Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSun, 22 Dec 2013 07:09:10 -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/2013/Dec/22/t138771423558magt9iv5wyd4q.htm/, Retrieved Sun, 05 Dec 2021 17:22:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232504, Retrieved Sun, 05 Dec 2021 17:22:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2013-12-22 12:09:10] [54713e3426a13268f2edfca2b563126c] [Current]
Feedback Forum

Post a new message
Dataseries X:
6.715
7.703
9.856
8.326
9.269
7.035
10.342
11.682
10.304
11.385
9.777
8.882
7.897
6.930
9.545
9.110
7.459
7.320
10.017
12.307
11.072
10.749
9.589
9.080
7.384
8.062
8.511
8.684
8.306
7.643
10.577
13.747
11.783
11.611
9.946
8.693
7.303
7.609
9.423
8.584
7.586
6.843
11.811
13.414
12.103
11.501
8.213
7.982
7.687
7.180
7.862
8.043
8.340
6.692
10.065
12.684
11.587
9.843
8.110
7.940
6.475
6.121
9.669
7.778
7.826
7.403
10.741
14.023
11.519
10.236
8.075
8.157




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232504&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232504&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232504&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.0401860.33860.367951
2-0.197297-1.66250.050416
3-0.222225-1.87250.032628
4-0.097854-0.82450.206199
50.1474061.24210.10915
6-0.248766-2.09610.019817
70.0456260.38450.350896
8-0.059955-0.50520.307496
9-0.227849-1.91990.029445
10-0.094483-0.79610.214306
110.1402961.18220.120545
120.6249375.26581e-06
130.1325091.11650.133977
14-0.183967-1.55010.062778
15-0.224981-1.89570.031034
16-0.086951-0.73270.233089
170.1442571.21550.114095
18-0.196635-1.65690.050979

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.040186 & 0.3386 & 0.367951 \tabularnewline
2 & -0.197297 & -1.6625 & 0.050416 \tabularnewline
3 & -0.222225 & -1.8725 & 0.032628 \tabularnewline
4 & -0.097854 & -0.8245 & 0.206199 \tabularnewline
5 & 0.147406 & 1.2421 & 0.10915 \tabularnewline
6 & -0.248766 & -2.0961 & 0.019817 \tabularnewline
7 & 0.045626 & 0.3845 & 0.350896 \tabularnewline
8 & -0.059955 & -0.5052 & 0.307496 \tabularnewline
9 & -0.227849 & -1.9199 & 0.029445 \tabularnewline
10 & -0.094483 & -0.7961 & 0.214306 \tabularnewline
11 & 0.140296 & 1.1822 & 0.120545 \tabularnewline
12 & 0.624937 & 5.2658 & 1e-06 \tabularnewline
13 & 0.132509 & 1.1165 & 0.133977 \tabularnewline
14 & -0.183967 & -1.5501 & 0.062778 \tabularnewline
15 & -0.224981 & -1.8957 & 0.031034 \tabularnewline
16 & -0.086951 & -0.7327 & 0.233089 \tabularnewline
17 & 0.144257 & 1.2155 & 0.114095 \tabularnewline
18 & -0.196635 & -1.6569 & 0.050979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232504&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]0.040186[/C][C]0.3386[/C][C]0.367951[/C][/ROW]
[ROW][C]2[/C][C]-0.197297[/C][C]-1.6625[/C][C]0.050416[/C][/ROW]
[ROW][C]3[/C][C]-0.222225[/C][C]-1.8725[/C][C]0.032628[/C][/ROW]
[ROW][C]4[/C][C]-0.097854[/C][C]-0.8245[/C][C]0.206199[/C][/ROW]
[ROW][C]5[/C][C]0.147406[/C][C]1.2421[/C][C]0.10915[/C][/ROW]
[ROW][C]6[/C][C]-0.248766[/C][C]-2.0961[/C][C]0.019817[/C][/ROW]
[ROW][C]7[/C][C]0.045626[/C][C]0.3845[/C][C]0.350896[/C][/ROW]
[ROW][C]8[/C][C]-0.059955[/C][C]-0.5052[/C][C]0.307496[/C][/ROW]
[ROW][C]9[/C][C]-0.227849[/C][C]-1.9199[/C][C]0.029445[/C][/ROW]
[ROW][C]10[/C][C]-0.094483[/C][C]-0.7961[/C][C]0.214306[/C][/ROW]
[ROW][C]11[/C][C]0.140296[/C][C]1.1822[/C][C]0.120545[/C][/ROW]
[ROW][C]12[/C][C]0.624937[/C][C]5.2658[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.132509[/C][C]1.1165[/C][C]0.133977[/C][/ROW]
[ROW][C]14[/C][C]-0.183967[/C][C]-1.5501[/C][C]0.062778[/C][/ROW]
[ROW][C]15[/C][C]-0.224981[/C][C]-1.8957[/C][C]0.031034[/C][/ROW]
[ROW][C]16[/C][C]-0.086951[/C][C]-0.7327[/C][C]0.233089[/C][/ROW]
[ROW][C]17[/C][C]0.144257[/C][C]1.2155[/C][C]0.114095[/C][/ROW]
[ROW][C]18[/C][C]-0.196635[/C][C]-1.6569[/C][C]0.050979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232504&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232504&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 kACF(k)T-STATP-value
10.0401860.33860.367951
2-0.197297-1.66250.050416
3-0.222225-1.87250.032628
4-0.097854-0.82450.206199
50.1474061.24210.10915
6-0.248766-2.09610.019817
70.0456260.38450.350896
8-0.059955-0.50520.307496
9-0.227849-1.91990.029445
10-0.094483-0.79610.214306
110.1402961.18220.120545
120.6249375.26581e-06
130.1325091.11650.133977
14-0.183967-1.55010.062778
15-0.224981-1.89570.031034
16-0.086951-0.73270.233089
170.1442571.21550.114095
18-0.196635-1.65690.050979







