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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 16 Dec 2016 08:44:54 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t14818745494l3vj6z7s17nun4.htm/, Retrieved Thu, 02 May 2024 21:35:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300079, Retrieved Thu, 02 May 2024 21:35:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [autocorrelation n...] [2016-12-16 07:44:54] [afe7f6443461a2cd6ee0b843643e84a9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3690
3878
3834
3780
3690
3202
3736
3480
3552
3372
3334
3502
3468
3480
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3594
3834
3954
4006
4102
4236
4086
4350
4224
4576
4678
4624
4404
4190
4414
4414
3998
3554
3974
3820
4102
3926
4056
4072
4246
4232
4244
3944
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Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig 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=300079&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=300079&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300079&T=0

As an alternative you can also use a QR Code:  
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 Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.8184515.4291e-06
20.7520574.98865e-06
30.6468214.29054.8e-05
40.6047134.01120.000115
50.5126643.40060.00072
60.3571732.36920.011139
70.2246271.490.071678
80.1427650.9470.174407
90.0773530.51310.305223
100.0207120.13740.445675
11-0.027619-0.18320.42774
12-0.12432-0.82460.207011
13-0.162377-1.07710.143656
14-0.215284-1.4280.080171
15-0.236971-1.57190.06157
16-0.280896-1.86330.034555
17-0.271641-1.80190.03921
18-0.315908-2.09550.020957
19-0.272369-1.80670.038826
20-0.282806-1.87590.033655
21-0.2772-1.83870.036355

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.818451 & 5.429 & 1e-06 \tabularnewline
2 & 0.752057 & 4.9886 & 5e-06 \tabularnewline
3 & 0.646821 & 4.2905 & 4.8e-05 \tabularnewline
4 & 0.604713 & 4.0112 & 0.000115 \tabularnewline
5 & 0.512664 & 3.4006 & 0.00072 \tabularnewline
6 & 0.357173 & 2.3692 & 0.011139 \tabularnewline
7 & 0.224627 & 1.49 & 0.071678 \tabularnewline
8 & 0.142765 & 0.947 & 0.174407 \tabularnewline
9 & 0.077353 & 0.5131 & 0.305223 \tabularnewline
10 & 0.020712 & 0.1374 & 0.445675 \tabularnewline
11 & -0.027619 & -0.1832 & 0.42774 \tabularnewline
12 & -0.12432 & -0.8246 & 0.207011 \tabularnewline
13 & -0.162377 & -1.0771 & 0.143656 \tabularnewline
14 & -0.215284 & -1.428 & 0.080171 \tabularnewline
