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, 16 Mar 2014 07:12:46 -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/2014/Mar/16/t1394968513q7efwba2dbkr6iv.htm/, Retrieved Mon, 13 May 2024 22:25:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234269, Retrieved Mon, 13 May 2024 22:25:20 +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

197

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

-       [(Partial) Autocorrelation Function] [] [2014-03-16 11:12:46] [73938b6dd5218abd99a1a1df7750ee20] [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	4 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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234269&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]4 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=234269&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234269&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	4 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.555768	-6.3611	0
2	0.013785	0.1578	0.437436
3	0.071746	0.8212	0.20652
4	-0.072697	-0.8321	0.203447
5	0.246815	2.8249	0.002735
6	-0.331849	-3.7982	0.000111
7	0.17986	2.0586	0.020758
8	-0.055116	-0.6308	0.264625
9	0.054901	0.6284	0.265426
10	0.058315	0.6674	0.252833
11	-0.472993	-5.4137	0
12	0.749867	8.5826	0
13	-0.449381	-5.1434	0
14	0.031135	0.3564	0.361072
15	0.070373	0.8055	0.211009
16	-0.094288	-1.0792	0.141246
17	0.213746	2.4464	0.007877
18	-0.243361	-2.7854	0.00307
19	0.096313	1.1023	0.136165
20	0.003132	0.0359	0.485728
21	0.034716	0.3973	0.345881

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.555768 & -6.3611 & 0 \tabularnewline
2 & 0.013785 & 0.1578 & 0.437436 \tabularnewline
3 & 0.071746 & 0.8212 & 0.20652 \tabularnewline
4 & -0.072697 & -0.8321 & 0.203447 \tabularnewline
5 & 0.246815 & 2.8249 & 0.002735 \tabularnewline
6 & -0.331849 & -3.7982 & 0.000111 \tabularnewline
7 & 0.17986 & 2.0586 & 0.020758 \tabularnewline
8 & -0.055116 & -0.6308 & 0.264625 \tabularnewline
9 & 0.054901 & 0.6284 & 0.265426 \tabularnewline
10 & 0.058315 & 0.6674 & 0.252833 \tabularnewline
11 & -0.472993 & -5.4137 & 0 \tabularnewline
12 & 0.749867 & 8.5826 & 0 \tabularnewline
13 & -0.449381 & -5.1434 & 0 \tabularnewline
14 & 0.031135 & 0.3564 & 0.361072 \tabularnewline
15 & 0.070373 & 0.8055 & 0.211009 \tabularnewline
16 & -0.094288 & -1.0792 & 0.141246 \tabularnewline
17 & 0.213746 & 2.4464 & 0.007877 \tabularnewline
