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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 14:44:44 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/14/t1481723144k1jqzd7vq68jthr.htm/, Retrieved Sat, 04 May 2024 04:18:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299434, Retrieved Sat, 04 May 2024 04:18:51 +0000

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

-       [(Partial) Autocorrelation Function] [] [2016-12-14 13:44:44] [2802fcbee976b89d2ab84425d3d65dcf] [Current]

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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=299434&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=299434&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299434&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	0.907925	5.3714	3e-06
2	0.814902	4.821	1.4e-05
3	0.72502	4.2893	6.7e-05
4	0.635366	3.7589	0.000312
5	0.55228	3.2673	0.001218
6	0.475239	2.8116	0.004012
7	0.399554	2.3638	0.011885
8	0.312027	1.846	0.036684
9	0.219097	1.2962	0.101695
10	0.125569	0.7429	0.231256
11	0.033439	0.1978	0.422162
12	-0.027359	-0.1619	0.436174
13	-0.086642	-0.5126	0.305732
14	-0.140545	-0.8315	0.205671
15	-0.184339	-1.0906	0.141458

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.907925 & 5.3714 & 3e-06 \tabularnewline
2 & 0.814902 & 4.821 & 1.4e-05 \tabularnewline
3 & 0.72502 & 4.2893 & 6.7e-05 \tabularnewline
4 & 0.635366 & 3.7589 & 0.000312 \tabularnewline
5 & 0.55228 & 3.2673 & 0.001218 \tabularnewline
6 & 0.475239 & 2.8116 & 0.004012 \tabularnewline
7 & 0.399554 & 2.3638 & 0.011885 \tabularnewline
8 & 0.312027 & 1.846 & 0.036684 \tabularnewline
9 & 0.219097 & 1.2962 & 0.101695 \tabularnewline
10 & 0.125569 & 0.7429 & 0.231256 \tabularnewline
11 & 0.033439 & 0.1978 & 0.422162 \tabularnewline
12 & -0.027359 & -0.1619 & 0.436174 \tabularnewline
13 & -0.086642 & -0.5126 & 0.305732 \tabularnewline
14 & -0.140545 & -0.8315 & 0.205671 \tabularnewline
15 & -0.184339 & -1.0906 & 0.141458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299434&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]0.907925[/C][C]5.3714[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.814902[/C][C]4.821[/C][C]1.4e-05[/C][/ROW]
[ROW][C]3[/C][C]0.72502[/C][C]4.2893[/C][C]6.7e-05[/C][/ROW]
[ROW][C]4[/C][C]0.635366[/C][C]3.7589[/C][C]0.000312[/C][/ROW]
[ROW][C]5[/C][C]0.55228[/C][C]3.2673[/C][C]0.001218[/C][/ROW]
[ROW][C]6[/C][C]0.475239[/C][C]2.8116[/C][C]0.004012[/C][/ROW]
[ROW][C]7[/C][C]0.399554[/C][C]2.3638[/C][C]0.011885[/C][/ROW]
[ROW][C]8[/C][C]0.312027[/C][C]1.846[/C][C]0.036684[/C][/ROW]
[ROW][C]9[/C][C]0.219097[/C][C]1.2962[/C][C]0.101695[/C][/ROW]
[ROW][C]10[/C][C]0.125569[/C][C]0.7429[/C][C]0.231256[/C][/ROW]
[ROW][C]11[/C][C]0.033439[/C][C]0.1978[/C][C]0.422162[/C][/ROW]
[ROW][C]12[/C][C]-0.027359[/C][C]-0.1619[/C][C]0.436174[/C][/ROW]
[ROW][C]13[/C][C]-0.086642[/C][C]-0.5126[/C][C]0.305732[/C][/ROW]
[ROW][C]14[/C][C]-0.140545[/C][C]-0.8315[/C][C]0.205671[/C][/ROW]
[ROW][C]15[/C][C]-0.184339[/C][C]-1.0906[/C][C]0.141458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299434&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299434&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	0.907925	5.3714	3e-06
2	0.814902	4.821	1.4e-05
3	0.72502	4.2893	6.7e-05
4	0.635366	3.7589	0.000312
5	0.55228	3.2673	0.001218
6	0.475239	2.8116	0.004012
7	0.399554	2.3638	0.011885
8	0.312027	1.846	0.036684
9	0.219097	1.2962	0.101695
10	0.125569	0.7429	0.231256
11	0.033439	0.1978	0.422162
12	-0.027359	-0.1619	0.436174
13	-0.086642	-0.5126	0.305732
14	-0.140545	-0.8315	0.205671
15	-0.184339	-1.0906	0.141458

