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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Feb 2018 09:35:35 +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/2018/Feb/01/t1517474144y1pql19hggcrvyg.htm/, Retrieved Sun, 28 Apr 2024 22:34:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=313669, Retrieved Sun, 28 Apr 2024 22:34:02 +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] [] [2018-02-01 08:35:35] [4d6b7e4aa0a442355d9e4013f368adc5] [Current]

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6.23997569975399e-11
6.73997108398115e-11
7.60996748213444e-11
6.73997049807968e-11
7.44996810521796e-11
7.25996854148587e-11
6.04997333480944e-11
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7.64996738196023e-11
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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=313669&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=313669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313669&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	0.002435	0.0344	0.486284
2	0.37242	5.2668	0
3	0.385879	5.4572	0
4	0.088162	1.2468	0.106965
5	0.277058	3.9182	6.1e-05
6	0.143466	2.0289	0.021896
7	-0.042118	-0.5956	0.276044
8	0.067806	0.9589	0.169376
9	-0.080377	-1.1367	0.128512
10	-0.13975	-1.9764	0.024744
11	0.001371	0.0194	0.492276
12	-0.480299	-6.7924	0
13	-0.046466	-0.6571	0.255925
14	-0.241727	-3.4185	0.000381
15	-0.202011	-2.8569	0.002365
16	-0.17017	-2.4066	0.008506
17	-0.201834	-2.8544	0.002383
18	-0.124822	-1.7652	0.039524
19	-0.16526	-2.3371	0.010211
20	-0.108726	-1.5376	0.062861
21	-0.027755	-0.3925	0.34755
22	-0.167164	-2.364	0.009517
23	0.036635	0.5181	0.302481

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.002435 & 0.0344 & 0.486284 \tabularnewline
2 & 0.37242 & 5.2668 & 0 \tabularnewline
3 & 0.385879 & 5.4572 & 0 \tabularnewline
4 & 0.088162 & 1.2468 & 0.106965 \tabularnewline
5 & 0.277058 & 3.9182 & 6.1e-05 \tabularnewline
6 & 0.143466 & 2.0289 & 0.021896 \tabularnewline
7 & -0.042118 & -0.5956 & 0.276044 \tabularnewline
8 & 0.067806 & 0.9589 & 0.169376 \tabularnewline
9 & -0.080377 & -1.1367 & 0.128512 \tabularnewline
10 & -0.13975 & -1.9764 & 0.024744 \tabularnewline
11 & 0.001371 & 0.0194 & 0.492276 \tabularnewline
12 & -0.480299 & -6.7924 & 0 \tabularnewline
13 & -0.046466 & -0.6571 & 0.255925 \tabularnewline
14 & -0.241727 & -3.4185 & 0.000381 \tabularnewline
15 & -0.202011 & -2.8569 & 0.002365 \tabularnewline
16 & -0.17017 & -2.4066 & 0.008506 \tabularnewline
17 & -0.201834 & -2.8544 & 0.002383 \tabularnewline
18 & -0.124822 & -1.7652 & 0.039524 \tabularnewline
