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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 computationMon, 27 Dec 2010 02:24:39 +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/2010/Dec/27/t1293416748plzubusovnovrch.htm/, Retrieved Mon, 06 May 2024 15:12:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115848, Retrieved Mon, 06 May 2024 15:12:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133

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] [] [2010-12-27 02:24:39] [c984196f1244e05baf3e7c2e52d47a33] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1
115.9
96
99.8
116.8
115.7
99.4
94.3
91
93.2
103.1
94.1
91.8
102.7
82.6
89.1
104.5
105.1
95.1
88.7
86.3

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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115848&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115848&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115848&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' @ 193.190.124.24






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.2882072.2510.014001
20.0287130.22430.411654
30.168561.31650.096466
40.1544141.2060.116235
50.377832.95090.002245
60.3826812.98880.002016
70.2218961.73310.044069
80.0576220.450.327139
9-0.013258-0.10360.458933
10-0.15304-1.19530.118302
110.0993710.77610.220342
120.4670663.64790.000275
13-0.015788-0.12330.451134
14-0.266114-2.07840.020943
15-0.225708-1.76280.041468
16-0.109108-0.85220.198729
170.0667690.52150.301961

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.288207 & 2.251 & 0.014001 \tabularnewline
2 & 0.028713 & 0.2243 & 0.411654 \tabularnewline
3 & 0.16856 & 1.3165 & 0.096466 \tabularnewline
4 & 0.154414 & 1.206 & 0.116235 \tabularnewline
5 & 0.37783 & 2.9509 & 0.002245 \tabularnewline
6 & 0.382681 & 2.9888 & 0.002016 \tabularnewline
7 & 0.221896 & 1.7331 & 0.044069 \tabularnewline
8 & 0.057622 & 0.45 & 0.327139 \tabularnewline
9 & -0.013258 & -0.1036 & 0.458933 \tabularnewline
10 & -0.15304 & -1.1953 & 0.118302 \tabularnewline
11 & 0.099371 & 0.7761 & 0.220342 \tabularnewline
12 & 0.467066 & 3.6479 & 0.000275 \tabularnewline
13 & -0.015788 & -0.1233 & 0.451134 \tabularnewline
14 & -0.266114 & -2.0784 & 0.020943 \tabularnewline
15 & -0.225708 & -1.7628 & 0.041468 \tabularnewline
16 & -0.109108 & -0.8522 & 0.198729 \tabularnewline
17 & 0.066769 & 0.5215 & 0.301961 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115848&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]0.288207[/C][C]2.251[/C][C]0.014001[/C][/ROW]
[ROW][C]2[/C][C]0.028713[/C][C]0.2243[/C][C]0.411654[/C][/ROW]
[ROW][C]3[/C][C]0.16856[/C][C]1.3165[/C][C]0.096466[/C][/ROW]
[ROW][C]4[/C][C]0.154414[/C][C]1.206[/C][C]0.116235[/C][/ROW]
[ROW][C]5[/C][C]0.37783[/C][C]2.9509[/C][C]0.002245[/C][/ROW]
[ROW][C]6[/C][C]0.382681[/C][C]2.9888[/C][C]0.002016[/C][/ROW]
[ROW][C]7[/C][C]0.221896[/C][C]1.7331[/C][C]0.044069[/C][/ROW]
[ROW][C]8[/C][C]0.057622[/C][C]0.45[/C][C]0.327139[/C][/ROW]
[ROW][C]9[/C][C]-0.013258[/C][C]-0.1036[/C][C]0.458933[/C][/ROW]
[ROW][C]10[/C][C]-0.15304[/C][C]-1.1953[/C][C]0.118302[/C][/ROW]
[ROW][C]11[/C][C]0.099371[/C][C]0.7761[/C][C]0.220342[/C][/ROW]
[ROW][C]12[/C][C]0.467066[/C][C]3.6479[/C][C]0.000275[/C][/ROW]
[ROW][C]13[/C][C]-0.015788[/C][C]-0.1233[/C][C]0.451134[/C][/ROW]
[ROW][C]14[/C][C]-0.266114[/C][C]-2.0784[/C][C]0.020943[/C][/ROW]
[ROW][C]15[/C][C]-0.225708[/C][C]-1.7628[/C][C]0.041468[/C][/ROW]
[ROW][C]16[/C][C]-0.109108[/C][C]-0.8522[/C][C]0.198729[/C][/ROW]
[ROW][C]17[/C][C]0.066769[/C][C]0.5215[/C][C]0.301961[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115848&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115848&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
10.2882072.2510.014001
20.0287130.22430.411654
30.168561.31650.096466
40.1544141.2060.116235
50.377832.95090.002245
60.3826812.98880.002016
70.2218961.73310.044069
80.0576220.450.327139
9-0.013258-0.10360.458933
10-0.15304-1.19530.118302
110.0993710.77610.220342
120.4670663.64790.000275
13-0.015788-0.12330.451134
14-0.266114-2.07840.020943
15-0.225708-1.76280.041468
16-0.109108-0.85220.198729
170.0667690.52150.301961