18 & -0.243361 & -2.7854 & 0.00307 \tabularnewline
19 & 0.096313 & 1.1023 & 0.136165 \tabularnewline
20 & 0.003132 & 0.0359 & 0.485728 \tabularnewline
21 & 0.034716 & 0.3973 & 0.345881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234269&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]-0.555768[/C][C]-6.3611[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.013785[/C][C]0.1578[/C][C]0.437436[/C][/ROW]
[ROW][C]3[/C][C]0.071746[/C][C]0.8212[/C][C]0.20652[/C][/ROW]
[ROW][C]4[/C][C]-0.072697[/C][C]-0.8321[/C][C]0.203447[/C][/ROW]
[ROW][C]5[/C][C]0.246815[/C][C]2.8249[/C][C]0.002735[/C][/ROW]
[ROW][C]6[/C][C]-0.331849[/C][C]-3.7982[/C][C]0.000111[/C][/ROW]
[ROW][C]7[/C][C]0.17986[/C][C]2.0586[/C][C]0.020758[/C][/ROW]
[ROW][C]8[/C][C]-0.055116[/C][C]-0.6308[/C][C]0.264625[/C][/ROW]
[ROW][C]9[/C][C]0.054901[/C][C]0.6284[/C][C]0.265426[/C][/ROW]
[ROW][C]10[/C][C]0.058315[/C][C]0.6674[/C][C]0.252833[/C][/ROW]
[ROW][C]11[/C][C]-0.472993[/C][C]-5.4137[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.749867[/C][C]8.5826[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.449381[/C][C]-5.1434[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.031135[/C][C]0.3564[/C][C]0.361072[/C][/ROW]
[ROW][C]15[/C][C]0.070373[/C][C]0.8055[/C][C]0.211009[/C][/ROW]
[ROW][C]16[/C][C]-0.094288[/C][C]-1.0792[/C][C]0.141246[/C][/ROW]
[ROW][C]17[/C][C]0.213746[/C][C]2.4464[/C][C]0.007877[/C][/ROW]
[ROW][C]18[/C][C]-0.243361[/C][C]-2.7854[/C][C]0.00307[/C][/ROW]
[ROW][C]19[/C][C]0.096313[/C][C]1.1023[/C][C]0.136165[/C][/ROW]
[ROW][C]20[/C][C]0.003132[/C][C]0.0359[/C][C]0.485728[/C][/ROW]
[ROW][C]21[/C][C]0.034716[/C][C]0.3973[/C][C]0.345881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234269&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234269&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	-0.555768	-6.3611	0
2	0.013785	0.1578	0.437436
3	0.071746	0.8212	0.20652
4	-0.072697	-0.8321	0.203447
5	0.246815	2.8249	0.002735
6	-0.331849	-3.7982	0.000111
7	0.17986	2.0586	0.020758
8	-0.055116	-0.6308	0.264625
9	0.054901	0.6284	0.265426
10	0.058315	0.6674	0.252833
11	-0.472993	-5.4137	0
12	0.749867	8.5826	0
13	-0.449381	-5.1434	0
14	0.031135	0.3564	0.361072
15	0.070373	0.8055	0.211009
16	-0.094288	-1.0792	0.141246
17	0.213746	2.4464	0.007877
18	-0.243361	-2.7854	0.00307
19	0.096313	1.1023	0.136165
20	0.003132	0.0359	0.485728
21	0.034716	0.3973	0.345881

