[/C][C]0.000137[/C][/ROW]
[ROW][C]9[/C][C]0.455245[/C][C]3.5263[/C][C]0.000407[/C][/ROW]
[ROW][C]10[/C][C]0.411555[/C][C]3.1879[/C][C]0.001139[/C][/ROW]
[ROW][C]11[/C][C]0.383261[/C][C]2.9687[/C][C]0.002146[/C][/ROW]
[ROW][C]12[/C][C]0.353111[/C][C]2.7352[/C][C]0.004093[/C][/ROW]
[ROW][C]13[/C][C]0.323113[/C][C]2.5028[/C][C]0.007531[/C][/ROW]
[ROW][C]14[/C][C]0.287337[/C][C]2.2257[/C][C]0.014902[/C][/ROW]
[ROW][C]15[/C][C]0.266839[/C][C]2.0669[/C][C]0.021532[/C][/ROW]
[ROW][C]16[/C][C]0.235901[/C][C]1.8273[/C][C]0.036316[/C][/ROW]
[ROW][C]17[/C][C]0.20438[/C][C]1.5831[/C][C]0.059326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164311&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	0.922888	7.1487	0
2	0.857935	6.6455	0
3	0.79104	6.1274	0
4	0.726338	5.6262	0
5	0.668287	5.1765	1e-06
6	0.612833	4.747	7e-06
7	0.555141	4.3001	3.2e-05
8	0.499281	3.8674	0.000137
9	0.455245	3.5263	0.000407
10	0.411555	3.1879	0.001139
11	0.383261	2.9687	0.002146
12	0.353111	2.7352	0.004093
13	0.323113	2.5028	0.007531
14	0.287337	2.2257	0.014902
15	0.266839	2.0669	0.021532
16	0.235901	1.8273	0.036316
17	0.20438	1.5831	0.059326

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.922888	7.1487	0
2	0.041901	0.3246	0.37332
3	-0.042096	-0.3261	0.372752
4	-0.023972	-0.1857	0.426658
5	0.009655	0.0748	0.470317
6	-0.011017	-0.0853	0.466139
7	-0.047576	-0.3685	0.35689
8	-0.026088	-0.2021	0.420271
9	0.047288	0.3663	0.357718
10	-0.01639	-0.127	0.449701
11	0.071163	0.5512	0.291763
12	-0.019891	-0.1541	0.439034
13	-0.019621	-0.152	0.439856
14	-0.059213	-0.4587	0.324067
15	0.076699	0.5941	0.277337
16	-0.073632	-0.5704	0.285284
17	-0.039174	-0.3034	0.381302

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.922888 & 7.1487 & 0 \tabularnewline
2 & 0.041901 & 0.3246 & 0.37332 \tabularnewline
3 & -0.042096 & -0.3261 & 0.372752 \tabularnewline
4 & -0.023972 & -0.1857 & 0.426658 \tabularnewline
5 & 0.009655 & 0.0748 & 0.470317 \tabularnewline
6 & -0.011017 & -0.0853 & 0.466139 \tabularnewline
7 & -0.047576 & -0.3685 & 0.35689 \tabularnewline
8 & -0.026088 & -0.2021 & 0.420271 \tabularnewline
9 & 0.047288 & 0.3663 & 0.357718 \tabularnewline
10 & -0.01639 & -0.127 & 0.449701 \tabularnewline
11 & 0.071163 & 0.5512 & 0.291763 \tabularnewline
12 & -0.019891 & -0.1541 & 0.439034 \tabularnewline
13 & -0.019621 & -0.152 & 0.439856 \tabularnewline
14 & -0.059213 & -0.4587 & 0.324067 \tabularnewline
15 & 0.076699 & 0.5941 & 0.277337 \tabularnewline
16 & -0.073632 & -0.5704 & 0.285284 \tabularnewline
17 & -0.039174 & -0.3034 & 0.381302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164311&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]0.922888[/C][C]7.1487[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.041901[/C][C]0.3246[/C][C]0.37332[/C][/ROW]
[ROW][C]3[/C][C]-0.042096[/C][C]-0.3261[/C][C]0.372752[/C][/ROW]
[ROW][C]4[/C][C]-0.023972[/C][C]-0.1857[/C][C]0.426658[/C][/ROW]
[ROW][C]5[/C][C]0.009655[/C][C]0.0748[/C][C]0.470317[/C][/ROW]
[ROW][C]6[/C][C]-0.011017[/C][C]-0.0853[/C][C]0.466139[/C][/ROW]
[ROW][C]7[/C][C]-0.047576[/C][C]-0.3685[/C][C]0.35689[/C][/ROW]
[ROW][C]8[/C][C]-0.026088[/C][C]-0.2021[/C][C]0.420271[/C][/ROW]
[ROW][C]9[/C][C]0.047288[/C][C]0.3663[/C][C]0.357718[/C][/ROW]
[ROW][C]10[/C][C]-0.01639[/C][C]-0.127[/C][C]0.449701[/C][/ROW]
[ROW][C]11[/C][C]0.071163[/C][C]0.5512[/C][C]0.291763[/C][/ROW]
[ROW][C]12[/C][C]-0.019891[/C][C]-0.1541[/C][C]0.439034[/C][/ROW]
[ROW][C]13[/C][C]-0.019621[/C][C]-0.152[/C][C]0.439856[/C][/ROW]
[ROW][C]14[/C][C]-0.059213[/C][C]-0.4587[/C][C]0.324067[/C][/ROW]
[ROW][C]15[/C][C]0.076699[/C][C]0.5941[/C][C]0.277337[/C][/ROW]
[ROW][C]16[/C][C]-0.073632[/C][C]-0.5704[/C][C]0.285284[/C][/ROW]
[ROW][C]17[/C][C]-0.039174[/C][C]-0.3034[/C][C]0.381302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164311&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	0.922888	7.1487	0
2	0.041901	0.3246	0.37332
3	-0.042096	-0.3261	0.372752
4	-0.023972	-0.1857	0.426658
5	0.009655	0.0748	0.470317
6	-0.011017	-0.0853	0.466139
7	-0.047576	-0.3685	0.35689
8	-0.026088	-0.2021	0.420271
9	0.047288	0.3663	0.357718
10	-0.01639	-0.127	0.449701
11	0.071163	0.5512	0.291763
12	-0.019891	-0.1541	0.439034
13	-0.019621	-0.152	0.439856
14	-0.059213	-0.4587	0.324067
15	0.076699	0.5941	0.277337
16	-0.073632	-0.5704	0.285284
17	-0.039174	-0.3034	0.381302

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)
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