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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 13:21:49 +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/t1482236548r1w3ce7qvxq6d5c.htm/, Retrieved Fri, 17 May 2024 15:09:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301627, Retrieved Fri, 17 May 2024 15:09:01 +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] [Partial Autocorre...] [2016-12-20 12:21:49] [86c9a777e8dbb7ef3face68c75fc8376] [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=301627&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=301627&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301627&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	-0.34393	-3.656	0.000195
2	-0.312146	-3.3182	0.00061
3	0.243411	2.5875	0.005468
4	-0.06815	-0.7244	0.235147
5	-0.001734	-0.0184	0.492665
6	0.061293	0.6516	0.258006
7	-0.080702	-0.8579	0.196389
8	-0.053872	-0.5727	0.284003
9	0.291157	3.095	0.001241
10	-0.272541	-2.8972	0.002262
11	-0.185438	-1.9712	0.025571
12	0.528121	5.614	0
13	-0.256586	-2.7275	0.0037
14	-0.134122	-1.4257	0.07835
15	0.199778	2.1237	0.017939
16	-0.045034	-0.4787	0.316532
17	-0.003072	-0.0327	0.487004
18	-0.045296	-0.4815	0.315545
19	0.022071	0.2346	0.407465
20	-0.021685	-0.2305	0.409054

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.34393 & -3.656 & 0.000195 \tabularnewline
2 & -0.312146 & -3.3182 & 0.00061 \tabularnewline
3 & 0.243411 & 2.5875 & 0.005468 \tabularnewline
4 & -0.06815 & -0.7244 & 0.235147 \tabularnewline
5 & -0.001734 & -0.0184 & 0.492665 \tabularnewline
6 & 0.061293 & 0.6516 & 0.258006 \tabularnewline
7 & -0.080702 & -0.8579 & 0.196389 \tabularnewline
8 & -0.053872 & -0.5727 & 0.284003 \tabularnewline
9 & 0.291157 & 3.095 & 0.001241 \tabularnewline
10 & -0.272541 & -2.8972 & 0.002262 \tabularnewline
11 & -0.185438 & -1.9712 & 0.025571 \tabularnewline
12 & 0.528121 & 5.614 & 0 \tabularnewline
13 & -0.256586 & -2.7275 & 0.0037 \tabularnewline
14 & -0.134122 & -1.4257 & 0.07835 \tabularnewline
15 & 0.199778 & 2.1237 & 0.017939 \tabularnewline
16 & -0.045034 & -0.4787 & 0.316532 \tabularnewline
17 & -0.003072 & -0.0327 & 0.487004 \tabularnewline
18 & -0.045296 & -0.4815 & 0.315545 \tabularnewline
