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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 computationWed, 24 Jan 2018 11:53:30 +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/2018/Jan/24/t15167912495f9n3j970xfajh0.htm/, Retrieved Sun, 05 May 2024 22:57:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=312828, Retrieved Sun, 05 May 2024 22:57:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact48

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] [] [2018-01-24 10:53:30] [adf822683be3c485e110928c6c74068d] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
15
14
14
8
19
17
18
10
15
16
12
13
10
14
15
20
9
12
13
16
12
14
15
19
16
16
14
14
14
13
18
15
15
15
13
14
15
14
19
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16
12
10
11
13
14
11
11
16
9
16
19
13
15
14
15
11
14
15
17
16
13
15
14
15
14
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12
15
17
13
5
7
10
15
9
9
15
14
11
18
20
20
16
15
14
13
18
14
12
9
19
13
12
14
6
14
11
11
14
12
19
13
14
17
12
16
15
15
15
16
15
12
13
14
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14
14
14
15
11
11
16
12
12
19
18
16
16
13
11
10
14
14
14
16
10
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7
16
15
17
11
11
10
13
14
13
13
12
10
15
6
15
15
11
14
14
16
12
15
20
12
9
13
15
19
11
11
17
15
14
15
11
12
15
16
16

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=312828&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=312828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312828&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
10.098891.32310.093752
20.0034440.04610.481648
3-0.037048-0.49570.31037
40.0643870.86140.195075
50.071620.95820.169625
6-0.085056-1.1380.128326
7-0.005433-0.07270.471068
8-0.026582-0.35560.361264
9-0.077087-1.03140.151882
10-0.017369-0.23240.408256
11-0.126003-1.68580.046788
12-0.140752-1.88310.030652
13-0.059394-0.79460.213937
14-0.016405-0.21950.413259
150.0005970.0080.49682
16-0.131972-1.76570.039578
17-0.019256-0.25760.398494
180.0283980.37990.352222
190.091781.22790.110542
20-0.077278-1.03390.151286
210.0510220.68260.247863
220.0355160.47520.317624