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.0401860.33860.367951
2-0.199233-1.67880.048797
3-0.213517-1.79910.038124
4-0.136928-1.15380.12623
50.0678140.57140.284762
6-0.380115-3.20290.001019
70.0515560.43440.33265
8-0.2175-1.83270.035521
9-0.427547-3.60260.00029
10-0.412202-3.47330.00044
11-0.172412-1.45280.075346
120.2779232.34180.011
130.1378551.16160.124647
140.1047270.88240.190257
15-0.044336-0.37360.354916
16-0.065648-0.55320.290945
170.0301260.25380.400175
18-0.145672-1.22750.111854

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.040186 & 0.3386 & 0.367951 \tabularnewline
2 & -0.199233 & -1.6788 & 0.048797 \tabularnewline
3 & -0.213517 & -1.7991 & 0.038124 \tabularnewline
4 & -0.136928 & -1.1538 & 0.12623 \tabularnewline
5 & 0.067814 & 0.5714 & 0.284762 \tabularnewline
6 & -0.380115 & -3.2029 & 0.001019 \tabularnewline
7 & 0.051556 & 0.4344 & 0.33265 \tabularnewline
8 & -0.2175 & -1.8327 & 0.035521 \tabularnewline
9 & -0.427547 & -3.6026 & 0.00029 \tabularnewline
10 & -0.412202 & -3.4733 & 0.00044 \tabularnewline
11 & -0.172412 & -1.4528 & 0.075346 \tabularnewline
12 & 0.277923 & 2.3418 & 0.011 \tabularnewline
13 & 0.137855 & 1.1616 & 0.124647 \tabularnewline
14 & 0.104727 & 0.8824 & 0.190257 \tabularnewline
15 & -0.044336 & -0.3736 & 0.354916 \tabularnewline
16 & -0.065648 & -0.5532 & 0.290945 \tabularnewline
17 & 0.030126 & 0.2538 & 0.400175 \tabularnewline
18 & -0.145672 & -1.2275 & 0.111854 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232504&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]0.040186[/C][C]0.3386[/C][C]0.367951[/C][/ROW]
[ROW][C]2[/C][C]-0.199233[/C][C]-1.6788[/C][C]0.048797[/C][/ROW]
[ROW][C]3[/C][C]-0.213517[/C][C]-1.7991[/C][C]0.038124[/C][/ROW]
[ROW][C]4[/C][C]-0.136928[/C][C]-1.1538[/C][C]0.12623[/C][/ROW]
[ROW][C]5[/C][C]0.067814[/C][C]0.5714[/C][C]0.284762[/C][/ROW]
[ROW][C]6[/C][C]-0.380115[/C][C]-3.2029[/C][C]0.001019[/C][/ROW]
[ROW][C]7[/C][C]0.051556[/C][C]0.4344[/C][C]0.33265[/C][/ROW]
[ROW][C]8[/C][C]-0.2175[/C][C]-1.8327[/C][C]0.035521[/C][/ROW]
[ROW][C]9[/C][C]-0.427547[/C][C]-3.6026[/C][C]0.00029[/C][/ROW]
[ROW][C]10[/C][C]-0.412202[/C][C]-3.4733[/C][C]0.00044[/C][/ROW]
[ROW][C]11[/C][C]-0.172412[/C][C]-1.4528[/C][C]0.075346[/C][/ROW]
[ROW][C]12[/C][C]0.277923[/C][C]2.3418[/C][C]0.011[/C][/ROW]
[ROW][C]13[/C][C]0.137855[/C][C]1.1616[/C][C]0.124647[/C][/ROW]
[ROW][C]14[/C][C]0.104727[/C][C]0.8824[/C][C]0.190257[/C][/ROW]
[ROW][C]15[/C][C]-0.044336[/C][C]-0.3736[/C][C]0.354916[/C][/ROW]
[ROW][C]16[/C][C]-0.065648[/C][C]-0.5532[/C][C]0.290945[/C][/ROW]
[ROW][C]17[/C][C]0.030126[/C][C]0.2538[/C][C]0.400175[/C][/ROW]
[ROW][C]18[/C][C]-0.145672[/C][C]-1.2275[/C][C]0.111854[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232504&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232504&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 kPACF(k)T-STATP-value
10.0401860.33860.367951
2-0.199233-1.67880.048797
3-0.213517-1.79910.038124
4-0.136928-1.15380.12623
50.0678140.57140.284762
6-0.380115-3.20290.001019
70.0515560.43440.33265
8-0.2175-1.83270.035521
9-0.427547-3.60260.00029
10-0.412202-3.47330.00044
11-0.172412-1.45280.075346
120.2779232.34180.011
130.1378551.16160.124647
140.1047270.88240.190257
15-0.044336-0.37360.354916
16-0.065648-0.55320.290945
170.0301260.25380.400175
18-0.145672-1.22750.111854



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')