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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationThu, 10 Mar 2016 07:43:36 +0000
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/Mar/10/t1457595880yrrbllbo26v0o85.htm/, Retrieved Wed, 08 May 2024 07:53:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293817, Retrieved Wed, 08 May 2024 07:53:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174

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] [(partial) Autocor...] [2016-03-10 07:25:19] [2067968a48489243c2d14909cd8d3ed5]
-   PD    [(Partial) Autocorrelation Function] [Autocorrelation c...] [2016-03-10 07:43:36] [4e1138fa3bff5f7fc8fdb388bb0b126b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
99.13
100.46
101.83
100.82
100.99
99.11
98.99
99.8
100.3
101.56
98.83
101.29
98.24
98.37
99.68
97.8
98.34
98.06
97.19
99.44
99.04
100.81
98.49
101.03
98.59
101.07
99.28
101.65
100.59
101.84
100.27
100.04
97.78
97.59
97.68
100.56
98.9
100.08
101.7
100.9
100.67
100.51
100.01
99.8
97.7
98.14
101.77
99.82
100.03
101.83
98.25
99.88
98.96
98.37
97.52
99.59
97.99
100.68
100.39
99.31
96.93
102.06
97.9
102.29
100.55
100.77
100.68
100.75
100.21
99.85
100.59
101.45

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293817&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293817&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293817&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.0945510.80230.212513
20.3299782.80.003278
3-0.022605-0.19180.424214
4-0.037352-0.31690.376102
5-0.206789-1.75470.041786
60.0526520.44680.328193
7-0.169382-1.43730.077489
80.0472850.40120.344721
9-0.082779-0.70240.242347
100.0387480.32880.371636
11-0.163465-1.3870.084853
120.044470.37730.353515
13-0.270338-2.29390.012358
14-0.113641-0.96430.169067
15-0.126599-1.07420.143154
16-0.065164-0.55290.29101
17-0.001547-0.01310.494781
180.1069610.90760.183559

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.094551 & 0.8023 & 0.212513 \tabularnewline
2 & 0.329978 & 2.8 & 0.003278 \tabularnewline
3 & -0.022605 & -0.1918 & 0.424214 \tabularnewline
4 & -0.037352 & -0.3169 & 0.376102 \tabularnewline
5 & -0.206789 & -1.7547 & 0.041786 \tabularnewline
6 & 0.052652 & 0.4468 & 0.328193 \tabularnewline
7 & -0.169382 & -1.4373 & 0.077489 \tabularnewline
8 & 0.047285 & 0.4012 & 0.344721 \tabularnewline
9 & -0.082779 & -0.7024 & 0.242347 \tabularnewline
10 & 0.038748 & 0.3288 & 0.371636 \tabularnewline
11 & -0.163465 & -1.387 & 0.084853 \tabularnewline
12 & 0.04447 & 0.3773 & 0.353515 \tabularnewline
13 & -0.270338 & -2.2939 & 0.012358 \tabularnewline
14 & -0.113641 & -0.9643 & 0.169067 \tabularnewline
15 & -0.126599 & -1.0742 & 0.143154 \tabularnewline
16 & -0.065164 & -0.5529 & 0.29101 \tabularnewline
17 & -0.001547 & -0.0131 & 0.494781 \tabularnewline
18 & 0.106961 & 0.9076 & 0.183559 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293817&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]0.094551[/C][C]0.8023[/C][C]0.212513[/C][/ROW]
[ROW][C]2[/C][C]0.329978[/C][C]2.8[/C][C]0.003278[/C][/ROW]
[ROW][C]3[/C][C]-0.022605[/C][C]-0.1918[/C][C]0.424214[/C][/ROW]
[ROW][C]4[/C][C]-0.037352[/C][C]-0.3169[/C][C]0.376102[/C][/ROW]
[ROW][C]5[/C][C]-0.206789[/C][C]-1.7547[/C][C]0.041786[/C][/ROW]
[ROW][C]6[/C][C]0.052652[/C][C]0.4468[/C][C]0.328193[/C][/ROW]
[ROW][C]7[/C][C]-0.169382[/C][C]-1.4373[/C][C]0.077489[/C][/ROW]
[ROW][C]8[/C][C]0.047285[/C][C]0.4012[/C][C]0.344721[/C][/ROW]
[ROW][C]9[/C][C]-0.082779[/C][C]-0.7024[/C][C]0.242347[/C][/ROW]
[ROW][C]10[/C][C]0.038748[/C][C]0.3288[/C][C]0.371636[/C][/ROW]
[ROW][C]11[/C][C]-0.163465[/C][C]-1.387[/C][C]0.084853[/C][/ROW]
[ROW][C]12[/C][C]0.04447[/C][C]0.3773[/C][C]0.353515[/C][/ROW]
[ROW][C]13[/C][C]-0.270338[/C][C]-2.2939[/C][C]0.012358[/C][/ROW]
[ROW][C]14[/C][C]-0.113641[/C][C]-0.9643[/C][C]0.169067[/C][/ROW]
[ROW][C]15[/C][C]-0.126599[/C][C]-1.0742[/C][C]0.143154[/C][/ROW]
[ROW][C]16[/C][C]-0.065164[/C][C]-0.5529[/C][C]0.29101[/C][/ROW]
[ROW][C]17[/C][C]-0.001547[/C][C]-0.0131[/C][C]0.494781[/C][/ROW]
[ROW][C]18[/C][C]0.106961[/C][C]0.9076[/C][C]0.183559[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293817&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293817&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
10.0945510.80230.212513
20.3299782.80.003278
3-0.022605-0.19180.424214
4-0.037352-0.31690.376102
5-0.206789-1.75470.041786
60.0526520.44680.328193
7-0.169382-1.43730.077489
80.0472850.40120.344721
9-0.082779-0.70240.242347
100.0387480.32880.371636
11-0.163465-1.3870.084853
120.044470.37730.353515
13-0.270338-2.29390.012358
14-0.113641-0.96430.169067
15-0.126599-1.07420.143154
16-0.065164-0.55290.29101
17-0.001547-0.01310.494781
180.1069610.90760.183559






