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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, 21 Dec 2011 04:56:48 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/21/t13244614164gk15374owqfjxg.htm/, Retrieved Tue, 07 May 2024 21:32:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=158408, Retrieved Tue, 07 May 2024 21:32:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70

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] [] [2011-12-21 09:56:48] [bbaf0bbad09b34135f8973992e5d67ea] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2.581
2.592
2.600
2.602
2.608
2.619
2.637
2.646
2.659
2.671
2.684
2.686
2.691
2.705
2.723
2.725
2.734
2.735
2.740
2.744
2.737
2.743
2.747
2.748
2.749
2.754
2.766
2.784
2.794
2.804
2.818
2.833
2.836
2.866
2.893
2.897
2.897
2.913
2.921
2.922
2.924
2.924
2.945
2.948
2.952
2.968
2.987
2.997
3.002
3.012
3.027
3.032
3.036
3.039
3.048
3.050
3.089
3.093
3.094
3.098
3.104
3.106
3.116
3.119
3.124
3.131
3.147
3.156

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158408&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158408&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.0785080.64260.261333
2-0.109909-0.89960.185765
30.0397720.32560.372889
40.1803871.47650.072243
5-0.070733-0.5790.282273
6-0.079173-0.64810.259582
7-0.129333-1.05860.146784
80.0117010.09580.461993
9-0.093387-0.76440.223654
10-0.16107-1.31840.095927
11-0.105953-0.86730.194447
120.0440760.36080.359699
13-0.122495-1.00270.159815
14-0.092876-0.76020.224895
15-0.094075-0.770.221991
160.0139420.11410.454743
17-0.002798-0.02290.490898
18-0.069597-0.56970.285401

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.078508 & 0.6426 & 0.261333 \tabularnewline
2 & -0.109909 & -0.8996 & 0.185765 \tabularnewline
3 & 0.039772 & 0.3256 & 0.372889 \tabularnewline
4 & 0.180387 & 1.4765 & 0.072243 \tabularnewline
5 & -0.070733 & -0.579 & 0.282273 \tabularnewline
6 & -0.079173 & -0.6481 & 0.259582 \tabularnewline
7 & -0.129333 & -1.0586 & 0.146784 \tabularnewline
8 & 0.011701 & 0.0958 & 0.461993 \tabularnewline
9 & -0.093387 & -0.7644 & 0.223654 \tabularnewline
10 & -0.16107 & -1.3184 & 0.095927 \tabularnewline
11 & -0.105953 & -0.8673 & 0.194447 \tabularnewline
12 & 0.044076 & 0.3608 & 0.359699 \tabularnewline
13 & -0.122495 & -1.0027 & 0.159815 \tabularnewline
14 & -0.092876 & -0.7602 & 0.224895 \tabularnewline
15 & -0.094075 & -0.77 & 0.221991 \tabularnewline
16 & 0.013942 & 0.1141 & 0.454743 \tabularnewline
17 & -0.002798 & -0.0229 & 0.490898 \tabularnewline
18 & -0.069597 & -0.5697 & 0.285401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158408&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]0.078508[/C][C]0.6426[/C][C]0.261333[/C][/ROW]
[ROW][C]2[/C][C]-0.109909[/C][C]-0.8996[/C][C]0.185765[/C][/ROW]
[ROW][C]3[/C][C]0.039772[/C][C]0.3256[/C][C]0.372889[/C][/ROW]
[ROW][C]4[/C][C]0.180387[/C][C]1.4765[/C][C]0.072243[/C][/ROW]
[ROW][C]5[/C][C]-0.070733[/C][C]-0.579[/C][C]0.282273[/C][/ROW]
[ROW][C]6[/C][C]-0.079173[/C][C]-0.6481[/C][C]0.259582[/C][/ROW]
[ROW][C]7[/C][C]-0.129333[/C][C]-1.0586[/C][C]0.146784[/C][/ROW]
[ROW][C]8[/C][C]0.011701[/C][C]0.0958[/C][C]0.461993[/C][/ROW]
[ROW][C]9[/C][C]-0.093387[/C][C]-0.7644[/C][C]0.223654[/C][/ROW]
[ROW][C]10[/C][C]-0.16107[/C][C]-1.3184[/C][C]0.095927[/C][/ROW]
[ROW][C]11[/C][C]-0.105953[/C][C]-0.8673[/C][C]0.194447[/C][/ROW]
[ROW][C]12[/C][C]0.044076[/C][C]0.3608[/C][C]0.359699[/C][/ROW]
[ROW][C]13[/C][C]-0.122495[/C][C]-1.0027[/C][C]0.159815[/C][/ROW]
[ROW][C]14[/C][C]-0.092876[/C][C]-0.7602[/C][C]0.224895[/C][/ROW]
[ROW][C]15[/C][C]-0.094075[/C][C]-0.77[/C][C]0.221991[/C][/ROW]
[ROW][C]16[/C][C]0.013942[/C][C]0.1141[/C][C]0.454743[/C][/ROW]
[ROW][C]17[/C][C]-0.002798[/C][C]-0.0229[/C][C]0.490898[/C][/ROW]
[ROW][C]18[/C][C]-0.069597[/C][C]-0.5697[/C][C]0.285401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158408&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
10.0785080.64260.261333
2-0.109909-0.89960.185765
30.0397720.32560.372889
40.1803871.47650.072243
5-0.070733-0.5790.282273
6-0.079173-0.64810.259582
7-0.129333-1.05860.146784
80.0117010.09580.461993
9-0.093387-0.76440.223654
10-0.16107-1.31840.095927
11-0.105953-0.86730.194447
120.0440760.36080.359699
13-0.122495-1.00270.159815
14-0.092876-0.76020.224895
15-0.094075-0.770.221991
160.0139420.11410.454743
17-0.002798-0.02290.490898
18-0.069597-0.56970.285401






