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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 17:07:57 +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/t1481904511hb1cgvy5kika9kx.htm/, Retrieved Fri, 03 May 2024 02:26:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300407, Retrieved Fri, 03 May 2024 02:26:02 +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) Autocor...] [2016-12-16 16:07:57] [2a4be59ea15844c348dc523b08af79fc] [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	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=300407&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=300407&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300407&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	-0.109906	-1.209	0.114517
2	-0.126841	-1.3952	0.082749
3	-0.188147	-2.0696	0.020308
4	-0.024276	-0.267	0.394947
5	0.005683	0.0625	0.475127
6	-0.05091	-0.56	0.288256
7	-0.088322	-0.9715	0.166608
8	-0.06523	-0.7175	0.237216
9	0.220373	2.4241	0.008413
10	-0.039979	-0.4398	0.330445
11	-0.012066	-0.1327	0.447317
12	-0.048209	-0.5303	0.29844
13	-0.042613	-0.4687	0.320047
14	0.019194	0.2111	0.41657
15	0.109182	1.201	0.116048
16	-0.010499	-0.1155	0.454126
17	-0.00262	-0.0288	0.488527
18	-0.074328	-0.8176	0.207593
19	-0.020536	-0.2259	0.410833
20	-0.008384	-0.0922	0.463335

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.109906 & -1.209 & 0.114517 \tabularnewline
2 & -0.126841 & -1.3952 & 0.082749 \tabularnewline
3 & -0.188147 & -2.0696 & 0.020308 \tabularnewline
4 & -0.024276 & -0.267 & 0.394947 \tabularnewline
5 & 0.005683 & 0.0625 & 0.475127 \tabularnewline
6 & -0.05091 & -0.56 & 0.288256 \tabularnewline
7 & -0.088322 & -0.9715 & 0.166608 \tabularnewline
8 & -0.06523 & -0.7175 & 0.237216 \tabularnewline
9 & 0.220373 & 2.4241 & 0.008413 \tabularnewline
10 & -0.039979 & -0.4398 & 0.330445 \tabularnewline
11 & -0.012066 & -0.1327 & 0.447317 \tabularnewline
12 & -0.048209 & -0.5303 & 0.29844 \tabularnewline
13 & -0.042613 & -0.4687 & 0.320047 \tabularnewline
14 & 0.019194 & 0.2111 & 0.41657 \tabularnewline
15 & 0.109182 & 1.201 & 0.116048 \tabularnewline
16 & -0.010499 & -0.1155 & 0.454126 \tabularnewline
17 & -0.00262 & -0.0288 & 0.488527 \tabularnewline
18 & -0.074328 & -0.8176 & 0.207593 \tabularnewline
19 & -0.020536 & -0.2259 & 0.410833 \tabularnewline
20 & -0.008384 & -0.0922 & 0.463335 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300407&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]-0.109906[/C][C]-1.209[/C][C]0.114517[/C][/ROW]
[ROW][C]2[/C][C]-0.126841[/C][C]-1.3952[/C][C]0.082749[/C][/ROW]
[ROW][C]3[/C][C]-0.188147[/C][C]-2.0696[/C][C]0.020308[/C][/ROW]
[ROW][C]4[/C][C]-0.024276[/C][C]-0.267[/C][C]0.394947[/C][/ROW]
[ROW][C]5[/C][C]0.005683[/C][C]0.0625[/C][C]0.475127[/C][/ROW]
[ROW][C]6[/C][C]-0.05091[/C][C]-0.56[/C][C]0.288256[/C][/ROW]
