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 09:48:05 +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/t14818781273iiaobkbu2fxrj0.htm/, Retrieved Thu, 02 May 2024 22:55:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300137, Retrieved Thu, 02 May 2024 22:55:52 +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 N247] [2016-12-16 08:48:05] [c0b73e623858a81821526bb2f691ccd9] [Current]
- R P     [(Partial) Autocorrelation Function] [Autocorrelation N...] [2016-12-16 13:04:03] [d1d385d9b7e195437bdc484ddbefdda4] 
- R         [(Partial) Autocorrelation Function] [autocorrelation m...] [2016-12-18 19:18:14] [d1d385d9b7e195437bdc484ddbefdda4] 
- R         [(Partial) Autocorrelation Function] [1x d] [2016-12-18 21:05:51] [d1d385d9b7e195437bdc484ddbefdda4] 

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	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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300137&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300137&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300137&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.454643	-4.8329	2e-06
2	-0.143922	-1.5299	0.064417
3	0.082464	0.8766	0.19128
4	0.03526	0.3748	0.354249
5	-0.003519	-0.0374	0.485112
6	-0.04827	-0.5131	0.304436
7	0.070288	0.7472	0.228255
8	-0.031909	-0.3392	0.367546
9	0.122827	1.3057	0.097158
10	-0.192702	-2.0485	0.021416
11	-0.236827	-2.5175	0.00661
12	0.635116	6.7514	0
13	-0.274557	-2.9186	0.002122
14	-0.148488	-1.5784	0.058629
15	0.124508	1.3235	0.094165
16	-0.06811	-0.724	0.235274
17	0.043537	0.4628	0.322198
18	-0.001177	-0.0125	0.495019
19	0.006182	0.0657	0.47386
20	-0.00408	-0.0434	0.482742

