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

Fri, 16 Dec 2016 17:00:12 +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/Dec/16/t1481904271vqqmah0u3i69wzh.htm/, Retrieved Thu, 02 May 2024 22:38:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300401, Retrieved Thu, 02 May 2024 22:38:11 +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] [autocorrelation] [2016-12-16 16:00:12] [e4ec2dc388263dc7bca2f210fca20b5e] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300401&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300401&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300401&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.065721	0.6986	0.243113
2	-0.236055	-2.5093	0.006757
3	-0.496894	-5.2821	0
4	-0.155982	-1.6581	0.050034
5	0.070875	0.7534	0.226384
6	0.521507	5.5437	0
7	0.070078	0.7449	0.228926
8	-0.142848	-1.5185	0.065841
9	-0.457681	-4.8652	2e-06
10	-0.226914	-2.4121	0.008735
11	0.135228	1.4375	0.076671
12	0.77853	8.2759	0
13	0.097145	1.0327	0.151982
14	-0.269979	-2.8699	0.002451
15	-0.40059	-4.2583	2.1e-05
16	-0.142557	-1.5154	0.066232
17	0.085424	0.9081	0.182887
18	0.432838	4.6011	6e-06
19	0.09256	0.9839	0.163626
20	-0.163854	-1.7418	0.042133

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.065721 & 0.6986 & 0.243113 \tabularnewline
2 & -0.236055 & -2.5093 & 0.006757 \tabularnewline
3 & -0.496894 & -5.2821 & 0 \tabularnewline
4 & -0.155982 & -1.6581 & 0.050034 \tabularnewline
5 & 0.070875 & 0.7534 & 0.226384 \tabularnewline
6 & 0.521507 & 5.5437 & 0 \tabularnewline
7 & 0.070078 & 0.7449 & 0.228926 \tabularnewline
8 & -0.142848 & -1.5185 & 0.065841 \tabularnewline
9 & -0.457681 & -4.8652 & 2e-06 \tabularnewline
10 & -0.226914 & -2.4121 & 0.008735 \tabularnewline
11 & 0.135228 & 1.4375 & 0.076671 \tabularnewline
12 & 0.77853 & 8.2759 & 0 \tabularnewline
13 & 0.097145 & 1.0327 & 0.151982 \tabularnewline
14 & -0.269979 & -2.8699 & 0.002451 \tabularnewline
15 & -0.40059 & -4.2583 & 2.1e-05 \tabularnewline
16 & -0.142557 & -1.5154 & 0.066232 \tabularnewline
17 & 0.085424 & 0.9081 & 0.182887 \tabularnewline
18 & 0.432838 & 4.6011 & 6e-06 \tabularnewline
19 & 0.09256 & 0.9839 & 0.163626 \tabularnewline
20 & -0.163854 & -1.7418 & 0.042133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300401&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]0.065721[/C][C]0.6986[/C][C]0.243113[/C][/ROW]
[ROW][C]2[/C][C]-0.236055[/C][C]-2.5093[/C][C]0.006757[/C][/ROW]
[ROW][C]3[/C][C]-0.496894[/C][C]-5.2821[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.155982[/C][C]-1.6581[/C][C]0.050034[/C][/ROW]
[ROW][C]5[/C][C]0.070875[/C][C]0.7534[/C][C]0.226384[/C][/ROW]
[ROW][C]6[/C][C]0.521507[/C][C]5.5437[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.070078[/C][C]0.7449[/C][C]0.228926[/C][/ROW]
[ROW][C]8[/C][C]-0.142848[/C][C]-1.5185[/C][C]0.065841[/C][/ROW]
[ROW][C]9[/C][C]-0.457681[/C][C]-4.8652[/C][C]2e-06[/C][/ROW]
[ROW][C]10[/C][C]-0.226914[/C][C]-2.4121[/C][C]0.008735[/C][/ROW]
[ROW][C]11[/C][C]0.135228[/C][C]1.4375[/C][C]0.076671[/C][/ROW]
[ROW][C]12[/C][C]0.77853[/C][C]8.2759[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.097145[/C][C]1.0327[/C][C]0.151982[/C][/ROW]
[ROW][C]14[/C][C]-0.269979[/C][C]-2.8699[/C][C]0.002451[/C][/ROW]
[ROW][C]15[/C][C]-0.40059[/C][C]-4.2583[/C][C]2.1e-05[/C][/ROW]
[ROW][C]16[/C][C]-0.142557[/C][C]-1.5154[/C][C]0.066232[/C][/ROW]
[ROW][C]17[/C][C]0.085424[/C][C]0.9081[/C][C]0.182887[/C][/ROW]
[ROW][C]18[/C][C]0.432838[/C][C]4.6011[/C][C]6e-06[/C][/ROW]
[ROW][C]19[/C][C]0.09256[/C][C]0.9839[/C][C]0.163626[/C][/ROW]
[ROW][C]20[/C][C]-0.163854[/C][C]-1.7418[/C][C]0.042133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300401&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300401&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	0.065721	0.6986	0.243113
2	-0.236055	-2.5093	0.006757
3	-0.496894	-5.2821	0
4	-0.155982	-1.6581	0.050034
5	0.070875	0.7534	0.226384
6	0.521507	5.5437	0
7	0.070078	0.7449	0.228926
8	-0.142848	-1.5185	0.065841
9	-0.457681	-4.8652	2e-06
10	-0.226914	-2.4121	0.008735
11	0.135228	1.4375	0.076671
12	0.77853	8.2759	0
13	0.097145	1.0327	0.151982
14	-0.269979	-2.8699	0.002451
15	-0.40059	-4.2583	2.1e-05
16	-0.142557	-1.5154	0.066232
17	0.085424	0.9081	0.182887
18	0.432838	4.6011	6e-06
19	0.09256	0.9839	0.163626
20	-0.163854	-1.7418	0.042133

