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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 13 Dec 2017 20:21:34 +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/2017/Dec/13/t1513192952qk0ugk7e9iqmtzy.htm/, Retrieved Wed, 15 May 2024 09:59:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309393, Retrieved Wed, 15 May 2024 09:59:28 +0000

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Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2017-12-13 19:21:34] [d2d54f927b4b6a5dbf001a3c29aa1f74] [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=309393&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=309393&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309393&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	-0.542537	-7.6534	0
2	-0.026325	-0.3714	0.355381
3	0.299602	4.2264	1.8e-05
4	-0.242896	-3.4265	0.000371
5	-0.013548	-0.1911	0.424313
6	0.284617	4.015	4.2e-05
7	-0.322638	-4.5514	5e-06
8	0.158051	2.2296	0.013447
9	0.120435	1.6989	0.045447
10	-0.251043	-3.5414	0.000248
11	0.206726	2.9162	0.001975
12	-0.087768	-1.2381	0.108566
13	-0.130532	-1.8414	0.033527
14	0.107723	1.5196	0.065097
15	0.096937	1.3675	0.08651
16	-0.248118	-3.5001	0.000287
17	0.202152	2.8517	0.002404
18	-0.065782	-0.928	0.177275
19	-0.065678	-0.9265	0.177655
20	0.092748	1.3084	0.096127
21	-0.044265	-0.6244	0.266528
22	-0.144689	-2.0411	0.021281
23	0.295216	4.1645	2.3e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.542537 & -7.6534 & 0 \tabularnewline
2 & -0.026325 & -0.3714 & 0.355381 \tabularnewline
3 & 0.299602 & 4.2264 & 1.8e-05 \tabularnewline
4 & -0.242896 & -3.4265 & 0.000371 \tabularnewline
5 & -0.013548 & -0.1911 & 0.424313 \tabularnewline
6 & 0.284617 & 4.015 & 4.2e-05 \tabularnewline
7 & -0.322638 & -4.5514 & 5e-06 \tabularnewline
8 & 0.158051 & 2.2296 & 0.013447 \tabularnewline
9 & 0.120435 & 1.6989 & 0.045447 \tabularnewline
10 & -0.251043 & -3.5414 & 0.000248 \tabularnewline
11 & 0.206726 & 2.9162 & 0.001975 \tabularnewline
12 & -0.087768 & -1.2381 & 0.108566 \tabularnewline
13 & -0.130532 & -1.8414 & 0.033527 \tabularnewline
14 & 0.107723 & 1.5196 & 0.065097 \tabularnewline
15 & 0.096937 & 1.3675 & 0.08651 \tabularnewline
16 & -0.248118 & -3.5001 & 0.000287 \tabularnewline
17 & 0.202152 & 2.8517 & 0.002404 \tabularnewline
18 & -0.065782 & -0.928 & 0.177275 \tabularnewline
19 & -0.065678 & -0.9265 & 0.177655 \tabularnewline
20 & 0.092748 & 1.3084 & 0.096127 \tabularnewline
21 & -0.044265 & -0.6244 & 0.266528 \tabularnewline
22 & -0.144689 & -2.0411 & 0.021281 \tabularnewline
23 & 0.295216 & 4.1645 & 2.3e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309393&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]-0.542537[/C][C]-7.6534[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.026325[/C][C]-0.3714[/C][C]0.355381[/C][/ROW]
