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

Tue, 20 Dec 2016 14:26:58 +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/20/t148224046853efxohxra96oop.htm/, Retrieved Sun, 28 Apr 2024 05:54:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301654, Retrieved Sun, 28 Apr 2024 05:54:01 +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] [PAF 3] [2016-12-20 13:26:58] [94c1b173d9287822f5e2740a4a602bdd] [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	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=301654&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=301654&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301654&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	0.95278	7.7404	0
2	0.921175	7.4837	0
3	0.885324	7.1924	0
4	0.855257	6.9481	0
5	0.81777	6.6436	0
6	0.774086	6.2887	0
7	0.739221	6.0055	0
8	0.698038	5.6709	0
9	0.647447	5.2599	1e-06
10	0.61043	4.9592	3e-06
11	0.566713	4.604	1e-05
12	0.535536	4.3507	2.4e-05
13	0.475729	3.8648	0.000128
14	0.431738	3.5075	0.00041
15	0.385393	3.1309	0.001298
16	0.339929	2.7616	0.003721
17	0.291287	2.3664	0.010452
18	0.241863	1.9649	0.026818

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95278 & 7.7404 & 0 \tabularnewline
2 & 0.921175 & 7.4837 & 0 \tabularnewline
3 & 0.885324 & 7.1924 & 0 \tabularnewline
4 & 0.855257 & 6.9481 & 0 \tabularnewline
5 & 0.81777 & 6.6436 & 0 \tabularnewline
6 & 0.774086 & 6.2887 & 0 \tabularnewline
7 & 0.739221 & 6.0055 & 0 \tabularnewline
8 & 0.698038 & 5.6709 & 0 \tabularnewline
9 & 0.647447 & 5.2599 & 1e-06 \tabularnewline
10 & 0.61043 & 4.9592 & 3e-06 \tabularnewline
11 & 0.566713 & 4.604 & 1e-05 \tabularnewline
12 & 0.535536 & 4.3507 & 2.4e-05 \tabularnewline
13 & 0.475729 & 3.8648 & 0.000128 \tabularnewline
14 & 0.431738 & 3.5075 & 0.00041 \tabularnewline
15 & 0.385393 & 3.1309 & 0.001298 \tabularnewline
16 & 0.339929 & 2.7616 & 0.003721 \tabularnewline
17 & 0.291287 & 2.3664 & 0.010452 \tabularnewline
18 & 0.241863 & 1.9649 & 0.026818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301654&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]0.95278[/C][C]7.7404[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.921175[/C][C]7.4837[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.885324[/C][C]7.1924[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.855257[/C][C]6.9481[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.81777[/C][C]6.6436[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.774086[/C][C]6.2887[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.739221[/C][C]6.0055[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.698038[/C][C]5.6709[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.647447[/C][C]5.2599[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.61043[/C][C]4.9592[/C][C]3e-06[/C][/ROW]
[ROW][C]11[/C][C]0.566713[/C][C]4.604[/C][C]1e-05[/C][/ROW]
[ROW][C]12[/C][C]0.535536[/C][C]4.3507[/C][C]2.4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.475729[/C][C]3.8648[/C][C]0.000128[/C][/ROW]
[ROW][C]14[/C][C]0.431738[/C][C]3.5075[/C][C]0.00041[/C][/ROW]
[ROW][C]15[/C][C]0.385393[/C][C]3.1309[/C][C]0.001298[/C][/ROW]
[ROW][C]16[/C][C]0.339929[/C][C]2.7616[/C][C]0.003721[/C][/ROW]
[ROW][C]17[/C][C]0.291287[/C][C]2.3664[/C][C]0.010452[/C][/ROW]
[ROW][C]18[/C][C]0.241863[/C][C]1.9649[/C][C]0.026818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301654&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301654&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	0.95278	7.7404	0
2	0.921175	7.4837	0
3	0.885324	7.1924	0
4	0.855257	6.9481	0
5	0.81777	6.6436	0
6	0.774086	6.2887	0
7	0.739221	6.0055	0
8	0.698038	5.6709	0
9	0.647447	5.2599	1e-06
10	0.61043	4.9592	3e-06
11	0.566713	4.604	1e-05
12	0.535536	4.3507	2.4e-05
13	0.475729	3.8648	0.000128
14	0.431738	3.5075	0.00041
15	0.385393	3.1309	0.001298
16	0.339929	2.7616	0.003721
17	0.291287	2.3664	0.010452
18	0.241863	1.9649	0.026818