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.065721	0.6986	0.243113
2	-0.241416	-2.5663	0.005794
3	-0.492474	-5.2351	0
4	-0.26703	-2.8386	0.002687
5	-0.277751	-2.9525	0.001917
6	0.224236	2.3837	0.009404
7	-0.106461	-1.1317	0.130079
8	-0.056782	-0.6036	0.273659
9	-0.282061	-2.9983	0.001669
10	-0.411336	-4.3726	1.4e-05
11	-0.313751	-3.3352	0.000577
12	0.469013	4.9857	1e-06
13	0.088362	0.9393	0.174791
14	-0.135608	-1.4415	0.076099
15	0.173915	1.8487	0.033554
16	0.141403	1.5031	0.067797
17	0.000192	0.002	0.499188
18	-0.088489	-0.9406	0.174446
19	0.018499	0.1966	0.42223
20	-0.035596	-0.3784	0.352924

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.065721 & 0.6986 & 0.243113 \tabularnewline
2 & -0.241416 & -2.5663 & 0.005794 \tabularnewline
3 & -0.492474 & -5.2351 & 0 \tabularnewline
4 & -0.26703 & -2.8386 & 0.002687 \tabularnewline
5 & -0.277751 & -2.9525 & 0.001917 \tabularnewline
6 & 0.224236 & 2.3837 & 0.009404 \tabularnewline
7 & -0.106461 & -1.1317 & 0.130079 \tabularnewline
8 & -0.056782 & -0.6036 & 0.273659 \tabularnewline
9 & -0.282061 & -2.9983 & 0.001669 \tabularnewline
10 & -0.411336 & -4.3726 & 1.4e-05 \tabularnewline
11 & -0.313751 & -3.3352 & 0.000577 \tabularnewline
12 & 0.469013 & 4.9857 & 1e-06 \tabularnewline
13 & 0.088362 & 0.9393 & 0.174791 \tabularnewline
14 & -0.135608 & -1.4415 & 0.076099 \tabularnewline
15 & 0.173915 & 1.8487 & 0.033554 \tabularnewline
16 & 0.141403 & 1.5031 & 0.067797 \tabularnewline
17 & 0.000192 & 0.002 & 0.499188 \tabularnewline
18 & -0.088489 & -0.9406 & 0.174446 \tabularnewline
19 & 0.018499 & 0.1966 & 0.42223 \tabularnewline
20 & -0.035596 & -0.3784 & 0.352924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300401&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]0.065721[/C][C]0.6986[/C][C]0.243113[/C][/ROW]
[ROW][C]2[/C][C]-0.241416[/C][C]-2.5663[/C][C]0.005794[/C][/ROW]
[ROW][C]3[/C][C]-0.492474[/C][C]-5.2351[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.26703[/C][C]-2.8386[/C][C]0.002687[/C][/ROW]
[ROW][C]5[/C][C]-0.277751[/C][C]-2.9525[/C][C]0.001917[/C][/ROW]
[ROW][C]6[/C][C]0.224236[/C][C]2.3837[/C][C]0.009404[/C][/ROW]
[ROW][C]7[/C][C]-0.106461[/C][C]-1.1317[/C][C]0.130079[/C][/ROW]
[ROW][C]8[/C][C]-0.056782[/C][C]-0.6036[/C][C]0.273659[/C][/ROW]
[ROW][C]9[/C][C]-0.282061[/C][C]-2.9983[/C][C]0.001669[/C][/ROW]
[ROW][C]10[/C][C]-0.411336[/C][C]-4.3726[/C][C]1.4e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.313751[/C][C]-3.3352[/C][C]0.000577[/C][/ROW]
[ROW][C]12[/C][C]0.469013[/C][C]4.9857[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.088362[/C][C]0.9393[/C][C]0.174791[/C][/ROW]
[ROW][C]14[/C][C]-0.135608[/C][C]-1.4415[/C][C]0.076099[/C][/ROW]
[ROW][C]15[/C][C]0.173915[/C][C]1.8487[/C][C]0.033554[/C][/ROW]
[ROW][C]16[/C][C]0.141403[/C][C]1.5031[/C][C]0.067797[/C][/ROW]
[ROW][C]17[/C][C]0.000192[/C][C]0.002[/C][C]0.499188[/C][/ROW]
[ROW][C]18[/C][C]-0.088489[/C][C]-0.9406[/C][C]0.174446[/C][/ROW]
[ROW][C]19[/C][C]0.018499[/C][C]0.1966[/C][C]0.42223[/C][/ROW]
[ROW][C]20[/C][C]-0.035596[/C][C]-0.3784[/C][C]0.352924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300401&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300401&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	0.065721	0.6986	0.243113
2	-0.241416	-2.5663	0.005794
3	-0.492474	-5.2351	0
4	-0.26703	-2.8386	0.002687
5	-0.277751	-2.9525	0.001917
6	0.224236	2.3837	0.009404
7	-0.106461	-1.1317	0.130079
8	-0.056782	-0.6036	0.273659
9	-0.282061	-2.9983	0.001669
10	-0.411336	-4.3726	1.4e-05
11	-0.313751	-3.3352	0.000577
12	0.469013	4.9857	1e-06
13	0.088362	0.9393	0.174791
14	-0.135608	-1.4415	0.076099
15	0.173915	1.8487	0.033554
16	0.141403	1.5031	0.067797
17	0.000192	0.002	0.499188
18	-0.088489	-0.9406	0.174446
19	0.018499	0.1966	0.42223
20	-0.035596	-0.3784	0.352924

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 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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