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.09889 & 1.3231 & 0.093752 \tabularnewline
2 & 0.003444 & 0.0461 & 0.481648 \tabularnewline
3 & -0.037048 & -0.4957 & 0.31037 \tabularnewline
4 & 0.064387 & 0.8614 & 0.195075 \tabularnewline
5 & 0.07162 & 0.9582 & 0.169625 \tabularnewline
6 & -0.085056 & -1.138 & 0.128326 \tabularnewline
7 & -0.005433 & -0.0727 & 0.471068 \tabularnewline
8 & -0.026582 & -0.3556 & 0.361264 \tabularnewline
9 & -0.077087 & -1.0314 & 0.151882 \tabularnewline
10 & -0.017369 & -0.2324 & 0.408256 \tabularnewline
11 & -0.126003 & -1.6858 & 0.046788 \tabularnewline
12 & -0.140752 & -1.8831 & 0.030652 \tabularnewline
13 & -0.059394 & -0.7946 & 0.213937 \tabularnewline
14 & -0.016405 & -0.2195 & 0.413259 \tabularnewline
15 & 0.000597 & 0.008 & 0.49682 \tabularnewline
16 & -0.131972 & -1.7657 & 0.039578 \tabularnewline
17 & -0.019256 & -0.2576 & 0.398494 \tabularnewline
18 & 0.028398 & 0.3799 & 0.352222 \tabularnewline
19 & 0.09178 & 1.2279 & 0.110542 \tabularnewline
20 & -0.077278 & -1.0339 & 0.151286 \tabularnewline
21 & 0.051022 & 0.6826 & 0.247863 \tabularnewline
22 & 0.035516 & 0.4752 & 0.317624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312828&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]0.09889[/C][C]1.3231[/C][C]0.093752[/C][/ROW]
[ROW][C]2[/C][C]0.003444[/C][C]0.0461[/C][C]0.481648[/C][/ROW]
[ROW][C]3[/C][C]-0.037048[/C][C]-0.4957[/C][C]0.31037[/C][/ROW]
[ROW][C]4[/C][C]0.064387[/C][C]0.8614[/C][C]0.195075[/C][/ROW]
[ROW][C]5[/C][C]0.07162[/C][C]0.9582[/C][C]0.169625[/C][/ROW]
[ROW][C]6[/C][C]-0.085056[/C][C]-1.138[/C][C]0.128326[/C][/ROW]
[ROW][C]7[/C][C]-0.005433[/C][C]-0.0727[/C][C]0.471068[/C][/ROW]
[ROW][C]8[/C][C]-0.026582[/C][C]-0.3556[/C][C]0.361264[/C][/ROW]
[ROW][C]9[/C][C]-0.077087[/C][C]-1.0314[/C][C]0.151882[/C][/ROW]
[ROW][C]10[/C][C]-0.017369[/C][C]-0.2324[/C][C]0.408256[/C][/ROW]
[ROW][C]11[/C][C]-0.126003[/C][C]-1.6858[/C][C]0.046788[/C][/ROW]
[ROW][C]12[/C][C]-0.140752[/C][C]-1.8831[/C][C]0.030652[/C][/ROW]
[ROW][C]13[/C][C]-0.059394[/C][C]-0.7946[/C][C]0.213937[/C][/ROW]
[ROW][C]14[/C][C]-0.016405[/C][C]-0.2195[/C][C]0.413259[/C][/ROW]
[ROW][C]15[/C][C]0.000597[/C][C]0.008[/C][C]0.49682[/C][/ROW]
[ROW][C]16[/C][C]-0.131972[/C][C]-1.7657[/C][C]0.039578[/C][/ROW]
[ROW][C]17[/C][C]-0.019256[/C][C]-0.2576[/C][C]0.398494[/C][/ROW]
[ROW][C]18[/C][C]0.028398[/C][C]0.3799[/C][C]0.352222[/C][/ROW]
[ROW][C]19[/C][C]0.09178[/C][C]1.2279[/C][C]0.110542[/C][/ROW]
[ROW][C]20[/C][C]-0.077278[/C][C]-1.0339[/C][C]0.151286[/C][/ROW]
[ROW][C]21[/C][C]0.051022[/C][C]0.6826[/C][C]0.247863[/C][/ROW]
[ROW][C]22[/C][C]0.035516[/C][C]0.4752[/C][C]0.317624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312828&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
10.098891.32310.093752
20.0034440.04610.481648
3-0.037048-0.49570.31037
40.0643870.86140.195075
50.071620.95820.169625
6-0.085056-1.1380.128326
7-0.005433-0.07270.471068
8-0.026582-0.35560.361264
9-0.077087-1.03140.151882
10-0.017369-0.23240.408256
11-0.126003-1.68580.046788
12-0.140752-1.88310.030652
13-0.059394-0.79460.213937
14-0.016405-0.21950.413259
150.0005970.0080.49682
16-0.131972-1.76570.039578
17-0.019256-0.25760.398494
180.0283980.37990.352222
190.091781.22790.110542
20-0.077278-1.03390.151286
210.0510220.68260.247863
220.0355160.47520.317624






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.098891.32310.093752
2-0.006397-0.08560.465943
3-0.037122-0.49670.310018
40.0725570.97070.166492
50.0589040.78810.215846
6-0.101767-1.36150.087526
70.0188870.25270.400398
8-0.026057-0.34860.363894
9-0.091823-1.22850.110434
100.0088220.1180.453088
11-0.118156-1.58080.057843
12-0.138066-1.84720.033184
13-0.017257-0.23090.408835
14-0.015402-0.20610.418486
15-0.013593-0.18190.427947
16-0.107076-1.43260.076861
17-0.003386-0.04530.48196
180.0052940.07080.471807
190.0718410.96120.168883
20-0.113426-1.51750.065448
210.0675010.90310.183841
22-0.011373-0.15220.439618