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.95278	7.7404	0
2	0.145152	1.1792	0.121272
3	-0.036052	-0.2929	0.385262
4	0.034753	0.2823	0.389284
5	-0.079548	-0.6463	0.260179
6	-0.115359	-0.9372	0.176042
7	0.055081	0.4475	0.327995
8	-0.067351	-0.5472	0.293056
9	-0.157369	-1.2785	0.10278
10	0.114315	0.9287	0.178215
11	-0.064546	-0.5244	0.300888
12	0.073435	0.5966	0.276412
13	-0.266253	-2.1631	0.017082
14	0.04736	0.3848	0.350828
15	-0.031839	-0.2587	0.398351
16	-0.032068	-0.2605	0.397637
17	-0.052496	-0.4265	0.335573
18	-0.035486	-0.2883	0.387014

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95278 & 7.7404 & 0 \tabularnewline
2 & 0.145152 & 1.1792 & 0.121272 \tabularnewline
3 & -0.036052 & -0.2929 & 0.385262 \tabularnewline
4 & 0.034753 & 0.2823 & 0.389284 \tabularnewline
5 & -0.079548 & -0.6463 & 0.260179 \tabularnewline
6 & -0.115359 & -0.9372 & 0.176042 \tabularnewline
7 & 0.055081 & 0.4475 & 0.327995 \tabularnewline
8 & -0.067351 & -0.5472 & 0.293056 \tabularnewline
9 & -0.157369 & -1.2785 & 0.10278 \tabularnewline
10 & 0.114315 & 0.9287 & 0.178215 \tabularnewline
11 & -0.064546 & -0.5244 & 0.300888 \tabularnewline
12 & 0.073435 & 0.5966 & 0.276412 \tabularnewline
13 & -0.266253 & -2.1631 & 0.017082 \tabularnewline
14 & 0.04736 & 0.3848 & 0.350828 \tabularnewline
15 & -0.031839 & -0.2587 & 0.398351 \tabularnewline
16 & -0.032068 & -0.2605 & 0.397637 \tabularnewline
17 & -0.052496 & -0.4265 & 0.335573 \tabularnewline
18 & -0.035486 & -0.2883 & 0.387014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301654&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]0.95278[/C][C]7.7404[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.145152[/C][C]1.1792[/C][C]0.121272[/C][/ROW]
[ROW][C]3[/C][C]-0.036052[/C][C]-0.2929[/C][C]0.385262[/C][/ROW]
[ROW][C]4[/C][C]0.034753[/C][C]0.2823[/C][C]0.389284[/C][/ROW]
[ROW][C]5[/C][C]-0.079548[/C][C]-0.6463[/C][C]0.260179[/C][/ROW]
[ROW][C]6[/C][C]-0.115359[/C][C]-0.9372[/C][C]0.176042[/C][/ROW]
[ROW][C]7[/C][C]0.055081[/C][C]0.4475[/C][C]0.327995[/C][/ROW]
[ROW][C]8[/C][C]-0.067351[/C][C]-0.5472[/C][C]0.293056[/C][/ROW]
[ROW][C]9[/C][C]-0.157369[/C][C]-1.2785[/C][C]0.10278[/C][/ROW]
[ROW][C]10[/C][C]0.114315[/C][C]0.9287[/C][C]0.178215[/C][/ROW]
[ROW][C]11[/C][C]-0.064546[/C][C]-0.5244[/C][C]0.300888[/C][/ROW]
[ROW][C]12[/C][C]0.073435[/C][C]0.5966[/C][C]0.276412[/C][/ROW]
[ROW][C]13[/C][C]-0.266253[/C][C]-2.1631[/C][C]0.017082[/C][/ROW]
[ROW][C]14[/C][C]0.04736[/C][C]0.3848[/C][C]0.350828[/C][/ROW]
[ROW][C]15[/C][C]-0.031839[/C][C]-0.2587[/C][C]0.398351[/C][/ROW]
[ROW][C]16[/C][C]-0.032068[/C][C]-0.2605[/C][C]0.397637[/C][/ROW]
[ROW][C]17[/C][C]-0.052496[/C][C]-0.4265[/C][C]0.335573[/C][/ROW]
[ROW][C]18[/C][C]-0.035486[/C][C]-0.2883[/C][C]0.387014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301654&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301654&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	0.95278	7.7404	0
2	0.145152	1.1792	0.121272
3	-0.036052	-0.2929	0.385262
4	0.034753	0.2823	0.389284
5	-0.079548	-0.6463	0.260179
6	-0.115359	-0.9372	0.176042
7	0.055081	0.4475	0.327995
8	-0.067351	-0.5472	0.293056
9	-0.157369	-1.2785	0.10278
10	0.114315	0.9287	0.178215
11	-0.064546	-0.5244	0.300888
12	0.073435	0.5966	0.276412
13	-0.266253	-2.1631	0.017082
14	0.04736	0.3848	0.350828
15	-0.031839	-0.2587	0.398351
16	-0.032068	-0.2605	0.397637
17	-0.052496	-0.4265	0.335573
18	-0.035486	-0.2883	0.387014

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):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

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)
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