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.555768	-6.3611	0
2	-0.426976	-4.887	1e-06
3	-0.273605	-3.1315	0.001073
4	-0.288051	-3.2969	0.000629
5	0.170502	1.9515	0.026567
6	-0.062102	-0.7108	0.239238
7	0.002026	0.0232	0.490766
8	-0.108715	-1.2443	0.107805
9	0.011605	0.1328	0.447269
10	0.145779	1.6685	0.0488
11	-0.552213	-6.3204	0
12	0.335253	3.8372	9.6e-05
13	0.063	0.7211	0.236078
14	0.055619	0.6366	0.262754
15	0.00971	0.1111	0.455838
16	0.019582	0.2241	0.411506
17	-0.155152	-1.7758	0.039044
18	0.024939	0.2854	0.387877
19	-0.104183	-1.1924	0.117623
20	0.048146	0.5511	0.291266
21	0.069573	0.7963	0.213649

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.555768 & -6.3611 & 0 \tabularnewline
2 & -0.426976 & -4.887 & 1e-06 \tabularnewline
3 & -0.273605 & -3.1315 & 0.001073 \tabularnewline
4 & -0.288051 & -3.2969 & 0.000629 \tabularnewline
5 & 0.170502 & 1.9515 & 0.026567 \tabularnewline
6 & -0.062102 & -0.7108 & 0.239238 \tabularnewline
7 & 0.002026 & 0.0232 & 0.490766 \tabularnewline
8 & -0.108715 & -1.2443 & 0.107805 \tabularnewline
9 & 0.011605 & 0.1328 & 0.447269 \tabularnewline
10 & 0.145779 & 1.6685 & 0.0488 \tabularnewline
11 & -0.552213 & -6.3204 & 0 \tabularnewline
12 & 0.335253 & 3.8372 & 9.6e-05 \tabularnewline
13 & 0.063 & 0.7211 & 0.236078 \tabularnewline
14 & 0.055619 & 0.6366 & 0.262754 \tabularnewline
15 & 0.00971 & 0.1111 & 0.455838 \tabularnewline
16 & 0.019582 & 0.2241 & 0.411506 \tabularnewline
17 & -0.155152 & -1.7758 & 0.039044 \tabularnewline
18 & 0.024939 & 0.2854 & 0.387877 \tabularnewline
19 & -0.104183 & -1.1924 & 0.117623 \tabularnewline
20 & 0.048146 & 0.5511 & 0.291266 \tabularnewline
21 & 0.069573 & 0.7963 & 0.213649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234269&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]-0.555768[/C][C]-6.3611[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.426976[/C][C]-4.887[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.273605[/C][C]-3.1315[/C][C]0.001073[/C][/ROW]
[ROW][C]4[/C][C]-0.288051[/C][C]-3.2969[/C][C]0.000629[/C][/ROW]
[ROW][C]5[/C][C]0.170502[/C][C]1.9515[/C][C]0.026567[/C][/ROW]
[ROW][C]6[/C][C]-0.062102[/C][C]-0.7108[/C][C]0.239238[/C][/ROW]
[ROW][C]7[/C][C]0.002026[/C][C]0.0232[/C][C]0.490766[/C][/ROW]
[ROW][C]8[/C][C]-0.108715[/C][C]-1.2443[/C][C]0.107805[/C][/ROW]
[ROW][C]9[/C][C]0.011605[/C][C]0.1328[/C][C]0.447269[/C][/ROW]
[ROW][C]10[/C][C]0.145779[/C][C]1.6685[/C][C]0.0488[/C][/ROW]
[ROW][C]11[/C][C]-0.552213[/C][C]-6.3204[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.335253[/C][C]3.8372[/C][C]9.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.063[/C][C]0.7211[/C][C]0.236078[/C][/ROW]
[ROW][C]14[/C][C]0.055619[/C][C]0.6366[/C][C]0.262754[/C][/ROW]
[ROW][C]15[/C][C]0.00971[/C][C]0.1111[/C][C]0.455838[/C][/ROW]
[ROW][C]16[/C][C]0.019582[/C][C]0.2241[/C][C]0.411506[/C][/ROW]
[ROW][C]17[/C][C]-0.155152[/C][C]-1.7758[/C][C]0.039044[/C][/ROW]
[ROW][C]18[/C][C]0.024939[/C][C]0.2854[/C][C]0.387877[/C][/ROW]
[ROW][C]19[/C][C]-0.104183[/C][C]-1.1924[/C][C]0.117623[/C][/ROW]
[ROW][C]20[/C][C]0.048146[/C][C]0.5511[/C][C]0.291266[/C][/ROW]
[ROW][C]21[/C][C]0.069573[/C][C]0.7963[/C][C]0.213649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234269&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234269&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	-0.555768	-6.3611	0
2	-0.426976	-4.887	1e-06
3	-0.273605	-3.1315	0.001073
4	-0.288051	-3.2969	0.000629
5	0.170502	1.9515	0.026567
6	-0.062102	-0.7108	0.239238
7	0.002026	0.0232	0.490766
8	-0.108715	-1.2443	0.107805
9	0.011605	0.1328	0.447269
10	0.145779	1.6685	0.0488
11	-0.552213	-6.3204	0
12	0.335253	3.8372	9.6e-05
13	0.063	0.7211	0.236078
14	0.055619	0.6366	0.262754
15	0.00971	0.1111	0.455838
16	0.019582	0.2241	0.411506
17	-0.155152	-1.7758	0.039044
18	0.024939	0.2854	0.387877
19	-0.104183	-1.1924	0.117623
20	0.048146	0.5511	0.291266
21	0.069573	0.7963	0.213649

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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