19 & -0.16526 & -2.3371 & 0.010211 \tabularnewline
20 & -0.108726 & -1.5376 & 0.062861 \tabularnewline
21 & -0.027755 & -0.3925 & 0.34755 \tabularnewline
22 & -0.167164 & -2.364 & 0.009517 \tabularnewline
23 & 0.036635 & 0.5181 & 0.302481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313669&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]0.002435[/C][C]0.0344[/C][C]0.486284[/C][/ROW]
[ROW][C]2[/C][C]0.37242[/C][C]5.2668[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.385879[/C][C]5.4572[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.088162[/C][C]1.2468[/C][C]0.106965[/C][/ROW]
[ROW][C]5[/C][C]0.277058[/C][C]3.9182[/C][C]6.1e-05[/C][/ROW]
[ROW][C]6[/C][C]0.143466[/C][C]2.0289[/C][C]0.021896[/C][/ROW]
[ROW][C]7[/C][C]-0.042118[/C][C]-0.5956[/C][C]0.276044[/C][/ROW]
[ROW][C]8[/C][C]0.067806[/C][C]0.9589[/C][C]0.169376[/C][/ROW]
[ROW][C]9[/C][C]-0.080377[/C][C]-1.1367[/C][C]0.128512[/C][/ROW]
[ROW][C]10[/C][C]-0.13975[/C][C]-1.9764[/C][C]0.024744[/C][/ROW]
[ROW][C]11[/C][C]0.001371[/C][C]0.0194[/C][C]0.492276[/C][/ROW]
[ROW][C]12[/C][C]-0.480299[/C][C]-6.7924[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.046466[/C][C]-0.6571[/C][C]0.255925[/C][/ROW]
[ROW][C]14[/C][C]-0.241727[/C][C]-3.4185[/C][C]0.000381[/C][/ROW]
[ROW][C]15[/C][C]-0.202011[/C][C]-2.8569[/C][C]0.002365[/C][/ROW]
[ROW][C]16[/C][C]-0.17017[/C][C]-2.4066[/C][C]0.008506[/C][/ROW]
[ROW][C]17[/C][C]-0.201834[/C][C]-2.8544[/C][C]0.002383[/C][/ROW]
[ROW][C]18[/C][C]-0.124822[/C][C]-1.7652[/C][C]0.039524[/C][/ROW]
[ROW][C]19[/C][C]-0.16526[/C][C]-2.3371[/C][C]0.010211[/C][/ROW]
[ROW][C]20[/C][C]-0.108726[/C][C]-1.5376[/C][C]0.062861[/C][/ROW]
[ROW][C]21[/C][C]-0.027755[/C][C]-0.3925[/C][C]0.34755[/C][/ROW]
[ROW][C]22[/C][C]-0.167164[/C][C]-2.364[/C][C]0.009517[/C][/ROW]
[ROW][C]23[/C][C]0.036635[/C][C]0.5181[/C][C]0.302481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313669&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	0.002435	0.0344	0.486284
2	0.37242	5.2668	0
3	0.385879	5.4572	0
4	0.088162	1.2468	0.106965
5	0.277058	3.9182	6.1e-05
6	0.143466	2.0289	0.021896
7	-0.042118	-0.5956	0.276044
8	0.067806	0.9589	0.169376
9	-0.080377	-1.1367	0.128512
10	-0.13975	-1.9764	0.024744
11	0.001371	0.0194	0.492276
12	-0.480299	-6.7924	0
13	-0.046466	-0.6571	0.255925
14	-0.241727	-3.4185	0.000381
15	-0.202011	-2.8569	0.002365
16	-0.17017	-2.4066	0.008506
17	-0.201834	-2.8544	0.002383
18	-0.124822	-1.7652	0.039524
19	-0.16526	-2.3371	0.010211
20	-0.108726	-1.5376	0.062861
21	-0.027755	-0.3925	0.34755
22	-0.167164	-2.364	0.009517
23	0.036635	0.5181	0.302481