19 & 0.022071 & 0.2346 & 0.407465 \tabularnewline
20 & -0.021685 & -0.2305 & 0.409054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301627&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]-0.34393[/C][C]-3.656[/C][C]0.000195[/C][/ROW]
[ROW][C]2[/C][C]-0.312146[/C][C]-3.3182[/C][C]0.00061[/C][/ROW]
[ROW][C]3[/C][C]0.243411[/C][C]2.5875[/C][C]0.005468[/C][/ROW]
[ROW][C]4[/C][C]-0.06815[/C][C]-0.7244[/C][C]0.235147[/C][/ROW]
[ROW][C]5[/C][C]-0.001734[/C][C]-0.0184[/C][C]0.492665[/C][/ROW]
[ROW][C]6[/C][C]0.061293[/C][C]0.6516[/C][C]0.258006[/C][/ROW]
[ROW][C]7[/C][C]-0.080702[/C][C]-0.8579[/C][C]0.196389[/C][/ROW]
[ROW][C]8[/C][C]-0.053872[/C][C]-0.5727[/C][C]0.284003[/C][/ROW]
[ROW][C]9[/C][C]0.291157[/C][C]3.095[/C][C]0.001241[/C][/ROW]
[ROW][C]10[/C][C]-0.272541[/C][C]-2.8972[/C][C]0.002262[/C][/ROW]
[ROW][C]11[/C][C]-0.185438[/C][C]-1.9712[/C][C]0.025571[/C][/ROW]
[ROW][C]12[/C][C]0.528121[/C][C]5.614[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.256586[/C][C]-2.7275[/C][C]0.0037[/C][/ROW]
[ROW][C]14[/C][C]-0.134122[/C][C]-1.4257[/C][C]0.07835[/C][/ROW]
[ROW][C]15[/C][C]0.199778[/C][C]2.1237[/C][C]0.017939[/C][/ROW]
[ROW][C]16[/C][C]-0.045034[/C][C]-0.4787[/C][C]0.316532[/C][/ROW]
[ROW][C]17[/C][C]-0.003072[/C][C]-0.0327[/C][C]0.487004[/C][/ROW]
[ROW][C]18[/C][C]-0.045296[/C][C]-0.4815[/C][C]0.315545[/C][/ROW]
[ROW][C]19[/C][C]0.022071[/C][C]0.2346[/C][C]0.407465[/C][/ROW]
[ROW][C]20[/C][C]-0.021685[/C][C]-0.2305[/C][C]0.409054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301627&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301627&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	-0.34393	-3.656	0.000195
2	-0.312146	-3.3182	0.00061
3	0.243411	2.5875	0.005468
4	-0.06815	-0.7244	0.235147
5	-0.001734	-0.0184	0.492665
6	0.061293	0.6516	0.258006
7	-0.080702	-0.8579	0.196389
8	-0.053872	-0.5727	0.284003
9	0.291157	3.095	0.001241
10	-0.272541	-2.8972	0.002262
11	-0.185438	-1.9712	0.025571
12	0.528121	5.614	0
13	-0.256586	-2.7275	0.0037
14	-0.134122	-1.4257	0.07835
15	0.199778	2.1237	0.017939
16	-0.045034	-0.4787	0.316532
17	-0.003072	-0.0327	0.487004
18	-0.045296	-0.4815	0.315545
19	0.022071	0.2346	0.407465
20	-0.021685	-0.2305	0.409054

