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

Fri, 07 Aug 2015 18:06:26 +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/2015/Aug/07/t1438967706pacuxky7ag7kp9g.htm/, Retrieved Wed, 15 May 2024 07:54:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279923, Retrieved Wed, 15 May 2024 07:54:49 +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

119

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

-       [(Partial) Autocorrelation Function] [] [2015-08-07 17:06:26] [70e23d918d09c907c02097a361cd6415] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279923&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279923&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279923&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.961988	11.1358	0
2	0.920574	10.6564	0
3	0.886112	10.2575	0
4	0.850005	9.8395	0
5	0.816571	9.4525	0
6	0.783359	9.068	0
7	0.749678	8.6782	0
8	0.718446	8.3166	0
9	0.687243	7.9554	0
10	0.652396	7.552	0
11	0.624062	7.224	0
12	0.599592	6.9408	0
13	0.573385	6.6374	0
14	0.538371	6.2321	0
15	0.507624	5.8762	0
16	0.484879	5.6129	0
17	0.456312	5.2822	0
18	0.424653	4.9157	1e-06
19	0.402944	4.6644	4e-06
20	0.386353	4.4724	8e-06
21	0.362597	4.1974	2.4e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.961988 & 11.1358 & 0 \tabularnewline
2 & 0.920574 & 10.6564 & 0 \tabularnewline
3 & 0.886112 & 10.2575 & 0 \tabularnewline
4 & 0.850005 & 9.8395 & 0 \tabularnewline
5 & 0.816571 & 9.4525 & 0 \tabularnewline
6 & 0.783359 & 9.068 & 0 \tabularnewline
7 & 0.749678 & 8.6782 & 0 \tabularnewline
8 & 0.718446 & 8.3166 & 0 \tabularnewline
9 & 0.687243 & 7.9554 & 0 \tabularnewline
10 & 0.652396 & 7.552 & 0 \tabularnewline
11 & 0.624062 & 7.224 & 0 \tabularnewline
12 & 0.599592 & 6.9408 & 0 \tabularnewline
13 & 0.573385 & 6.6374 & 0 \tabularnewline
14 & 0.538371 & 6.2321 & 0 \tabularnewline
15 & 0.507624 & 5.8762 & 0 \tabularnewline
16 & 0.484879 & 5.6129 & 0 \tabularnewline
17 & 0.456312 & 5.2822 & 0 \tabularnewline
18 & 0.424653 & 4.9157 & 1e-06 \tabularnewline
19 & 0.402944 & 4.6644 & 4e-06 \tabularnewline
20 & 0.386353 & 4.4724 & 8e-06 \tabularnewline
21 & 0.362597 & 4.1974 & 2.4e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279923&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]0.961988[/C][C]11.1358[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.920574[/C][C]10.6564[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.886112[/C][C]10.2575[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.850005[/C][C]9.8395[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.816571[/C][C]9.4525[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.783359[/C][C]9.068[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.749678[/C][C]8.6782[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.718446[/C][C]8.3166[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.687243[/C][C]7.9554[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.652396[/C][C]7.552[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.624062[/C][C]7.224[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.599592[/C][C]6.9408[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.573385[/C][C]6.6374[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.538371[/C][C]6.2321[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.507624[/C][C]5.8762[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.484879[/C][C]5.6129[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.456312[/C][C]5.2822[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.424653[/C][C]4.9157[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.402944[/C][C]4.6644[/C][C]4e-06[/C][/ROW]
[ROW][C]20[/C][C]0.386353[/C][C]4.4724[/C][C]8e-06[/C][/ROW]
[ROW][C]21[/C][C]0.362597[/C][C]4.1974[/C][C]2.4e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279923&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279923&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	0.961988	11.1358	0
2	0.920574	10.6564	0
3	0.886112	10.2575	0
4	0.850005	9.8395	0
5	0.816571	9.4525	0
6	0.783359	9.068	0
7	0.749678	8.6782	0
8	0.718446	8.3166	0
9	0.687243	7.9554	0
10	0.652396	7.552	0
11	0.624062	7.224	0
12	0.599592	6.9408	0
13	0.573385	6.6374	0
14	0.538371	6.2321	0
15	0.507624	5.8762	0
16	0.484879	5.6129	0
17	0.456312	5.2822	0
18	0.424653	4.9157	1e-06
19	0.402944	4.6644	4e-06
20	0.386353	4.4724	8e-06
21	0.362597	4.1974	2.4e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.961988	11.1358	0
2	-0.064992	-0.7523	0.226584
3	0.074008	0.8567	0.19657
4	-0.049455	-0.5725	0.283976
5	0.028022	0.3244	0.373078
6	-0.024805	-0.2871	0.387225
7	-0.016346	-0.1892	0.425104
8	0.011706	0.1355	0.446207
9	-0.020096	-0.2326	0.408202
10	-0.061932	-0.7169	0.237337
11	0.070833	0.82	0.206849
12	0.018771	0.2173	0.414156
13	-0.025533	-0.2956	0.384012
14	-0.136613	-1.5814	0.058071
15	0.053321	0.6172	0.269064
16	0.066797	0.7732	0.220374
17	-0.09576	-1.1085	0.134815
18	-0.04786	-0.554	0.290246
19	0.118004	1.366	0.087115
20	0.040437	0.4681	0.32024
21	-0.118968	-1.3772	0.08538