[ROW][C]3[/C][C]0.299602[/C][C]4.2264[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.242896[/C][C]-3.4265[/C][C]0.000371[/C][/ROW]
[ROW][C]5[/C][C]-0.013548[/C][C]-0.1911[/C][C]0.424313[/C][/ROW]
[ROW][C]6[/C][C]0.284617[/C][C]4.015[/C][C]4.2e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.322638[/C][C]-4.5514[/C][C]5e-06[/C][/ROW]
[ROW][C]8[/C][C]0.158051[/C][C]2.2296[/C][C]0.013447[/C][/ROW]
[ROW][C]9[/C][C]0.120435[/C][C]1.6989[/C][C]0.045447[/C][/ROW]
[ROW][C]10[/C][C]-0.251043[/C][C]-3.5414[/C][C]0.000248[/C][/ROW]
[ROW][C]11[/C][C]0.206726[/C][C]2.9162[/C][C]0.001975[/C][/ROW]
[ROW][C]12[/C][C]-0.087768[/C][C]-1.2381[/C][C]0.108566[/C][/ROW]
[ROW][C]13[/C][C]-0.130532[/C][C]-1.8414[/C][C]0.033527[/C][/ROW]
[ROW][C]14[/C][C]0.107723[/C][C]1.5196[/C][C]0.065097[/C][/ROW]
[ROW][C]15[/C][C]0.096937[/C][C]1.3675[/C][C]0.08651[/C][/ROW]
[ROW][C]16[/C][C]-0.248118[/C][C]-3.5001[/C][C]0.000287[/C][/ROW]
[ROW][C]17[/C][C]0.202152[/C][C]2.8517[/C][C]0.002404[/C][/ROW]
[ROW][C]18[/C][C]-0.065782[/C][C]-0.928[/C][C]0.177275[/C][/ROW]
[ROW][C]19[/C][C]-0.065678[/C][C]-0.9265[/C][C]0.177655[/C][/ROW]
[ROW][C]20[/C][C]0.092748[/C][C]1.3084[/C][C]0.096127[/C][/ROW]
[ROW][C]21[/C][C]-0.044265[/C][C]-0.6244[/C][C]0.266528[/C][/ROW]
[ROW][C]22[/C][C]-0.144689[/C][C]-2.0411[/C][C]0.021281[/C][/ROW]
[ROW][C]23[/C][C]0.295216[/C][C]4.1645[/C][C]2.3e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309393&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309393&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	-0.542537	-7.6534	0
2	-0.026325	-0.3714	0.355381
3	0.299602	4.2264	1.8e-05
4	-0.242896	-3.4265	0.000371
5	-0.013548	-0.1911	0.424313
6	0.284617	4.015	4.2e-05
7	-0.322638	-4.5514	5e-06
8	0.158051	2.2296	0.013447
9	0.120435	1.6989	0.045447
10	-0.251043	-3.5414	0.000248
11	0.206726	2.9162	0.001975
12	-0.087768	-1.2381	0.108566
13	-0.130532	-1.8414	0.033527
14	0.107723	1.5196	0.065097
15	0.096937	1.3675	0.08651
16	-0.248118	-3.5001	0.000287
17	0.202152	2.8517	0.002404
18	-0.065782	-0.928	0.177275
19	-0.065678	-0.9265	0.177655
20	0.092748	1.3084	0.096127
21	-0.044265	-0.6244	0.266528
22	-0.144689	-2.0411	0.021281
23	0.295216	4.1645	2.3e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.542537	-7.6534	0
2	-0.454433	-6.4106	0
3	0.057654	0.8133	0.208506
4	0.011074	0.1562	0.43801
5	-0.125617	-1.772	0.038959
6	0.187746	2.6485	0.004367
7	-0.017197	-0.2426	0.404283
8	0.035127	0.4955	0.31039
9	0.139677	1.9704	0.025091
10	0.007693	0.1085	0.456842
11	0.088701	1.2513	0.106149
12	-0.100818	-1.4222	0.078266
13	-0.170516	-2.4054	0.008534
14	-0.273132	-3.853	7.9e-05
15	0.052572	0.7416	0.229596
16	-0.063223	-0.8919	0.186771
17	-0.054697	-0.7716	0.220633
18	-0.01071	-0.1511	0.44003
19	0.036762	0.5186	0.302311
20	0.043537	0.6142	0.269904
21	0.024271	0.3424	0.366209
22	-0.139368	-1.966	0.025343
23	0.132667	1.8715	0.031372

