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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 computationFri, 23 Oct 2015 19:47:59 +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/2015/Oct/23/t1445626122owm10cg5kdci284.htm/, Retrieved Mon, 13 May 2024 21:06:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282967, Retrieved Mon, 13 May 2024 21:06:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2015-10-02 20:20:26] [102949d3707834b83d58a354234a805f]
- RMP     [(Partial) Autocorrelation Function] [] [2015-10-23 18:47:59] [7e1e09e1787c74b32ad6066a9a323b17] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
92.44
94.36
93.42
92.97
94.83
91.47
88.42
86.36
86.01
87.87
89.81
88.41
86.33
89.64
89.53
88.3
99.49
98.81
90.97
92.58
92.98
95
92.47
88.65
84.81
88.6
89.31
92.34
91.53
96.95
95.44
89.59
89.86
91.66
92.7
90.54
86.17
89.15
89.73
91.07
93.36
96.27
95
94.72
97.16
100.92
98.66
95.87
94.6
98.41
98.05
99.82
106.96
107.45
100.25
99.28
101.38
101
97.43
95.38
95.17
94.13
96.43
105.38
98.39
99.8
94.43
90.16
85.49
90.57
88.22
89.66

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'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282967&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282967&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282967&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'Gwilym Jenkins' @ jenkins.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.219161-1.68340.048791
2-0.29488-2.2650.013599
30.2420281.85910.034005
40.1116170.85730.197361
5-0.145428-1.11710.134251
6-0.07356-0.5650.287099
70.0242940.18660.426304
80.0277420.21310.415995
9-0.08502-0.65310.258129
100.1793731.37780.086736
110.0661170.50790.306725
12-0.368503-2.83050.003172
130.1501891.15360.126653
140.0972840.74730.228939
15-0.086083-0.66120.255525
16-0.110165-0.84620.200431
17-0.050984-0.39160.348375
180.1426781.09590.13878

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.219161 & -1.6834 & 0.048791 \tabularnewline
2 & -0.29488 & -2.265 & 0.013599 \tabularnewline
3 & 0.242028 & 1.8591 & 0.034005 \tabularnewline
4 & 0.111617 & 0.8573 & 0.197361 \tabularnewline
5 & -0.145428 & -1.1171 & 0.134251 \tabularnewline
6 & -0.07356 & -0.565 & 0.287099 \tabularnewline
7 & 0.024294 & 0.1866 & 0.426304 \tabularnewline
8 & 0.027742 & 0.2131 & 0.415995 \tabularnewline
9 & -0.08502 & -0.6531 & 0.258129 \tabularnewline
10 & 0.179373 & 1.3778 & 0.086736 \tabularnewline
11 & 0.066117 & 0.5079 & 0.306725 \tabularnewline
12 & -0.368503 & -2.8305 & 0.003172 \tabularnewline
13 & 0.150189 & 1.1536 & 0.126653 \tabularnewline
14 & 0.097284 & 0.7473 & 0.228939 \tabularnewline
15 & -0.086083 & -0.6612 & 0.255525 \tabularnewline
16 & -0.110165 & -0.8462 & 0.200431 \tabularnewline
17 & -0.050984 & -0.3916 & 0.348375 \tabularnewline
18 & 0.142678 & 1.0959 & 0.13878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282967&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]-0.219161[/C][C]-1.6834[/C][C]0.048791[/C][/ROW]
[ROW][C]2[/C][C]-0.29488[/C][C]-2.265[/C][C]0.013599[/C][/ROW]
[ROW][C]3[/C][C]0.242028[/C][C]1.8591[/C][C]0.034005[/C][/ROW]
[ROW][C]4[/C][C]0.111617[/C][C]0.8573[/C][C]0.197361[/C][/ROW]
[ROW][C]5[/C][C]-0.145428[/C][C]-1.1171[/C][C]0.134251[/C][/ROW]
[ROW][C]6[/C][C]-0.07356[/C][C]-0.565[/C][C]0.287099[/C][/ROW]
[ROW][C]7[/C][C]0.024294[/C][C]0.1866[/C][C]0.426304[/C][/ROW]
[ROW][C]8[/C][C]0.027742[/C][C]0.2131[/C][C]0.415995[/C][/ROW]
[ROW][C]9[/C][C]-0.08502[/C][C]-0.6531[/C][C]0.258129[/C][/ROW]
[ROW][C]10[/C][C]0.179373[/C][C]1.3778[/C][C]0.086736[/C][/ROW]
[ROW][C]11[/C][C]0.066117[/C][C]0.5079[/C][C]0.306725[/C][/ROW]
[ROW][C]12[/C][C]-0.368503[/C][C]-2.8305[/C][C]0.003172[/C][/ROW]
[ROW][C]13[/C][C]0.150189[/C][C]1.1536[/C][C]0.126653[/C][/ROW]
[ROW][C]14[/C][C]0.097284[/C][C]0.7473[/C][C]0.228939[/C][/ROW]
[ROW][C]15[/C][C]-0.086083[/C][C]-0.6612[/C][C]0.255525[/C][/ROW]
[ROW][C]16[/C][C]-0.110165[/C][C]-0.8462[/C][C]0.200431[/C][/ROW]
[ROW][C]17[/C][C]-0.050984[/C][C]-0.3916[/C][C]0.348375[/C][/ROW]
[ROW][C]18[/C][C]0.142678[/C][C]1.0959[/C][C]0.13878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282967&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282967&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
1-0.219161-1.68340.048791
2-0.29488-2.2650.013599
30.2420281.85910.034005
40.1116170.85730.197361
5-0.145428-1.11710.134251
6-0.07356-0.5650.287099
70.0242940.18660.426304
80.0277420.21310.415995
9-0.08502-0.65310.258129
100.1793731.37780.086736
110.0661170.50790.306725
12-0.368503-2.83050.003172
130.1501891.15360.126653
140.0972840.74730.228939
15-0.086083-0.66120.255525
16-0.110165-0.84620.200431
17-0.050984-0.39160.348375
180.1426781.09590.13878