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.961988 & 11.1358 & 0 \tabularnewline
2 & -0.064992 & -0.7523 & 0.226584 \tabularnewline
3 & 0.074008 & 0.8567 & 0.19657 \tabularnewline
4 & -0.049455 & -0.5725 & 0.283976 \tabularnewline
5 & 0.028022 & 0.3244 & 0.373078 \tabularnewline
6 & -0.024805 & -0.2871 & 0.387225 \tabularnewline
7 & -0.016346 & -0.1892 & 0.425104 \tabularnewline
8 & 0.011706 & 0.1355 & 0.446207 \tabularnewline
9 & -0.020096 & -0.2326 & 0.408202 \tabularnewline
10 & -0.061932 & -0.7169 & 0.237337 \tabularnewline
11 & 0.070833 & 0.82 & 0.206849 \tabularnewline
12 & 0.018771 & 0.2173 & 0.414156 \tabularnewline
13 & -0.025533 & -0.2956 & 0.384012 \tabularnewline
14 & -0.136613 & -1.5814 & 0.058071 \tabularnewline
15 & 0.053321 & 0.6172 & 0.269064 \tabularnewline
16 & 0.066797 & 0.7732 & 0.220374 \tabularnewline
17 & -0.09576 & -1.1085 & 0.134815 \tabularnewline
18 & -0.04786 & -0.554 & 0.290246 \tabularnewline
19 & 0.118004 & 1.366 & 0.087115 \tabularnewline
20 & 0.040437 & 0.4681 & 0.32024 \tabularnewline
21 & -0.118968 & -1.3772 & 0.08538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279923&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]0.961988[/C][C]11.1358[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.064992[/C][C]-0.7523[/C][C]0.226584[/C][/ROW]
[ROW][C]3[/C][C]0.074008[/C][C]0.8567[/C][C]0.19657[/C][/ROW]
[ROW][C]4[/C][C]-0.049455[/C][C]-0.5725[/C][C]0.283976[/C][/ROW]
[ROW][C]5[/C][C]0.028022[/C][C]0.3244[/C][C]0.373078[/C][/ROW]
[ROW][C]6[/C][C]-0.024805[/C][C]-0.2871[/C][C]0.387225[/C][/ROW]
[ROW][C]7[/C][C]-0.016346[/C][C]-0.1892[/C][C]0.425104[/C][/ROW]
[ROW][C]8[/C][C]0.011706[/C][C]0.1355[/C][C]0.446207[/C][/ROW]
[ROW][C]9[/C][C]-0.020096[/C][C]-0.2326[/C][C]0.408202[/C][/ROW]
[ROW][C]10[/C][C]-0.061932[/C][C]-0.7169[/C][C]0.237337[/C][/ROW]
[ROW][C]11[/C][C]0.070833[/C][C]0.82[/C][C]0.206849[/C][/ROW]
[ROW][C]12[/C][C]0.018771[/C][C]0.2173[/C][C]0.414156[/C][/ROW]
[ROW][C]13[/C][C]-0.025533[/C][C]-0.2956[/C][C]0.384012[/C][/ROW]
[ROW][C]14[/C][C]-0.136613[/C][C]-1.5814[/C][C]0.058071[/C][/ROW]
[ROW][C]15[/C][C]0.053321[/C][C]0.6172[/C][C]0.269064[/C][/ROW]
[ROW][C]16[/C][C]0.066797[/C][C]0.7732[/C][C]0.220374[/C][/ROW]
[ROW][C]17[/C][C]-0.09576[/C][C]-1.1085[/C][C]0.134815[/C][/ROW]
[ROW][C]18[/C][C]-0.04786[/C][C]-0.554[/C][C]0.290246[/C][/ROW]
[ROW][C]19[/C][C]0.118004[/C][C]1.366[/C][C]0.087115[/C][/ROW]
[ROW][C]20[/C][C]0.040437[/C][C]0.4681[/C][C]0.32024[/C][/ROW]
[ROW][C]21[/C][C]-0.118968[/C][C]-1.3772[/C][C]0.08538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279923&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279923&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	0.961988	11.1358	0
2	-0.064992	-0.7523	0.226584
3	0.074008	0.8567	0.19657
4	-0.049455	-0.5725	0.283976
5	0.028022	0.3244	0.373078
6	-0.024805	-0.2871	0.387225
7	-0.016346	-0.1892	0.425104
8	0.011706	0.1355	0.446207
9	-0.020096	-0.2326	0.408202
10	-0.061932	-0.7169	0.237337
11	0.070833	0.82	0.206849
12	0.018771	0.2173	0.414156
13	-0.025533	-0.2956	0.384012
14	-0.136613	-1.5814	0.058071
15	0.053321	0.6172	0.269064
16	0.066797	0.7732	0.220374
17	-0.09576	-1.1085	0.134815
18	-0.04786	-0.554	0.290246
19	0.118004	1.366	0.087115
20	0.040437	0.4681	0.32024
21	-0.118968	-1.3772	0.08538

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 = 0.1 ; par2 = 0.9 ; par3 = 0.01 ;

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