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

Sun, 11 Dec 2016 17:49:55 +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/11/t1481475021kbsrsw85y4hrdni.htm/, Retrieved Thu, 02 May 2024 13:19:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298830, Retrieved Thu, 02 May 2024 13:19:08 +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 F...] [2016-12-11 16:49:55] [10299735033611e1e2dae6371997f8c9] [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=298830&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=298830&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298830&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	-0.170699	-1.7821	0.038755
2	-0.513382	-5.3599	0
3	0.027233	0.2843	0.388353
4	0.475966	4.9692	1e-06
5	0.117925	1.2312	0.110455
6	-0.821824	-8.5801	0
7	0.114523	1.1957	0.117214
8	0.459307	4.7953	3e-06
9	-0.00966	-0.1009	0.459926
10	-0.440169	-4.5955	6e-06
11	-0.09983	-1.0423	0.1498
12	0.67923	7.0914	0
13	-0.069057	-0.721	0.236232
14	-0.436595	-4.5582	7e-06
15	0.017501	0.1827	0.427679
16	0.414634	4.3289	1.7e-05
17	0.101108	1.0556	0.146742
18	-0.642443	-6.7073	0
19	0.067595	0.7057	0.240935
20	0.451713	4.716	4e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.170699 & -1.7821 & 0.038755 \tabularnewline
2 & -0.513382 & -5.3599 & 0 \tabularnewline
3 & 0.027233 & 0.2843 & 0.388353 \tabularnewline
4 & 0.475966 & 4.9692 & 1e-06 \tabularnewline
5 & 0.117925 & 1.2312 & 0.110455 \tabularnewline
6 & -0.821824 & -8.5801 & 0 \tabularnewline
7 & 0.114523 & 1.1957 & 0.117214 \tabularnewline
8 & 0.459307 & 4.7953 & 3e-06 \tabularnewline
9 & -0.00966 & -0.1009 & 0.459926 \tabularnewline
10 & -0.440169 & -4.5955 & 6e-06 \tabularnewline
11 & -0.09983 & -1.0423 & 0.1498 \tabularnewline
12 & 0.67923 & 7.0914 & 0 \tabularnewline
13 & -0.069057 & -0.721 & 0.236232 \tabularnewline
14 & -0.436595 & -4.5582 & 7e-06 \tabularnewline
15 & 0.017501 & 0.1827 & 0.427679 \tabularnewline
16 & 0.414634 & 4.3289 & 1.7e-05 \tabularnewline
17 & 0.101108 & 1.0556 & 0.146742 \tabularnewline
18 & -0.642443 & -6.7073 & 0 \tabularnewline
19 & 0.067595 & 0.7057 & 0.240935 \tabularnewline
20 & 0.451713 & 4.716 & 4e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298830&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]-0.170699[/C][C]-1.7821[/C][C]0.038755[/C][/ROW]
[ROW][C]2[/C][C]-0.513382[/C][C]-5.3599[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.027233[/C][C]0.2843[/C][C]0.388353[/C][/ROW]
[ROW][C]4[/C][C]0.475966[/C][C]4.9692[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.117925[/C][C]1.2312[/C][C]0.110455[/C][/ROW]
[ROW][C]6[/C][C]-0.821824[/C][C]-8.5801[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.114523[/C][C]1.1957[/C][C]0.117214[/C][/ROW]
[ROW][C]8[/C][C]0.459307[/C][C]4.7953[/C][C]3e-06[/C][/ROW]
[ROW][C]9[/C][C]-0.00966[/C][C]-0.1009[/C][C]0.459926[/C][/ROW]
[ROW][C]10[/C][C]-0.440169[/C][C]-4.5955[/C][C]6e-06[/C][/ROW]
[ROW][C]11[/C][C]-0.09983[/C][C]-1.0423[/C][C]0.1498[/C][/ROW]
[ROW][C]12[/C][C]0.67923[/C][C]7.0914[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.069057[/C][C]-0.721[/C][C]0.236232[/C][/ROW]
[ROW][C]14[/C][C]-0.436595[/C][C]-4.5582[/C][C]7e-06[/C][/ROW]
[ROW][C]15[/C][C]0.017501[/C][C]0.1827[/C][C]0.427679[/C][/ROW]
[ROW][C]16[/C][C]0.414634[/C][C]4.3289[/C][C]1.7e-05[/C][/ROW]
[ROW][C]17[/C][C]0.101108[/C][C]1.0556[/C][C]0.146742[/C][/ROW]
[ROW][C]18[/C][C]-0.642443[/C][C]-6.7073[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.067595[/C][C]0.7057[/C][C]0.240935[/C][/ROW]
[ROW][C]20[/C][C]0.451713[/C][C]4.716[/C][C]4e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298830&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298830&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	-0.170699	-1.7821	0.038755
2	-0.513382	-5.3599	0
3	0.027233	0.2843	0.388353
4	0.475966	4.9692	1e-06
5	0.117925	1.2312	0.110455
6	-0.821824	-8.5801	0
7	0.114523	1.1957	0.117214
8	0.459307	4.7953	3e-06
9	-0.00966	-0.1009	0.459926
10	-0.440169	-4.5955	6e-06
11	-0.09983	-1.0423	0.1498
12	0.67923	7.0914	0
13	-0.069057	-0.721	0.236232
14	-0.436595	-4.5582	7e-06
15	0.017501	0.1827	0.427679
16	0.414634	4.3289	1.7e-05
17	0.101108	1.0556	0.146742
18	-0.642443	-6.7073	0
19	0.067595	0.7057	0.240935
20	0.451713	4.716	4e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.170699	-1.7821	0.038755
2	-0.558803	-5.8341	0
3	-0.306661	-3.2016	0.000896
4	0.176493	1.8426	0.034049
5	0.38744	4.045	4.9e-05
6	-0.654867	-6.837	0
7	-0.237473	-2.4793	0.007348
8	-0.294836	-3.0782	0.001317
9	-0.034532	-0.3605	0.359575
10	-0.039764	-0.4152	0.339423
11	-0.028524	-0.2978	0.38321
12	-0.053715	-0.5608	0.288041
13	-0.034577	-0.361	0.3594
14	-0.131334	-1.3712	0.086569
15	-0.012715	-0.1328	0.447318
16	0.01262	0.1318	0.447709
17	0.143423	1.4974	0.068593
18	-0.204493	-2.135	0.017502
19	-0.049882	-0.5208	0.301786
20	-0.00338	-0.0353	0.485959