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.002435	0.0344	0.486284
2	0.372416	5.2668	0
3	0.446306	6.3117	0
4	0.017662	0.2498	0.401507
5	-0.023174	-0.3277	0.37173
6	-0.034228	-0.4841	0.314437
7	-0.236142	-3.3396	5e-04
8	-0.203661	-2.8802	0.002204
9	-0.125776	-1.7787	0.0384
10	-0.110443	-1.5619	0.059946
11	0.101874	1.4407	0.075614
12	-0.393586	-5.5661	0
13	-0.081157	-1.1477	0.126224
14	0.096493	1.3646	0.086954
15	0.297765	4.211	1.9e-05
16	0.011797	0.1668	0.433832
17	-0.040522	-0.5731	0.283621
18	0.051702	0.7312	0.232765
19	-0.171103	-2.4198	0.008212
20	-0.245529	-3.4723	0.000316
21	0.013475	0.1906	0.42453
22	-0.09855	-1.3937	0.082476
23	0.083129	1.1756	0.120573

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.002435 & 0.0344 & 0.486284 \tabularnewline
2 & 0.372416 & 5.2668 & 0 \tabularnewline
3 & 0.446306 & 6.3117 & 0 \tabularnewline
4 & 0.017662 & 0.2498 & 0.401507 \tabularnewline
5 & -0.023174 & -0.3277 & 0.37173 \tabularnewline
6 & -0.034228 & -0.4841 & 0.314437 \tabularnewline
7 & -0.236142 & -3.3396 & 5e-04 \tabularnewline
8 & -0.203661 & -2.8802 & 0.002204 \tabularnewline
9 & -0.125776 & -1.7787 & 0.0384 \tabularnewline
10 & -0.110443 & -1.5619 & 0.059946 \tabularnewline
11 & 0.101874 & 1.4407 & 0.075614 \tabularnewline
12 & -0.393586 & -5.5661 & 0 \tabularnewline
13 & -0.081157 & -1.1477 & 0.126224 \tabularnewline
14 & 0.096493 & 1.3646 & 0.086954 \tabularnewline
15 & 0.297765 & 4.211 & 1.9e-05 \tabularnewline
16 & 0.011797 & 0.1668 & 0.433832 \tabularnewline
17 & -0.040522 & -0.5731 & 0.283621 \tabularnewline
18 & 0.051702 & 0.7312 & 0.232765 \tabularnewline
19 & -0.171103 & -2.4198 & 0.008212 \tabularnewline
20 & -0.245529 & -3.4723 & 0.000316 \tabularnewline
21 & 0.013475 & 0.1906 & 0.42453 \tabularnewline
22 & -0.09855 & -1.3937 & 0.082476 \tabularnewline
23 & 0.083129 & 1.1756 & 0.120573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313669&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]0.002435[/C][C]0.0344[/C][C]0.486284[/C][/ROW]
[ROW][C]2[/C][C]0.372416[/C][C]5.2668[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.446306[/C][C]6.3117[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.017662[/C][C]0.2498[/C][C]0.401507[/C][/ROW]
[ROW][C]5[/C][C]-0.023174[/C][C]-0.3277[/C][C]0.37173[/C][/ROW]
[ROW][C]6[/C][C]-0.034228[/C][C]-0.4841[/C][C]0.314437[/C][/ROW]
[ROW][C]7[/C][C]-0.236142[/C][C]-3.3396[/C][C]5e-04[/C][/ROW]
[ROW][C]8[/C][C]-0.203661[/C][C]-2.8802[/C][C]0.002204[/C][/ROW]
[ROW][C]9[/C][C]-0.125776[/C][C]-1.7787[/C][C]0.0384[/C][/ROW]
[ROW][C]10[/C][C]-0.110443[/C][C]-1.5619[/C][C]0.059946[/C][/ROW]
[ROW][C]11[/C][C]0.101874[/C][C]1.4407[/C][C]0.075614[/C][/ROW]
[ROW][C]12[/C][C]-0.393586[/C][C]-5.5661[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.081157[/C][C]-1.1477[/C][C]0.126224[/C][/ROW]
[ROW][C]14[/C][C]0.096493[/C][C]1.3646[/C][C]0.086954[/C][/ROW]
[ROW][C]15[/C][C]0.297765[/C][C]4.211[/C][C]1.9e-05[/C][/ROW]
[ROW][C]16[/C][C]0.011797[/C][C]0.1668[/C][C]0.433832[/C][/ROW]
[ROW][C]17[/C][C]-0.040522[/C][C]-0.5731[/C][C]0.283621[/C][/ROW]
[ROW][C]18[/C][C]0.051702[/C][C]0.7312[/C][C]0.232765[/C][/ROW]
[ROW][C]19[/C][C]-0.171103[/C][C]-2.4198[/C][C]0.008212[/C][/ROW]
[ROW][C]20[/C][C]-0.245529[/C][C]-3.4723[/C][C]0.000316[/C][/ROW]
[ROW][C]21[/C][C]0.013475[/C][C]0.1906[/C][C]0.42453[/C][/ROW]
[ROW][C]22[/C][C]-0.09855[/C][C]-1.3937[/C][C]0.082476[/C][/ROW]
[ROW][C]23[/C][C]0.083129[/C][C]1.1756[/C][C]0.120573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313669&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	0.002435	0.0344	0.486284
2	0.372416	5.2668	0
3	0.446306	6.3117	0
4	0.017662	0.2498	0.401507
5	-0.023174	-0.3277	0.37173
6	-0.034228	-0.4841	0.314437
7	-0.236142	-3.3396	5e-04
8	-0.203661	-2.8802	0.002204
9	-0.125776	-1.7787	0.0384
10	-0.110443	-1.5619	0.059946
11	0.101874	1.4407	0.075614
12	-0.393586	-5.5661	0
13	-0.081157	-1.1477	0.126224
14	0.096493	1.3646	0.086954
15	0.297765	4.211	1.9e-05
16	0.011797	0.1668	0.433832
17	-0.040522	-0.5731	0.283621
18	0.051702	0.7312	0.232765
19	-0.171103	-2.4198	0.008212
20	-0.245529	-3.4723	0.000316
21	0.013475	0.1906	0.42453
22	-0.09855	-1.3937	0.082476
23	0.083129	1.1756	0.120573

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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par6 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; 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