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.2882072.2510.014001
2-0.059274-0.46290.322526
30.1935811.51190.06786
40.0552920.43180.33369
50.3745822.92560.002411
60.2113761.65090.051949
70.1563881.22140.113311
8-0.092549-0.72280.236273
9-0.142674-1.11430.134756
10-0.488067-3.81190.000162
11-0.126857-0.99080.162851
120.3715792.90210.002575
13-0.086418-0.67490.251131
14-0.139583-1.09020.139961
15-0.17453-1.36310.088928
160.0690230.53910.295894
17-0.061774-0.48250.315599

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.288207 & 2.251 & 0.014001 \tabularnewline
2 & -0.059274 & -0.4629 & 0.322526 \tabularnewline
3 & 0.193581 & 1.5119 & 0.06786 \tabularnewline
4 & 0.055292 & 0.4318 & 0.33369 \tabularnewline
5 & 0.374582 & 2.9256 & 0.002411 \tabularnewline
6 & 0.211376 & 1.6509 & 0.051949 \tabularnewline
7 & 0.156388 & 1.2214 & 0.113311 \tabularnewline
8 & -0.092549 & -0.7228 & 0.236273 \tabularnewline
9 & -0.142674 & -1.1143 & 0.134756 \tabularnewline
10 & -0.488067 & -3.8119 & 0.000162 \tabularnewline
11 & -0.126857 & -0.9908 & 0.162851 \tabularnewline
12 & 0.371579 & 2.9021 & 0.002575 \tabularnewline
13 & -0.086418 & -0.6749 & 0.251131 \tabularnewline
14 & -0.139583 & -1.0902 & 0.139961 \tabularnewline
15 & -0.17453 & -1.3631 & 0.088928 \tabularnewline
16 & 0.069023 & 0.5391 & 0.295894 \tabularnewline
17 & -0.061774 & -0.4825 & 0.315599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115848&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]0.288207[/C][C]2.251[/C][C]0.014001[/C][/ROW]
[ROW][C]2[/C][C]-0.059274[/C][C]-0.4629[/C][C]0.322526[/C][/ROW]
[ROW][C]3[/C][C]0.193581[/C][C]1.5119[/C][C]0.06786[/C][/ROW]
[ROW][C]4[/C][C]0.055292[/C][C]0.4318[/C][C]0.33369[/C][/ROW]
[ROW][C]5[/C][C]0.374582[/C][C]2.9256[/C][C]0.002411[/C][/ROW]
[ROW][C]6[/C][C]0.211376[/C][C]1.6509[/C][C]0.051949[/C][/ROW]
[ROW][C]7[/C][C]0.156388[/C][C]1.2214[/C][C]0.113311[/C][/ROW]
[ROW][C]8[/C][C]-0.092549[/C][C]-0.7228[/C][C]0.236273[/C][/ROW]
[ROW][C]9[/C][C]-0.142674[/C][C]-1.1143[/C][C]0.134756[/C][/ROW]
[ROW][C]10[/C][C]-0.488067[/C][C]-3.8119[/C][C]0.000162[/C][/ROW]
[ROW][C]11[/C][C]-0.126857[/C][C]-0.9908[/C][C]0.162851[/C][/ROW]
[ROW][C]12[/C][C]0.371579[/C][C]2.9021[/C][C]0.002575[/C][/ROW]
[ROW][C]13[/C][C]-0.086418[/C][C]-0.6749[/C][C]0.251131[/C][/ROW]
[ROW][C]14[/C][C]-0.139583[/C][C]-1.0902[/C][C]0.139961[/C][/ROW]
[ROW][C]15[/C][C]-0.17453[/C][C]-1.3631[/C][C]0.088928[/C][/ROW]
[ROW][C]16[/C][C]0.069023[/C][C]0.5391[/C][C]0.295894[/C][/ROW]
[ROW][C]17[/C][C]-0.061774[/C][C]-0.4825[/C][C]0.315599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115848&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115848&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
10.2882072.2510.014001
2-0.059274-0.46290.322526
30.1935811.51190.06786
40.0552920.43180.33369
50.3745822.92560.002411
60.2113761.65090.051949
70.1563881.22140.113311
8-0.092549-0.72280.236273
9-0.142674-1.11430.134756
10-0.488067-3.81190.000162
11-0.126857-0.99080.162851
120.3715792.90210.002575
13-0.086418-0.67490.251131
14-0.139583-1.09020.139961
15-0.17453-1.36310.088928
160.0690230.53910.295894
17-0.061774-0.48250.315599


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)
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')