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.454643 & -4.8329 & 2e-06 \tabularnewline
2 & -0.143922 & -1.5299 & 0.064417 \tabularnewline
3 & 0.082464 & 0.8766 & 0.19128 \tabularnewline
4 & 0.03526 & 0.3748 & 0.354249 \tabularnewline
5 & -0.003519 & -0.0374 & 0.485112 \tabularnewline
6 & -0.04827 & -0.5131 & 0.304436 \tabularnewline
7 & 0.070288 & 0.7472 & 0.228255 \tabularnewline
8 & -0.031909 & -0.3392 & 0.367546 \tabularnewline
9 & 0.122827 & 1.3057 & 0.097158 \tabularnewline
10 & -0.192702 & -2.0485 & 0.021416 \tabularnewline
11 & -0.236827 & -2.5175 & 0.00661 \tabularnewline
12 & 0.635116 & 6.7514 & 0 \tabularnewline
13 & -0.274557 & -2.9186 & 0.002122 \tabularnewline
14 & -0.148488 & -1.5784 & 0.058629 \tabularnewline
15 & 0.124508 & 1.3235 & 0.094165 \tabularnewline
16 & -0.06811 & -0.724 & 0.235274 \tabularnewline
17 & 0.043537 & 0.4628 & 0.322198 \tabularnewline
18 & -0.001177 & -0.0125 & 0.495019 \tabularnewline
19 & 0.006182 & 0.0657 & 0.47386 \tabularnewline
20 & -0.00408 & -0.0434 & 0.482742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300137&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]-0.454643[/C][C]-4.8329[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.143922[/C][C]-1.5299[/C][C]0.064417[/C][/ROW]
[ROW][C]3[/C][C]0.082464[/C][C]0.8766[/C][C]0.19128[/C][/ROW]
[ROW][C]4[/C][C]0.03526[/C][C]0.3748[/C][C]0.354249[/C][/ROW]
[ROW][C]5[/C][C]-0.003519[/C][C]-0.0374[/C][C]0.485112[/C][/ROW]
[ROW][C]6[/C][C]-0.04827[/C][C]-0.5131[/C][C]0.304436[/C][/ROW]
[ROW][C]7[/C][C]0.070288[/C][C]0.7472[/C][C]0.228255[/C][/ROW]
[ROW][C]8[/C][C]-0.031909[/C][C]-0.3392[/C][C]0.367546[/C][/ROW]
[ROW][C]9[/C][C]0.122827[/C][C]1.3057[/C][C]0.097158[/C][/ROW]
[ROW][C]10[/C][C]-0.192702[/C][C]-2.0485[/C][C]0.021416[/C][/ROW]
[ROW][C]11[/C][C]-0.236827[/C][C]-2.5175[/C][C]0.00661[/C][/ROW]
[ROW][C]12[/C][C]0.635116[/C][C]6.7514[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.274557[/C][C]-2.9186[/C][C]0.002122[/C][/ROW]
[ROW][C]14[/C][C]-0.148488[/C][C]-1.5784[/C][C]0.058629[/C][/ROW]
[ROW][C]15[/C][C]0.124508[/C][C]1.3235[/C][C]0.094165[/C][/ROW]
[ROW][C]16[/C][C]-0.06811[/C][C]-0.724[/C][C]0.235274[/C][/ROW]
[ROW][C]17[/C][C]0.043537[/C][C]0.4628[/C][C]0.322198[/C][/ROW]
[ROW][C]18[/C][C]-0.001177[/C][C]-0.0125[/C][C]0.495019[/C][/ROW]
[ROW][C]19[/C][C]0.006182[/C][C]0.0657[/C][C]0.47386[/C][/ROW]
[ROW][C]20[/C][C]-0.00408[/C][C]-0.0434[/C][C]0.482742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300137&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300137&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	-0.454643	-4.8329	2e-06
2	-0.143922	-1.5299	0.064417
3	0.082464	0.8766	0.19128
4	0.03526	0.3748	0.354249
5	-0.003519	-0.0374	0.485112
6	-0.04827	-0.5131	0.304436
7	0.070288	0.7472	0.228255
8	-0.031909	-0.3392	0.367546
9	0.122827	1.3057	0.097158
10	-0.192702	-2.0485	0.021416
11	-0.236827	-2.5175	0.00661
12	0.635116	6.7514	0
13	-0.274557	-2.9186	0.002122
14	-0.148488	-1.5784	0.058629
15	0.124508	1.3235	0.094165
16	-0.06811	-0.724	0.235274
17	0.043537	0.4628	0.322198
18	-0.001177	-0.0125	0.495019
19	0.006182	0.0657	0.47386
20	-0.00408	-0.0434	0.482742

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.454643	-4.8329	2e-06
2	-0.44198	-4.6983	4e-06
3	-0.333419	-3.5443	0.000287
4	-0.255885	-2.7201	0.003779
5	-0.184226	-1.9584	0.026327
6	-0.206754	-2.1978	0.015001
7	-0.099441	-1.0571	0.146367
8	-0.08438	-0.897	0.185821
9	0.219891	2.3375	0.010587
10	0.097178	1.033	0.1519
11	-0.523087	-5.5605	0
12	0.156548	1.6641	0.049429
13	0.18492	1.9657	0.025892
14	0.091338	0.9709	0.166826
15	0.224682	2.3884	0.00929
16	-0.095949	-1.02	0.154964
17	-0.075427	-0.8018	0.212177
18	0.072043	0.7658	0.222689
19	-0.075774	-0.8055	0.211116
20	0.013579	0.1443	0.442741