[ROW][C]7[/C][C]-0.088322[/C][C]-0.9715[/C][C]0.166608[/C][/ROW]
[ROW][C]8[/C][C]-0.06523[/C][C]-0.7175[/C][C]0.237216[/C][/ROW]
[ROW][C]9[/C][C]0.220373[/C][C]2.4241[/C][C]0.008413[/C][/ROW]
[ROW][C]10[/C][C]-0.039979[/C][C]-0.4398[/C][C]0.330445[/C][/ROW]
[ROW][C]11[/C][C]-0.012066[/C][C]-0.1327[/C][C]0.447317[/C][/ROW]
[ROW][C]12[/C][C]-0.048209[/C][C]-0.5303[/C][C]0.29844[/C][/ROW]
[ROW][C]13[/C][C]-0.042613[/C][C]-0.4687[/C][C]0.320047[/C][/ROW]
[ROW][C]14[/C][C]0.019194[/C][C]0.2111[/C][C]0.41657[/C][/ROW]
[ROW][C]15[/C][C]0.109182[/C][C]1.201[/C][C]0.116048[/C][/ROW]
[ROW][C]16[/C][C]-0.010499[/C][C]-0.1155[/C][C]0.454126[/C][/ROW]
[ROW][C]17[/C][C]-0.00262[/C][C]-0.0288[/C][C]0.488527[/C][/ROW]
[ROW][C]18[/C][C]-0.074328[/C][C]-0.8176[/C][C]0.207593[/C][/ROW]
[ROW][C]19[/C][C]-0.020536[/C][C]-0.2259[/C][C]0.410833[/C][/ROW]
[ROW][C]20[/C][C]-0.008384[/C][C]-0.0922[/C][C]0.463335[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300407&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300407&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	-0.109906	-1.209	0.114517
2	-0.126841	-1.3952	0.082749
3	-0.188147	-2.0696	0.020308
4	-0.024276	-0.267	0.394947
5	0.005683	0.0625	0.475127
6	-0.05091	-0.56	0.288256
7	-0.088322	-0.9715	0.166608
8	-0.06523	-0.7175	0.237216
9	0.220373	2.4241	0.008413
10	-0.039979	-0.4398	0.330445
11	-0.012066	-0.1327	0.447317
12	-0.048209	-0.5303	0.29844
13	-0.042613	-0.4687	0.320047
14	0.019194	0.2111	0.41657
15	0.109182	1.201	0.116048
16	-0.010499	-0.1155	0.454126
17	-0.00262	-0.0288	0.488527
18	-0.074328	-0.8176	0.207593
19	-0.020536	-0.2259	0.410833
20	-0.008384	-0.0922	0.463335

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.109906	-1.209	0.114517
2	-0.140619	-1.5468	0.062261
3	-0.226669	-2.4934	0.007003
4	-0.109088	-1.2	0.116247
5	-0.084744	-0.9322	0.176548
6	-0.142974	-1.5727	0.059198
7	-0.185272	-2.038	0.021865
8	-0.203595	-2.2395	0.013473
9	0.074112	0.8152	0.208272
10	-0.126007	-1.3861	0.084137
11	-0.088437	-0.9728	0.166295
12	-0.076684	-0.8435	0.200299
13	-0.148231	-1.6305	0.052794
14	-0.113389	-1.2473	0.107351
15	0.019281	0.2121	0.416198
16	-0.0429	-0.4719	0.318924
17	-0.004778	-0.0526	0.479085
18	-0.135672	-1.4924	0.0691
19	-0.082613	-0.9087	0.182647
20	-0.109027	-1.1993	0.116379

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.109906 & -1.209 & 0.114517 \tabularnewline
2 & -0.140619 & -1.5468 & 0.062261 \tabularnewline
3 & -0.226669 & -2.4934 & 0.007003 \tabularnewline
4 & -0.109088 & -1.2 & 0.116247 \tabularnewline
5 & -0.084744 & -0.9322 & 0.176548 \tabularnewline
6 & -0.142974 & -1.5727 & 0.059198 \tabularnewline
7 & -0.185272 & -2.038 & 0.021865 \tabularnewline
8 & -0.203595 & -2.2395 & 0.013473 \tabularnewline
9 & 0.074112 & 0.8152 & 0.208272 \tabularnewline