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.542537 & -7.6534 & 0 \tabularnewline
2 & -0.454433 & -6.4106 & 0 \tabularnewline
3 & 0.057654 & 0.8133 & 0.208506 \tabularnewline
4 & 0.011074 & 0.1562 & 0.43801 \tabularnewline
5 & -0.125617 & -1.772 & 0.038959 \tabularnewline
6 & 0.187746 & 2.6485 & 0.004367 \tabularnewline
7 & -0.017197 & -0.2426 & 0.404283 \tabularnewline
8 & 0.035127 & 0.4955 & 0.31039 \tabularnewline
9 & 0.139677 & 1.9704 & 0.025091 \tabularnewline
10 & 0.007693 & 0.1085 & 0.456842 \tabularnewline
11 & 0.088701 & 1.2513 & 0.106149 \tabularnewline
12 & -0.100818 & -1.4222 & 0.078266 \tabularnewline
13 & -0.170516 & -2.4054 & 0.008534 \tabularnewline
14 & -0.273132 & -3.853 & 7.9e-05 \tabularnewline
15 & 0.052572 & 0.7416 & 0.229596 \tabularnewline
16 & -0.063223 & -0.8919 & 0.186771 \tabularnewline
17 & -0.054697 & -0.7716 & 0.220633 \tabularnewline
18 & -0.01071 & -0.1511 & 0.44003 \tabularnewline
19 & 0.036762 & 0.5186 & 0.302311 \tabularnewline
20 & 0.043537 & 0.6142 & 0.269904 \tabularnewline
21 & 0.024271 & 0.3424 & 0.366209 \tabularnewline
22 & -0.139368 & -1.966 & 0.025343 \tabularnewline
23 & 0.132667 & 1.8715 & 0.031372 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309393&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]-0.542537[/C][C]-7.6534[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.454433[/C][C]-6.4106[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.057654[/C][C]0.8133[/C][C]0.208506[/C][/ROW]
[ROW][C]4[/C][C]0.011074[/C][C]0.1562[/C][C]0.43801[/C][/ROW]
[ROW][C]5[/C][C]-0.125617[/C][C]-1.772[/C][C]0.038959[/C][/ROW]
[ROW][C]6[/C][C]0.187746[/C][C]2.6485[/C][C]0.004367[/C][/ROW]
[ROW][C]7[/C][C]-0.017197[/C][C]-0.2426[/C][C]0.404283[/C][/ROW]
[ROW][C]8[/C][C]0.035127[/C][C]0.4955[/C][C]0.31039[/C][/ROW]
[ROW][C]9[/C][C]0.139677[/C][C]1.9704[/C][C]0.025091[/C][/ROW]
[ROW][C]10[/C][C]0.007693[/C][C]0.1085[/C][C]0.456842[/C][/ROW]
[ROW][C]11[/C][C]0.088701[/C][C]1.2513[/C][C]0.106149[/C][/ROW]
[ROW][C]12[/C][C]-0.100818[/C][C]-1.4222[/C][C]0.078266[/C][/ROW]
[ROW][C]13[/C][C]-0.170516[/C][C]-2.4054[/C][C]0.008534[/C][/ROW]
[ROW][C]14[/C][C]-0.273132[/C][C]-3.853[/C][C]7.9e-05[/C][/ROW]
[ROW][C]15[/C][C]0.052572[/C][C]0.7416[/C][C]0.229596[/C][/ROW]
[ROW][C]16[/C][C]-0.063223[/C][C]-0.8919[/C][C]0.186771[/C][/ROW]
[ROW][C]17[/C][C]-0.054697[/C][C]-0.7716[/C][C]0.220633[/C][/ROW]
[ROW][C]18[/C][C]-0.01071[/C][C]-0.1511[/C][C]0.44003[/C][/ROW]
[ROW][C]19[/C][C]0.036762[/C][C]0.5186[/C][C]0.302311[/C][/ROW]
[ROW][C]20[/C][C]0.043537[/C][C]0.6142[/C][C]0.269904[/C][/ROW]
[ROW][C]21[/C][C]0.024271[/C][C]0.3424[/C][C]0.366209[/C][/ROW]
[ROW][C]22[/C][C]-0.139368[/C][C]-1.966[/C][C]0.025343[/C][/ROW]
[ROW][C]23[/C][C]0.132667[/C][C]1.8715[/C][C]0.031372[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309393&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309393&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	-0.542537	-7.6534	0
2	-0.454433	-6.4106	0
3	0.057654	0.8133	0.208506
4	0.011074	0.1562	0.43801
5	-0.125617	-1.772	0.038959
6	0.187746	2.6485	0.004367
7	-0.017197	-0.2426	0.404283
8	0.035127	0.4955	0.31039
9	0.139677	1.9704	0.025091
10	0.007693	0.1085	0.456842
11	0.088701	1.2513	0.106149
12	-0.100818	-1.4222	0.078266
13	-0.170516	-2.4054	0.008534
14	-0.273132	-3.853	7.9e-05
15	0.052572	0.7416	0.229596
16	-0.063223	-0.8919	0.186771
17	-0.054697	-0.7716	0.220633
18	-0.01071	-0.1511	0.44003
19	0.036762	0.5186	0.302311
20	0.043537	0.6142	0.269904
21	0.024271	0.3424	0.366209
22	-0.139368	-1.966	0.025343
23	0.132667	1.8715	0.031372

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

Parameters (R input):

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