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.0785080.64260.261333
2-0.116793-0.9560.171257
30.0597570.48910.313174
40.1622871.32840.094281
5-0.094479-0.77330.22102
6-0.031446-0.25740.398831
7-0.158094-1.29410.100045
80.0035310.02890.488515
9-0.097032-0.79420.21493
10-0.130944-1.07180.143822
11-0.068263-0.55880.289095
120.0060180.04930.48043
13-0.129356-1.05880.146742
14-0.058691-0.48040.316252
15-0.135696-1.11070.135329
16-0.052611-0.43060.334056
17-0.038293-0.31340.377459
18-0.12419-1.01650.156516

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.078508 & 0.6426 & 0.261333 \tabularnewline
2 & -0.116793 & -0.956 & 0.171257 \tabularnewline
3 & 0.059757 & 0.4891 & 0.313174 \tabularnewline
4 & 0.162287 & 1.3284 & 0.094281 \tabularnewline
5 & -0.094479 & -0.7733 & 0.22102 \tabularnewline
6 & -0.031446 & -0.2574 & 0.398831 \tabularnewline
7 & -0.158094 & -1.2941 & 0.100045 \tabularnewline
8 & 0.003531 & 0.0289 & 0.488515 \tabularnewline
9 & -0.097032 & -0.7942 & 0.21493 \tabularnewline
10 & -0.130944 & -1.0718 & 0.143822 \tabularnewline
11 & -0.068263 & -0.5588 & 0.289095 \tabularnewline
12 & 0.006018 & 0.0493 & 0.48043 \tabularnewline
13 & -0.129356 & -1.0588 & 0.146742 \tabularnewline
14 & -0.058691 & -0.4804 & 0.316252 \tabularnewline
15 & -0.135696 & -1.1107 & 0.135329 \tabularnewline
16 & -0.052611 & -0.4306 & 0.334056 \tabularnewline
17 & -0.038293 & -0.3134 & 0.377459 \tabularnewline
18 & -0.12419 & -1.0165 & 0.156516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=158408&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]0.078508[/C][C]0.6426[/C][C]0.261333[/C][/ROW]
[ROW][C]2[/C][C]-0.116793[/C][C]-0.956[/C][C]0.171257[/C][/ROW]
[ROW][C]3[/C][C]0.059757[/C][C]0.4891[/C][C]0.313174[/C][/ROW]
[ROW][C]4[/C][C]0.162287[/C][C]1.3284[/C][C]0.094281[/C][/ROW]
[ROW][C]5[/C][C]-0.094479[/C][C]-0.7733[/C][C]0.22102[/C][/ROW]
[ROW][C]6[/C][C]-0.031446[/C][C]-0.2574[/C][C]0.398831[/C][/ROW]
[ROW][C]7[/C][C]-0.158094[/C][C]-1.2941[/C][C]0.100045[/C][/ROW]
[ROW][C]8[/C][C]0.003531[/C][C]0.0289[/C][C]0.488515[/C][/ROW]
[ROW][C]9[/C][C]-0.097032[/C][C]-0.7942[/C][C]0.21493[/C][/ROW]
[ROW][C]10[/C][C]-0.130944[/C][C]-1.0718[/C][C]0.143822[/C][/ROW]
[ROW][C]11[/C][C]-0.068263[/C][C]-0.5588[/C][C]0.289095[/C][/ROW]
[ROW][C]12[/C][C]0.006018[/C][C]0.0493[/C][C]0.48043[/C][/ROW]
[ROW][C]13[/C][C]-0.129356[/C][C]-1.0588[/C][C]0.146742[/C][/ROW]
[ROW][C]14[/C][C]-0.058691[/C][C]-0.4804[/C][C]0.316252[/C][/ROW]
[ROW][C]15[/C][C]-0.135696[/C][C]-1.1107[/C][C]0.135329[/C][/ROW]
[ROW][C]16[/C][C]-0.052611[/C][C]-0.4306[/C][C]0.334056[/C][/ROW]
[ROW][C]17[/C][C]-0.038293[/C][C]-0.3134[/C][C]0.377459[/C][/ROW]
[ROW][C]18[/C][C]-0.12419[/C][C]-1.0165[/C][C]0.156516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=158408&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=158408&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
10.0785080.64260.261333
2-0.116793-0.9560.171257
30.0597570.48910.313174
40.1622871.32840.094281
5-0.094479-0.77330.22102
6-0.031446-0.25740.398831
7-0.158094-1.29410.100045
80.0035310.02890.488515
9-0.097032-0.79420.21493
10-0.130944-1.07180.143822
11-0.068263-0.55880.289095
120.0060180.04930.48043
13-0.129356-1.05880.146742
14-0.058691-0.48040.316252
15-0.135696-1.11070.135329
16-0.052611-0.43060.334056
17-0.038293-0.31340.377459
18-0.12419-1.01650.156516


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; 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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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')