10 & -0.126007 & -1.3861 & 0.084137 \tabularnewline
11 & -0.088437 & -0.9728 & 0.166295 \tabularnewline
12 & -0.076684 & -0.8435 & 0.200299 \tabularnewline
13 & -0.148231 & -1.6305 & 0.052794 \tabularnewline
14 & -0.113389 & -1.2473 & 0.107351 \tabularnewline
15 & 0.019281 & 0.2121 & 0.416198 \tabularnewline
16 & -0.0429 & -0.4719 & 0.318924 \tabularnewline
17 & -0.004778 & -0.0526 & 0.479085 \tabularnewline
18 & -0.135672 & -1.4924 & 0.0691 \tabularnewline
19 & -0.082613 & -0.9087 & 0.182647 \tabularnewline
20 & -0.109027 & -1.1993 & 0.116379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300407&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]-0.109906[/C][C]-1.209[/C][C]0.114517[/C][/ROW]
[ROW][C]2[/C][C]-0.140619[/C][C]-1.5468[/C][C]0.062261[/C][/ROW]
[ROW][C]3[/C][C]-0.226669[/C][C]-2.4934[/C][C]0.007003[/C][/ROW]
[ROW][C]4[/C][C]-0.109088[/C][C]-1.2[/C][C]0.116247[/C][/ROW]
[ROW][C]5[/C][C]-0.084744[/C][C]-0.9322[/C][C]0.176548[/C][/ROW]
[ROW][C]6[/C][C]-0.142974[/C][C]-1.5727[/C][C]0.059198[/C][/ROW]
[ROW][C]7[/C][C]-0.185272[/C][C]-2.038[/C][C]0.021865[/C][/ROW]
[ROW][C]8[/C][C]-0.203595[/C][C]-2.2395[/C][C]0.013473[/C][/ROW]
[ROW][C]9[/C][C]0.074112[/C][C]0.8152[/C][C]0.208272[/C][/ROW]
[ROW][C]10[/C][C]-0.126007[/C][C]-1.3861[/C][C]0.084137[/C][/ROW]
[ROW][C]11[/C][C]-0.088437[/C][C]-0.9728[/C][C]0.166295[/C][/ROW]
[ROW][C]12[/C][C]-0.076684[/C][C]-0.8435[/C][C]0.200299[/C][/ROW]
[ROW][C]13[/C][C]-0.148231[/C][C]-1.6305[/C][C]0.052794[/C][/ROW]
[ROW][C]14[/C][C]-0.113389[/C][C]-1.2473[/C][C]0.107351[/C][/ROW]
[ROW][C]15[/C][C]0.019281[/C][C]0.2121[/C][C]0.416198[/C][/ROW]
[ROW][C]16[/C][C]-0.0429[/C][C]-0.4719[/C][C]0.318924[/C][/ROW]
[ROW][C]17[/C][C]-0.004778[/C][C]-0.0526[/C][C]0.479085[/C][/ROW]
[ROW][C]18[/C][C]-0.135672[/C][C]-1.4924[/C][C]0.0691[/C][/ROW]
[ROW][C]19[/C][C]-0.082613[/C][C]-0.9087[/C][C]0.182647[/C][/ROW]
[ROW][C]20[/C][C]-0.109027[/C][C]-1.1993[/C][C]0.116379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300407&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300407&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	-0.109906	-1.209	0.114517
2	-0.140619	-1.5468	0.062261
3	-0.226669	-2.4934	0.007003
4	-0.109088	-1.2	0.116247
5	-0.084744	-0.9322	0.176548
6	-0.142974	-1.5727	0.059198
7	-0.185272	-2.038	0.021865
8	-0.203595	-2.2395	0.013473
9	0.074112	0.8152	0.208272
10	-0.126007	-1.3861	0.084137
11	-0.088437	-0.9728	0.166295
12	-0.076684	-0.8435	0.200299
13	-0.148231	-1.6305	0.052794
14	-0.113389	-1.2473	0.107351
15	0.019281	0.2121	0.416198
16	-0.0429	-0.4719	0.318924
17	-0.004778	-0.0526	0.479085
18	-0.135672	-1.4924	0.0691
19	-0.082613	-0.9087	0.182647
20	-0.109027	-1.1993	0.116379

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 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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