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.454643 & -4.8329 & 2e-06 \tabularnewline
2 & -0.44198 & -4.6983 & 4e-06 \tabularnewline
3 & -0.333419 & -3.5443 & 0.000287 \tabularnewline
4 & -0.255885 & -2.7201 & 0.003779 \tabularnewline
5 & -0.184226 & -1.9584 & 0.026327 \tabularnewline
6 & -0.206754 & -2.1978 & 0.015001 \tabularnewline
7 & -0.099441 & -1.0571 & 0.146367 \tabularnewline
8 & -0.08438 & -0.897 & 0.185821 \tabularnewline
9 & 0.219891 & 2.3375 & 0.010587 \tabularnewline
10 & 0.097178 & 1.033 & 0.1519 \tabularnewline
11 & -0.523087 & -5.5605 & 0 \tabularnewline
12 & 0.156548 & 1.6641 & 0.049429 \tabularnewline
13 & 0.18492 & 1.9657 & 0.025892 \tabularnewline
14 & 0.091338 & 0.9709 & 0.166826 \tabularnewline
15 & 0.224682 & 2.3884 & 0.00929 \tabularnewline
16 & -0.095949 & -1.02 & 0.154964 \tabularnewline
17 & -0.075427 & -0.8018 & 0.212177 \tabularnewline
18 & 0.072043 & 0.7658 & 0.222689 \tabularnewline
19 & -0.075774 & -0.8055 & 0.211116 \tabularnewline
20 & 0.013579 & 0.1443 & 0.442741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300137&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]-0.454643[/C][C]-4.8329[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.44198[/C][C]-4.6983[/C][C]4e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.333419[/C][C]-3.5443[/C][C]0.000287[/C][/ROW]
[ROW][C]4[/C][C]-0.255885[/C][C]-2.7201[/C][C]0.003779[/C][/ROW]
[ROW][C]5[/C][C]-0.184226[/C][C]-1.9584[/C][C]0.026327[/C][/ROW]
[ROW][C]6[/C][C]-0.206754[/C][C]-2.1978[/C][C]0.015001[/C][/ROW]
[ROW][C]7[/C][C]-0.099441[/C][C]-1.0571[/C][C]0.146367[/C][/ROW]
[ROW][C]8[/C][C]-0.08438[/C][C]-0.897[/C][C]0.185821[/C][/ROW]
[ROW][C]9[/C][C]0.219891[/C][C]2.3375[/C][C]0.010587[/C][/ROW]
[ROW][C]10[/C][C]0.097178[/C][C]1.033[/C][C]0.1519[/C][/ROW]
[ROW][C]11[/C][C]-0.523087[/C][C]-5.5605[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.156548[/C][C]1.6641[/C][C]0.049429[/C][/ROW]
[ROW][C]13[/C][C]0.18492[/C][C]1.9657[/C][C]0.025892[/C][/ROW]
[ROW][C]14[/C][C]0.091338[/C][C]0.9709[/C][C]0.166826[/C][/ROW]
[ROW][C]15[/C][C]0.224682[/C][C]2.3884[/C][C]0.00929[/C][/ROW]
[ROW][C]16[/C][C]-0.095949[/C][C]-1.02[/C][C]0.154964[/C][/ROW]
[ROW][C]17[/C][C]-0.075427[/C][C]-0.8018[/C][C]0.212177[/C][/ROW]
[ROW][C]18[/C][C]0.072043[/C][C]0.7658[/C][C]0.222689[/C][/ROW]
[ROW][C]19[/C][C]-0.075774[/C][C]-0.8055[/C][C]0.211116[/C][/ROW]
[ROW][C]20[/C][C]0.013579[/C][C]0.1443[/C][C]0.442741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300137&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300137&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	-0.454643	-4.8329	2e-06
2	-0.44198	-4.6983	4e-06
3	-0.333419	-3.5443	0.000287
4	-0.255885	-2.7201	0.003779
5	-0.184226	-1.9584	0.026327
6	-0.206754	-2.1978	0.015001
7	-0.099441	-1.0571	0.146367
8	-0.08438	-0.897	0.185821
9	0.219891	2.3375	0.010587
10	0.097178	1.033	0.1519
11	-0.523087	-5.5605	0
12	0.156548	1.6641	0.049429
13	0.18492	1.9657	0.025892
14	0.091338	0.9709	0.166826
15	0.224682	2.3884	0.00929
16	-0.095949	-1.02	0.154964
17	-0.075427	-0.8018	0.212177
18	0.072043	0.7658	0.222689
19	-0.075774	-0.8055	0.211116
20	0.013579	0.1443	0.442741

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
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