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.34393	-3.656	0.000195
2	-0.48818	-5.1894	0
3	-0.125456	-1.3336	0.092506
4	-0.218199	-2.3195	0.011083
5	-0.050981	-0.5419	0.294463
6	-0.019702	-0.2094	0.417242
7	-0.042609	-0.4529	0.325731
8	-0.13818	-1.4689	0.072323
9	0.257265	2.7348	0.003625
10	-0.114726	-1.2196	0.112586
11	-0.251374	-2.6721	0.004326
12	0.26396	2.8059	0.002955
13	-0.024978	-0.2655	0.395546
14	0.025334	0.2693	0.394095
15	0.04443	0.4723	0.318812
16	0.120578	1.2818	0.101274
17	0.101516	1.0791	0.141413
18	-0.118904	-1.264	0.104422
19	0.11531	1.2258	0.111419
20	0.027624	0.2936	0.384785

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.34393 & -3.656 & 0.000195 \tabularnewline
2 & -0.48818 & -5.1894 & 0 \tabularnewline
3 & -0.125456 & -1.3336 & 0.092506 \tabularnewline
4 & -0.218199 & -2.3195 & 0.011083 \tabularnewline
5 & -0.050981 & -0.5419 & 0.294463 \tabularnewline
6 & -0.019702 & -0.2094 & 0.417242 \tabularnewline
7 & -0.042609 & -0.4529 & 0.325731 \tabularnewline
8 & -0.13818 & -1.4689 & 0.072323 \tabularnewline
9 & 0.257265 & 2.7348 & 0.003625 \tabularnewline
10 & -0.114726 & -1.2196 & 0.112586 \tabularnewline
11 & -0.251374 & -2.6721 & 0.004326 \tabularnewline
12 & 0.26396 & 2.8059 & 0.002955 \tabularnewline
13 & -0.024978 & -0.2655 & 0.395546 \tabularnewline
14 & 0.025334 & 0.2693 & 0.394095 \tabularnewline
15 & 0.04443 & 0.4723 & 0.318812 \tabularnewline
16 & 0.120578 & 1.2818 & 0.101274 \tabularnewline
17 & 0.101516 & 1.0791 & 0.141413 \tabularnewline
18 & -0.118904 & -1.264 & 0.104422 \tabularnewline
19 & 0.11531 & 1.2258 & 0.111419 \tabularnewline
20 & 0.027624 & 0.2936 & 0.384785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301627&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]-0.34393[/C][C]-3.656[/C][C]0.000195[/C][/ROW]
[ROW][C]2[/C][C]-0.48818[/C][C]-5.1894[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.125456[/C][C]-1.3336[/C][C]0.092506[/C][/ROW]
[ROW][C]4[/C][C]-0.218199[/C][C]-2.3195[/C][C]0.011083[/C][/ROW]
[ROW][C]5[/C][C]-0.050981[/C][C]-0.5419[/C][C]0.294463[/C][/ROW]
[ROW][C]6[/C][C]-0.019702[/C][C]-0.2094[/C][C]0.417242[/C][/ROW]
[ROW][C]7[/C][C]-0.042609[/C][C]-0.4529[/C][C]0.325731[/C][/ROW]
[ROW][C]8[/C][C]-0.13818[/C][C]-1.4689[/C][C]0.072323[/C][/ROW]
[ROW][C]9[/C][C]0.257265[/C][C]2.7348[/C][C]0.003625[/C][/ROW]
[ROW][C]10[/C][C]-0.114726[/C][C]-1.2196[/C][C]0.112586[/C][/ROW]
[ROW][C]11[/C][C]-0.251374[/C][C]-2.6721[/C][C]0.004326[/C][/ROW]
[ROW][C]12[/C][C]0.26396[/C][C]2.8059[/C][C]0.002955[/C][/ROW]
[ROW][C]13[/C][C]-0.024978[/C][C]-0.2655[/C][C]0.395546[/C][/ROW]
[ROW][C]14[/C][C]0.025334[/C][C]0.2693[/C][C]0.394095[/C][/ROW]
[ROW][C]15[/C][C]0.04443[/C][C]0.4723[/C][C]0.318812[/C][/ROW]
[ROW][C]16[/C][C]0.120578[/C][C]1.2818[/C][C]0.101274[/C][/ROW]
[ROW][C]17[/C][C]0.101516[/C][C]1.0791[/C][C]0.141413[/C][/ROW]
[ROW][C]18[/C][C]-0.118904[/C][C]-1.264[/C][C]0.104422[/C][/ROW]
[ROW][C]19[/C][C]0.11531[/C][C]1.2258[/C][C]0.111419[/C][/ROW]
[ROW][C]20[/C][C]0.027624[/C][C]0.2936[/C][C]0.384785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301627&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301627&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	-0.34393	-3.656	0.000195
2	-0.48818	-5.1894	0
3	-0.125456	-1.3336	0.092506
4	-0.218199	-2.3195	0.011083
5	-0.050981	-0.5419	0.294463
6	-0.019702	-0.2094	0.417242
7	-0.042609	-0.4529	0.325731
8	-0.13818	-1.4689	0.072323
9	0.257265	2.7348	0.003625
10	-0.114726	-1.2196	0.112586
11	-0.251374	-2.6721	0.004326
12	0.26396	2.8059	0.002955
13	-0.024978	-0.2655	0.395546
14	0.025334	0.2693	0.394095
15	0.04443	0.4723	0.318812
16	0.120578	1.2818	0.101274
17	0.101516	1.0791	0.141413
18	-0.118904	-1.264	0.104422
19	0.11531	1.2258	0.111419
20	0.027624	0.2936	0.384785

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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):

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