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.907925	5.3714	3e-06
2	-0.053656	-0.3174	0.3764
3	-0.033302	-0.197	0.422478
4	-0.050995	-0.3017	0.382336
5	-0.016938	-0.1002	0.460377
6	-0.019494	-0.1153	0.454423
7	-0.044319	-0.2622	0.397354
8	-0.121867	-0.721	0.237856
9	-0.095895	-0.5673	0.287059
10	-0.078889	-0.4667	0.321798
11	-0.073486	-0.4347	0.333207
12	0.093749	0.5546	0.291338
13	-0.06519	-0.3857	0.351037
14	-0.036978	-0.2188	0.414053
15	-0.008157	-0.0483	0.480892

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.907925 & 5.3714 & 3e-06 \tabularnewline
2 & -0.053656 & -0.3174 & 0.3764 \tabularnewline
3 & -0.033302 & -0.197 & 0.422478 \tabularnewline
4 & -0.050995 & -0.3017 & 0.382336 \tabularnewline
5 & -0.016938 & -0.1002 & 0.460377 \tabularnewline
6 & -0.019494 & -0.1153 & 0.454423 \tabularnewline
7 & -0.044319 & -0.2622 & 0.397354 \tabularnewline
8 & -0.121867 & -0.721 & 0.237856 \tabularnewline
9 & -0.095895 & -0.5673 & 0.287059 \tabularnewline
10 & -0.078889 & -0.4667 & 0.321798 \tabularnewline
11 & -0.073486 & -0.4347 & 0.333207 \tabularnewline
12 & 0.093749 & 0.5546 & 0.291338 \tabularnewline
13 & -0.06519 & -0.3857 & 0.351037 \tabularnewline
14 & -0.036978 & -0.2188 & 0.414053 \tabularnewline
15 & -0.008157 & -0.0483 & 0.480892 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299434&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]0.907925[/C][C]5.3714[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.053656[/C][C]-0.3174[/C][C]0.3764[/C][/ROW]
[ROW][C]3[/C][C]-0.033302[/C][C]-0.197[/C][C]0.422478[/C][/ROW]
[ROW][C]4[/C][C]-0.050995[/C][C]-0.3017[/C][C]0.382336[/C][/ROW]
[ROW][C]5[/C][C]-0.016938[/C][C]-0.1002[/C][C]0.460377[/C][/ROW]
[ROW][C]6[/C][C]-0.019494[/C][C]-0.1153[/C][C]0.454423[/C][/ROW]
[ROW][C]7[/C][C]-0.044319[/C][C]-0.2622[/C][C]0.397354[/C][/ROW]
[ROW][C]8[/C][C]-0.121867[/C][C]-0.721[/C][C]0.237856[/C][/ROW]
[ROW][C]9[/C][C]-0.095895[/C][C]-0.5673[/C][C]0.287059[/C][/ROW]
[ROW][C]10[/C][C]-0.078889[/C][C]-0.4667[/C][C]0.321798[/C][/ROW]
[ROW][C]11[/C][C]-0.073486[/C][C]-0.4347[/C][C]0.333207[/C][/ROW]
[ROW][C]12[/C][C]0.093749[/C][C]0.5546[/C][C]0.291338[/C][/ROW]
[ROW][C]13[/C][C]-0.06519[/C][C]-0.3857[/C][C]0.351037[/C][/ROW]
[ROW][C]14[/C][C]-0.036978[/C][C]-0.2188[/C][C]0.414053[/C][/ROW]
[ROW][C]15[/C][C]-0.008157[/C][C]-0.0483[/C][C]0.480892[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299434&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299434&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	0.907925	5.3714	3e-06
2	-0.053656	-0.3174	0.3764
3	-0.033302	-0.197	0.422478
4	-0.050995	-0.3017	0.382336
5	-0.016938	-0.1002	0.460377
6	-0.019494	-0.1153	0.454423
7	-0.044319	-0.2622	0.397354
8	-0.121867	-0.721	0.237856
9	-0.095895	-0.5673	0.287059
10	-0.078889	-0.4667	0.321798
11	-0.073486	-0.4347	0.333207
12	0.093749	0.5546	0.291338
13	-0.06519	-0.3857	0.351037
14	-0.036978	-0.2188	0.414053
15	-0.008157	-0.0483	0.480892

Figure 1

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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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

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Input Parameters & R Code