15 & -0.236971 & -1.5719 & 0.06157 \tabularnewline
16 & -0.280896 & -1.8633 & 0.034555 \tabularnewline
17 & -0.271641 & -1.8019 & 0.03921 \tabularnewline
18 & -0.315908 & -2.0955 & 0.020957 \tabularnewline
19 & -0.272369 & -1.8067 & 0.038826 \tabularnewline
20 & -0.282806 & -1.8759 & 0.033655 \tabularnewline
21 & -0.2772 & -1.8387 & 0.036355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300079&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]0.818451[/C][C]5.429[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.752057[/C][C]4.9886[/C][C]5e-06[/C][/ROW]
[ROW][C]3[/C][C]0.646821[/C][C]4.2905[/C][C]4.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.604713[/C][C]4.0112[/C][C]0.000115[/C][/ROW]
[ROW][C]5[/C][C]0.512664[/C][C]3.4006[/C][C]0.00072[/C][/ROW]
[ROW][C]6[/C][C]0.357173[/C][C]2.3692[/C][C]0.011139[/C][/ROW]
[ROW][C]7[/C][C]0.224627[/C][C]1.49[/C][C]0.071678[/C][/ROW]
[ROW][C]8[/C][C]0.142765[/C][C]0.947[/C][C]0.174407[/C][/ROW]
[ROW][C]9[/C][C]0.077353[/C][C]0.5131[/C][C]0.305223[/C][/ROW]
[ROW][C]10[/C][C]0.020712[/C][C]0.1374[/C][C]0.445675[/C][/ROW]
[ROW][C]11[/C][C]-0.027619[/C][C]-0.1832[/C][C]0.42774[/C][/ROW]
[ROW][C]12[/C][C]-0.12432[/C][C]-0.8246[/C][C]0.207011[/C][/ROW]
[ROW][C]13[/C][C]-0.162377[/C][C]-1.0771[/C][C]0.143656[/C][/ROW]
[ROW][C]14[/C][C]-0.215284[/C][C]-1.428[/C][C]0.080171[/C][/ROW]
[ROW][C]15[/C][C]-0.236971[/C][C]-1.5719[/C][C]0.06157[/C][/ROW]
[ROW][C]16[/C][C]-0.280896[/C][C]-1.8633[/C][C]0.034555[/C][/ROW]
[ROW][C]17[/C][C]-0.271641[/C][C]-1.8019[/C][C]0.03921[/C][/ROW]
[ROW][C]18[/C][C]-0.315908[/C][C]-2.0955[/C][C]0.020957[/C][/ROW]
[ROW][C]19[/C][C]-0.272369[/C][C]-1.8067[/C][C]0.038826[/C][/ROW]
[ROW][C]20[/C][C]-0.282806[/C][C]-1.8759[/C][C]0.033655[/C][/ROW]
[ROW][C]21[/C][C]-0.2772[/C][C]-1.8387[/C][C]0.036355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300079&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300079&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.8184515.4291e-06
20.7520574.98865e-06
30.6468214.29054.8e-05
40.6047134.01120.000115
50.5126643.40060.00072
60.3571732.36920.011139
70.2246271.490.071678
80.1427650.9470.174407
90.0773530.51310.305223
100.0207120.13740.445675
11-0.027619-0.18320.42774
12-0.12432-0.82460.207011
13-0.162377-1.07710.143656
14-0.215284-1.4280.080171
15-0.236971-1.57190.06157
16-0.280896-1.86330.034555
17-0.271641-1.80190.03921
18-0.315908-2.09550.020957
19-0.272369-1.80670.038826
20-0.282806-1.87590.033655
21-0.2772-1.83870.036355