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.170699 & -1.7821 & 0.038755 \tabularnewline
2 & -0.558803 & -5.8341 & 0 \tabularnewline
3 & -0.306661 & -3.2016 & 0.000896 \tabularnewline
4 & 0.176493 & 1.8426 & 0.034049 \tabularnewline
5 & 0.38744 & 4.045 & 4.9e-05 \tabularnewline
6 & -0.654867 & -6.837 & 0 \tabularnewline
7 & -0.237473 & -2.4793 & 0.007348 \tabularnewline
8 & -0.294836 & -3.0782 & 0.001317 \tabularnewline
9 & -0.034532 & -0.3605 & 0.359575 \tabularnewline
10 & -0.039764 & -0.4152 & 0.339423 \tabularnewline
11 & -0.028524 & -0.2978 & 0.38321 \tabularnewline
12 & -0.053715 & -0.5608 & 0.288041 \tabularnewline
13 & -0.034577 & -0.361 & 0.3594 \tabularnewline
14 & -0.131334 & -1.3712 & 0.086569 \tabularnewline
15 & -0.012715 & -0.1328 & 0.447318 \tabularnewline
16 & 0.01262 & 0.1318 & 0.447709 \tabularnewline
17 & 0.143423 & 1.4974 & 0.068593 \tabularnewline
18 & -0.204493 & -2.135 & 0.017502 \tabularnewline
19 & -0.049882 & -0.5208 & 0.301786 \tabularnewline
20 & -0.00338 & -0.0353 & 0.485959 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298830&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]-0.170699[/C][C]-1.7821[/C][C]0.038755[/C][/ROW]
[ROW][C]2[/C][C]-0.558803[/C][C]-5.8341[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.306661[/C][C]-3.2016[/C][C]0.000896[/C][/ROW]
[ROW][C]4[/C][C]0.176493[/C][C]1.8426[/C][C]0.034049[/C][/ROW]
[ROW][C]5[/C][C]0.38744[/C][C]4.045[/C][C]4.9e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.654867[/C][C]-6.837[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.237473[/C][C]-2.4793[/C][C]0.007348[/C][/ROW]
[ROW][C]8[/C][C]-0.294836[/C][C]-3.0782[/C][C]0.001317[/C][/ROW]
[ROW][C]9[/C][C]-0.034532[/C][C]-0.3605[/C][C]0.359575[/C][/ROW]
[ROW][C]10[/C][C]-0.039764[/C][C]-0.4152[/C][C]0.339423[/C][/ROW]
[ROW][C]11[/C][C]-0.028524[/C][C]-0.2978[/C][C]0.38321[/C][/ROW]
[ROW][C]12[/C][C]-0.053715[/C][C]-0.5608[/C][C]0.288041[/C][/ROW]
[ROW][C]13[/C][C]-0.034577[/C][C]-0.361[/C][C]0.3594[/C][/ROW]
[ROW][C]14[/C][C]-0.131334[/C][C]-1.3712[/C][C]0.086569[/C][/ROW]
[ROW][C]15[/C][C]-0.012715[/C][C]-0.1328[/C][C]0.447318[/C][/ROW]
[ROW][C]16[/C][C]0.01262[/C][C]0.1318[/C][C]0.447709[/C][/ROW]
[ROW][C]17[/C][C]0.143423[/C][C]1.4974[/C][C]0.068593[/C][/ROW]
[ROW][C]18[/C][C]-0.204493[/C][C]-2.135[/C][C]0.017502[/C][/ROW]
[ROW][C]19[/C][C]-0.049882[/C][C]-0.5208[/C][C]0.301786[/C][/ROW]
[ROW][C]20[/C][C]-0.00338[/C][C]-0.0353[/C][C]0.485959[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298830&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298830&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	-0.170699	-1.7821	0.038755
2	-0.558803	-5.8341	0
3	-0.306661	-3.2016	0.000896
4	0.176493	1.8426	0.034049
5	0.38744	4.045	4.9e-05
6	-0.654867	-6.837	0
7	-0.237473	-2.4793	0.007348
8	-0.294836	-3.0782	0.001317
9	-0.034532	-0.3605	0.359575
10	-0.039764	-0.4152	0.339423
11	-0.028524	-0.2978	0.38321
12	-0.053715	-0.5608	0.288041
13	-0.034577	-0.361	0.3594
14	-0.131334	-1.3712	0.086569
15	-0.012715	-0.1328	0.447318
16	0.01262	0.1318	0.447709
17	0.143423	1.4974	0.068593
18	-0.204493	-2.135	0.017502
19	-0.049882	-0.5208	0.301786
20	-0.00338	-0.0353	0.485959

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 = 1 ; par5 = 6 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 6 ; 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,'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