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.09889 & 1.3231 & 0.093752 \tabularnewline
2 & -0.006397 & -0.0856 & 0.465943 \tabularnewline
3 & -0.037122 & -0.4967 & 0.310018 \tabularnewline
4 & 0.072557 & 0.9707 & 0.166492 \tabularnewline
5 & 0.058904 & 0.7881 & 0.215846 \tabularnewline
6 & -0.101767 & -1.3615 & 0.087526 \tabularnewline
7 & 0.018887 & 0.2527 & 0.400398 \tabularnewline
8 & -0.026057 & -0.3486 & 0.363894 \tabularnewline
9 & -0.091823 & -1.2285 & 0.110434 \tabularnewline
10 & 0.008822 & 0.118 & 0.453088 \tabularnewline
11 & -0.118156 & -1.5808 & 0.057843 \tabularnewline
12 & -0.138066 & -1.8472 & 0.033184 \tabularnewline
13 & -0.017257 & -0.2309 & 0.408835 \tabularnewline
14 & -0.015402 & -0.2061 & 0.418486 \tabularnewline
15 & -0.013593 & -0.1819 & 0.427947 \tabularnewline
16 & -0.107076 & -1.4326 & 0.076861 \tabularnewline
17 & -0.003386 & -0.0453 & 0.48196 \tabularnewline
18 & 0.005294 & 0.0708 & 0.471807 \tabularnewline
19 & 0.071841 & 0.9612 & 0.168883 \tabularnewline
20 & -0.113426 & -1.5175 & 0.065448 \tabularnewline
21 & 0.067501 & 0.9031 & 0.183841 \tabularnewline
22 & -0.011373 & -0.1522 & 0.439618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=312828&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]0.09889[/C][C]1.3231[/C][C]0.093752[/C][/ROW]
[ROW][C]2[/C][C]-0.006397[/C][C]-0.0856[/C][C]0.465943[/C][/ROW]
[ROW][C]3[/C][C]-0.037122[/C][C]-0.4967[/C][C]0.310018[/C][/ROW]
[ROW][C]4[/C][C]0.072557[/C][C]0.9707[/C][C]0.166492[/C][/ROW]
[ROW][C]5[/C][C]0.058904[/C][C]0.7881[/C][C]0.215846[/C][/ROW]
[ROW][C]6[/C][C]-0.101767[/C][C]-1.3615[/C][C]0.087526[/C][/ROW]
[ROW][C]7[/C][C]0.018887[/C][C]0.2527[/C][C]0.400398[/C][/ROW]
[ROW][C]8[/C][C]-0.026057[/C][C]-0.3486[/C][C]0.363894[/C][/ROW]
[ROW][C]9[/C][C]-0.091823[/C][C]-1.2285[/C][C]0.110434[/C][/ROW]
[ROW][C]10[/C][C]0.008822[/C][C]0.118[/C][C]0.453088[/C][/ROW]
[ROW][C]11[/C][C]-0.118156[/C][C]-1.5808[/C][C]0.057843[/C][/ROW]
[ROW][C]12[/C][C]-0.138066[/C][C]-1.8472[/C][C]0.033184[/C][/ROW]
[ROW][C]13[/C][C]-0.017257[/C][C]-0.2309[/C][C]0.408835[/C][/ROW]
[ROW][C]14[/C][C]-0.015402[/C][C]-0.2061[/C][C]0.418486[/C][/ROW]
[ROW][C]15[/C][C]-0.013593[/C][C]-0.1819[/C][C]0.427947[/C][/ROW]
[ROW][C]16[/C][C]-0.107076[/C][C]-1.4326[/C][C]0.076861[/C][/ROW]
[ROW][C]17[/C][C]-0.003386[/C][C]-0.0453[/C][C]0.48196[/C][/ROW]
[ROW][C]18[/C][C]0.005294[/C][C]0.0708[/C][C]0.471807[/C][/ROW]
[ROW][C]19[/C][C]0.071841[/C][C]0.9612[/C][C]0.168883[/C][/ROW]
[ROW][C]20[/C][C]-0.113426[/C][C]-1.5175[/C][C]0.065448[/C][/ROW]
[ROW][C]21[/C][C]0.067501[/C][C]0.9031[/C][C]0.183841[/C][/ROW]
[ROW][C]22[/C][C]-0.011373[/C][C]-0.1522[/C][C]0.439618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=312828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=312828&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
10.098891.32310.093752
2-0.006397-0.08560.465943
3-0.037122-0.49670.310018
40.0725570.97070.166492
50.0589040.78810.215846
6-0.101767-1.36150.087526
70.0188870.25270.400398
8-0.026057-0.34860.363894
9-0.091823-1.22850.110434
100.0088220.1180.453088
11-0.118156-1.58080.057843
12-0.138066-1.84720.033184
13-0.017257-0.23090.408835
14-0.015402-0.20610.418486
15-0.013593-0.18190.427947
16-0.107076-1.43260.076861
17-0.003386-0.04530.48196
180.0052940.07080.471807
190.0718410.96120.168883
20-0.113426-1.51750.065448
210.0675010.90310.183841
22-0.011373-0.15220.439618


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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')