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.8184515.4291e-06
20.248971.65150.052881
3-0.062077-0.41180.341252
40.103730.68810.247512
5-0.091073-0.60410.274436
6-0.338434-2.24490.014925
7-0.157839-1.0470.150412
80.0624440.41420.340368
90.0247250.1640.435239
100.0701190.46510.322071
110.133060.88260.191119
12-0.224867-1.49160.07147
13-0.118237-0.78430.218535
14-0.09338-0.61940.26942
15-0.081105-0.5380.296648
16-0.03089-0.20490.419296
170.2686271.78190.040836
18-0.089903-0.59630.277
190.0997460.66160.255826
20-0.048157-0.31940.375455
21-0.283039-1.87750.033547

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.818451 & 5.429 & 1e-06 \tabularnewline
2 & 0.24897 & 1.6515 & 0.052881 \tabularnewline
3 & -0.062077 & -0.4118 & 0.341252 \tabularnewline
4 & 0.10373 & 0.6881 & 0.247512 \tabularnewline
5 & -0.091073 & -0.6041 & 0.274436 \tabularnewline
6 & -0.338434 & -2.2449 & 0.014925 \tabularnewline
7 & -0.157839 & -1.047 & 0.150412 \tabularnewline
8 & 0.062444 & 0.4142 & 0.340368 \tabularnewline
9 & 0.024725 & 0.164 & 0.435239 \tabularnewline
10 & 0.070119 & 0.4651 & 0.322071 \tabularnewline
11 & 0.13306 & 0.8826 & 0.191119 \tabularnewline
12 & -0.224867 & -1.4916 & 0.07147 \tabularnewline
13 & -0.118237 & -0.7843 & 0.218535 \tabularnewline
14 & -0.09338 & -0.6194 & 0.26942 \tabularnewline
15 & -0.081105 & -0.538 & 0.296648 \tabularnewline
16 & -0.03089 & -0.2049 & 0.419296 \tabularnewline
17 & 0.268627 & 1.7819 & 0.040836 \tabularnewline
18 & -0.089903 & -0.5963 & 0.277 \tabularnewline
19 & 0.099746 & 0.6616 & 0.255826 \tabularnewline
20 & -0.048157 & -0.3194 & 0.375455 \tabularnewline
21 & -0.283039 & -1.8775 & 0.033547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300079&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]0.818451[/C][C]5.429[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.24897[/C][C]1.6515[/C][C]0.052881[/C][/ROW]
[ROW][C]3[/C][C]-0.062077[/C][C]-0.4118[/C][C]0.341252[/C][/ROW]
[ROW][C]4[/C][C]0.10373[/C][C]0.6881[/C][C]0.247512[/C][/ROW]
[ROW][C]5[/C][C]-0.091073[/C][C]-0.6041[/C][C]0.274436[/C][/ROW]
[ROW][C]6[/C][C]-0.338434[/C][C]-2.2449[/C][C]0.014925[/C][/ROW]
[ROW][C]7[/C][C]-0.157839[/C][C]-1.047[/C][C]0.150412[/C][/ROW]
[ROW][C]8[/C][C]0.062444[/C][C]0.4142[/C][C]0.340368[/C][/ROW]
[ROW][C]9[/C][C]0.024725[/C][C]0.164[/C][C]0.435239[/C][/ROW]
[ROW][C]10[/C][C]0.070119[/C][C]0.4651[/C][C]0.322071[/C][/ROW]
[ROW][C]11[/C][C]0.13306[/C][C]0.8826[/C][C]0.191119[/C][/ROW]
[ROW][C]12[/C][C]-0.224867[/C][C]-1.4916[/C][C]0.07147[/C][/ROW]
[ROW][C]13[/C][C]-0.118237[/C][C]-0.7843[/C][C]0.218535[/C][/ROW]
[ROW][C]14[/C][C]-0.09338[/C][C]-0.6194[/C][C]0.26942[/C][/ROW]
[ROW][C]15[/C][C]-0.081105[/C][C]-0.538[/C][C]0.296648[/C][/ROW]
[ROW][C]16[/C][C]-0.03089[/C][C]-0.2049[/C][C]0.419296[/C][/ROW]
[ROW][C]17[/C][C]0.268627[/C][C]1.7819[/C][C]0.040836[/C][/ROW]
[ROW][C]18[/C][C]-0.089903[/C][C]-0.5963[/C][C]0.277[/C][/ROW]
[ROW][C]19[/C][C]0.099746[/C][C]0.6616[/C][C]0.255826[/C][/ROW]
[ROW][C]20[/C][C]-0.048157[/C][C]-0.3194[/C][C]0.375455[/C][/ROW]
[ROW][C]21[/C][C]-0.283039[/C][C]-1.8775[/C][C]0.033547[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300079&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300079&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.8184515.4291e-06
20.248971.65150.052881
3-0.062077-0.41180.341252
40.103730.68810.247512
5-0.091073-0.60410.274436
6-0.338434-2.24490.014925
7-0.157839-1.0470.150412
80.0624440.41420.340368
90.0247250.1640.435239
100.0701190.46510.322071
110.133060.88260.191119
12-0.224867-1.49160.07147
13-0.118237-0.78430.218535
14-0.09338-0.61940.26942
15-0.081105-0.5380.296648
16-0.03089-0.20490.419296
170.2686271.78190.040836
18-0.089903-0.59630.277
190.0997460.66160.255826
20-0.048157-0.31940.375455
21-0.283039-1.87750.033547


Figures (Output of Computation)

Input Parameters & R Code

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')