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.0945510.80230.212513
20.3239342.74870.003779
3-0.083789-0.7110.239698
4-0.154432-1.31040.097112
5-0.183371-1.5560.062052
60.168781.43210.078215
7-0.061968-0.52580.300316
8-0.028157-0.23890.405924
9-0.054592-0.46320.322299
100.0249520.21170.416461
11-0.13753-1.1670.123535
120.0079660.06760.473147
13-0.196907-1.67080.049551
14-0.156588-1.32870.094073
150.0414970.35210.362892
16-0.029938-0.2540.400096
170.0235130.19950.421211
18-0.015713-0.13330.447153

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.094551 & 0.8023 & 0.212513 \tabularnewline
2 & 0.323934 & 2.7487 & 0.003779 \tabularnewline
3 & -0.083789 & -0.711 & 0.239698 \tabularnewline
4 & -0.154432 & -1.3104 & 0.097112 \tabularnewline
5 & -0.183371 & -1.556 & 0.062052 \tabularnewline
6 & 0.16878 & 1.4321 & 0.078215 \tabularnewline
7 & -0.061968 & -0.5258 & 0.300316 \tabularnewline
8 & -0.028157 & -0.2389 & 0.405924 \tabularnewline
9 & -0.054592 & -0.4632 & 0.322299 \tabularnewline
10 & 0.024952 & 0.2117 & 0.416461 \tabularnewline
11 & -0.13753 & -1.167 & 0.123535 \tabularnewline
12 & 0.007966 & 0.0676 & 0.473147 \tabularnewline
13 & -0.196907 & -1.6708 & 0.049551 \tabularnewline
14 & -0.156588 & -1.3287 & 0.094073 \tabularnewline
15 & 0.041497 & 0.3521 & 0.362892 \tabularnewline
16 & -0.029938 & -0.254 & 0.400096 \tabularnewline
17 & 0.023513 & 0.1995 & 0.421211 \tabularnewline
18 & -0.015713 & -0.1333 & 0.447153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293817&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]0.094551[/C][C]0.8023[/C][C]0.212513[/C][/ROW]
[ROW][C]2[/C][C]0.323934[/C][C]2.7487[/C][C]0.003779[/C][/ROW]
[ROW][C]3[/C][C]-0.083789[/C][C]-0.711[/C][C]0.239698[/C][/ROW]
[ROW][C]4[/C][C]-0.154432[/C][C]-1.3104[/C][C]0.097112[/C][/ROW]
[ROW][C]5[/C][C]-0.183371[/C][C]-1.556[/C][C]0.062052[/C][/ROW]
[ROW][C]6[/C][C]0.16878[/C][C]1.4321[/C][C]0.078215[/C][/ROW]
[ROW][C]7[/C][C]-0.061968[/C][C]-0.5258[/C][C]0.300316[/C][/ROW]
[ROW][C]8[/C][C]-0.028157[/C][C]-0.2389[/C][C]0.405924[/C][/ROW]
[ROW][C]9[/C][C]-0.054592[/C][C]-0.4632[/C][C]0.322299[/C][/ROW]
[ROW][C]10[/C][C]0.024952[/C][C]0.2117[/C][C]0.416461[/C][/ROW]
[ROW][C]11[/C][C]-0.13753[/C][C]-1.167[/C][C]0.123535[/C][/ROW]
[ROW][C]12[/C][C]0.007966[/C][C]0.0676[/C][C]0.473147[/C][/ROW]
[ROW][C]13[/C][C]-0.196907[/C][C]-1.6708[/C][C]0.049551[/C][/ROW]
[ROW][C]14[/C][C]-0.156588[/C][C]-1.3287[/C][C]0.094073[/C][/ROW]
[ROW][C]15[/C][C]0.041497[/C][C]0.3521[/C][C]0.362892[/C][/ROW]
[ROW][C]16[/C][C]-0.029938[/C][C]-0.254[/C][C]0.400096[/C][/ROW]
[ROW][C]17[/C][C]0.023513[/C][C]0.1995[/C][C]0.421211[/C][/ROW]
[ROW][C]18[/C][C]-0.015713[/C][C]-0.1333[/C][C]0.447153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293817&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293817&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
10.0945510.80230.212513
20.3239342.74870.003779
3-0.083789-0.7110.239698
4-0.154432-1.31040.097112
5-0.183371-1.5560.062052
60.168781.43210.078215
7-0.061968-0.52580.300316
8-0.028157-0.23890.405924
9-0.054592-0.46320.322299
100.0249520.21170.416461
11-0.13753-1.1670.123535
120.0079660.06760.473147
13-0.196907-1.67080.049551
14-0.156588-1.32870.094073
150.0414970.35210.362892
16-0.029938-0.2540.400096
170.0235130.19950.421211
18-0.015713-0.13330.447153


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,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')