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.219161-1.68340.048791
2-0.360213-2.76690.003774
30.0907450.6970.244261
40.1186680.91150.182869
50.0228620.17560.430603
6-0.086928-0.66770.253463
7-0.120371-0.92460.179474
8-0.038289-0.29410.384857
9-0.06739-0.51760.303324
100.2323761.78490.039708
110.1739321.3360.09334
12-0.300201-2.30590.012325
13-0.091245-0.70090.24307
14-0.159701-1.22670.112406
150.1351.0370.151995
160.0482970.3710.355991
17-0.146175-1.12280.133037
18-0.058604-0.45010.327128

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.219161 & -1.6834 & 0.048791 \tabularnewline
2 & -0.360213 & -2.7669 & 0.003774 \tabularnewline
3 & 0.090745 & 0.697 & 0.244261 \tabularnewline
4 & 0.118668 & 0.9115 & 0.182869 \tabularnewline
5 & 0.022862 & 0.1756 & 0.430603 \tabularnewline
6 & -0.086928 & -0.6677 & 0.253463 \tabularnewline
7 & -0.120371 & -0.9246 & 0.179474 \tabularnewline
8 & -0.038289 & -0.2941 & 0.384857 \tabularnewline
9 & -0.06739 & -0.5176 & 0.303324 \tabularnewline
10 & 0.232376 & 1.7849 & 0.039708 \tabularnewline
11 & 0.173932 & 1.336 & 0.09334 \tabularnewline
12 & -0.300201 & -2.3059 & 0.012325 \tabularnewline
13 & -0.091245 & -0.7009 & 0.24307 \tabularnewline
14 & -0.159701 & -1.2267 & 0.112406 \tabularnewline
15 & 0.135 & 1.037 & 0.151995 \tabularnewline
16 & 0.048297 & 0.371 & 0.355991 \tabularnewline
17 & -0.146175 & -1.1228 & 0.133037 \tabularnewline
18 & -0.058604 & -0.4501 & 0.327128 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282967&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]-0.219161[/C][C]-1.6834[/C][C]0.048791[/C][/ROW]
[ROW][C]2[/C][C]-0.360213[/C][C]-2.7669[/C][C]0.003774[/C][/ROW]
[ROW][C]3[/C][C]0.090745[/C][C]0.697[/C][C]0.244261[/C][/ROW]
[ROW][C]4[/C][C]0.118668[/C][C]0.9115[/C][C]0.182869[/C][/ROW]
[ROW][C]5[/C][C]0.022862[/C][C]0.1756[/C][C]0.430603[/C][/ROW]
[ROW][C]6[/C][C]-0.086928[/C][C]-0.6677[/C][C]0.253463[/C][/ROW]
[ROW][C]7[/C][C]-0.120371[/C][C]-0.9246[/C][C]0.179474[/C][/ROW]
[ROW][C]8[/C][C]-0.038289[/C][C]-0.2941[/C][C]0.384857[/C][/ROW]
[ROW][C]9[/C][C]-0.06739[/C][C]-0.5176[/C][C]0.303324[/C][/ROW]
[ROW][C]10[/C][C]0.232376[/C][C]1.7849[/C][C]0.039708[/C][/ROW]
[ROW][C]11[/C][C]0.173932[/C][C]1.336[/C][C]0.09334[/C][/ROW]
[ROW][C]12[/C][C]-0.300201[/C][C]-2.3059[/C][C]0.012325[/C][/ROW]
[ROW][C]13[/C][C]-0.091245[/C][C]-0.7009[/C][C]0.24307[/C][/ROW]
[ROW][C]14[/C][C]-0.159701[/C][C]-1.2267[/C][C]0.112406[/C][/ROW]
[ROW][C]15[/C][C]0.135[/C][C]1.037[/C][C]0.151995[/C][/ROW]
[ROW][C]16[/C][C]0.048297[/C][C]0.371[/C][C]0.355991[/C][/ROW]
[ROW][C]17[/C][C]-0.146175[/C][C]-1.1228[/C][C]0.133037[/C][/ROW]
[ROW][C]18[/C][C]-0.058604[/C][C]-0.4501[/C][C]0.327128[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282967&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282967&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
1-0.219161-1.68340.048791
2-0.360213-2.76690.003774
30.0907450.6970.244261
40.1186680.91150.182869
50.0228620.17560.430603
6-0.086928-0.66770.253463
7-0.120371-0.92460.179474
8-0.038289-0.29410.384857
9-0.06739-0.51760.303324
100.2323761.78490.039708
110.1739321.3360.09334
12-0.300201-2.30590.012325
13-0.091245-0.70090.24307
14-0.159701-1.22670.112406
150.1351.0370.151995
160.0482970.3710.355991
17-0.146175-1.12280.133037
18-0.058604-0.45010.327128


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')