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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 computationSat, 25 Dec 2010 10:24:30 +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/25/t12932728197iqk90ee7y8grzl.htm/, Retrieved Sun, 28 Apr 2024 22:25:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115343, Retrieved Sun, 28 Apr 2024 22:25:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

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] [ACF d=0 D=0] [2010-12-25 10:24:30] [346ac46ef4f6bb745e48fc42fac6253b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
104,79
104,82
104,94
105,04
105,17
105,4
105,56
105,66
105,96
105,92
106,03
106,16
106,39
106,41
106,66
106,76
106,97
107,07
107,29
107,39
107,5
107,79
107,77
107,84
108,09
108,28
108,49
108,73
108,84
108,94
109,08
109,38
109,42
109,59
109,83
109,89
110,29
110,33
110,54
110,69
110,77
111,01
111,25
111,09
111,32
111,36
111,31
111,37
111,49
111,49
111,55
111,56
111,66
111,68
111,71
111,76
111,82
111,87
111,94
112,05

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115343&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]2 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=115343&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115343&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9579917.42060
20.9150817.08820
30.8713226.74920
40.8260646.39870
50.7802676.04390
60.7351065.69410
70.6891095.33781e-06
80.6420774.97353e-06
90.5969094.62361e-05
100.5488984.25173.8e-05
110.5000583.87340.000134
120.4502833.48790.000459
130.4021833.11530.001409
140.3523662.72940.004157
150.3029292.34650.011136
160.252741.95770.027459
170.2052151.58960.058591

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.957991 & 7.4206 & 0 \tabularnewline
2 & 0.915081 & 7.0882 & 0 \tabularnewline
3 & 0.871322 & 6.7492 & 0 \tabularnewline
4 & 0.826064 & 6.3987 & 0 \tabularnewline
5 & 0.780267 & 6.0439 & 0 \tabularnewline
6 & 0.735106 & 5.6941 & 0 \tabularnewline
7 & 0.689109 & 5.3378 & 1e-06 \tabularnewline
8 & 0.642077 & 4.9735 & 3e-06 \tabularnewline
9 & 0.596909 & 4.6236 & 1e-05 \tabularnewline
10 & 0.548898 & 4.2517 & 3.8e-05 \tabularnewline
11 & 0.500058 & 3.8734 & 0.000134 \tabularnewline
12 & 0.450283 & 3.4879 & 0.000459 \tabularnewline
13 & 0.402183 & 3.1153 & 0.001409 \tabularnewline
14 & 0.352366 & 2.7294 & 0.004157 \tabularnewline
15 & 0.302929 & 2.3465 & 0.011136 \tabularnewline
16 & 0.25274 & 1.9577 & 0.027459 \tabularnewline
17 & 0.205215 & 1.5896 & 0.058591 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115343&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]0.957991[/C][C]7.4206[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.915081[/C][C]7.0882[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.871322[/C][C]6.7492[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.826064[/C][C]6.3987[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.780267[/C][C]6.0439[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.735106[/C][C]5.6941[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.689109[/C][C]5.3378[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.642077[/C][C]4.9735[/C][C]3e-06[/C][/ROW]
[ROW][C]9[/C][C]0.596909[/C][C]4.6236[/C][C]1e-05[/C][/ROW]
[ROW][C]10[/C][C]0.548898[/C][C]4.2517[/C][C]3.8e-05[/C][/ROW]
[ROW][C]11[/C][C]0.500058[/C][C]3.8734[/C][C]0.000134[/C][/ROW]
[ROW][C]12[/C][C]0.450283[/C][C]3.4879[/C][C]0.000459[/C][/ROW]
[ROW][C]13[/C][C]0.402183[/C][C]3.1153[/C][C]0.001409[/C][/ROW]
[ROW][C]14[/C][C]0.352366[/C][C]2.7294[/C][C]0.004157[/C][/ROW]
[ROW][C]15[/C][C]0.302929[/C][C]2.3465[/C][C]0.011136[/C][/ROW]
[ROW][C]16[/C][C]0.25274[/C][C]1.9577[/C][C]0.027459[/C][/ROW]
[ROW][C]17[/C][C]0.205215[/C][C]1.5896[/C][C]0.058591[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115343&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115343&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
10.9579917.42060
20.9150817.08820
30.8713226.74920
40.8260646.39870
50.7802676.04390
60.7351065.69410
70.6891095.33781e-06
80.6420774.97353e-06
90.5969094.62361e-05
100.5488984.25173.8e-05
110.5000583.87340.000134
120.4502833.48790.000459
130.4021833.11530.001409
140.3523662.72940.004157
150.3029292.34650.011136
160.252741.95770.027459
170.2052151.58960.058591






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9579917.42060
2-0.032414-0.25110.401305
3-0.032615-0.25260.400706
4-0.04145-0.32110.374636
5-0.030935-0.23960.40572
6-0.017526-0.13580.446235
7-0.035956-0.27850.390788
8-0.039664-0.30720.379865
9-0.005672-0.04390.482551
10-0.063079-0.48860.313451
11-0.040429-0.31320.377623
12-0.044207-0.34240.366615
13-0.012718-0.09850.460926
14-0.054448-0.42180.337355
15-0.032622-0.25270.400685
16-0.04784-0.37060.356133
17-0.005322-0.04120.483627

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.957991 & 7.4206 & 0 \tabularnewline
2 & -0.032414 & -0.2511 & 0.401305 \tabularnewline
3 & -0.032615 & -0.2526 & 0.400706 \tabularnewline
4 & -0.04145 & -0.3211 & 0.374636 \tabularnewline
5 & -0.030935 & -0.2396 & 0.40572 \tabularnewline
6 & -0.017526 & -0.1358 & 0.446235 \tabularnewline
7 & -0.035956 & -0.2785 & 0.390788 \tabularnewline
8 & -0.039664 & -0.3072 & 0.379865 \tabularnewline
9 & -0.005672 & -0.0439 & 0.482551 \tabularnewline
10 & -0.063079 & -0.4886 & 0.313451 \tabularnewline
11 & -0.040429 & -0.3132 & 0.377623 \tabularnewline
12 & -0.044207 & -0.3424 & 0.366615 \tabularnewline
13 & -0.012718 & -0.0985 & 0.460926 \tabularnewline
14 & -0.054448 & -0.4218 & 0.337355 \tabularnewline
15 & -0.032622 & -0.2527 & 0.400685 \tabularnewline
16 & -0.04784 & -0.3706 & 0.356133 \tabularnewline
17 & -0.005322 & -0.0412 & 0.483627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115343&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]0.957991[/C][C]7.4206[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.032414[/C][C]-0.2511[/C][C]0.401305[/C][/ROW]
[ROW][C]3[/C][C]-0.032615[/C][C]-0.2526[/C][C]0.400706[/C][/ROW]
[ROW][C]4[/C][C]-0.04145[/C][C]-0.3211[/C][C]0.374636[/C][/ROW]
[ROW][C]5[/C][C]-0.030935[/C][C]-0.2396[/C][C]0.40572[/C][/ROW]
[ROW][C]6[/C][C]-0.017526[/C][C]-0.1358[/C][C]0.446235[/C][/ROW]
[ROW][C]7[/C][C]-0.035956[/C][C]-0.2785[/C][C]0.390788[/C][/ROW]
[ROW][C]8[/C][C]-0.039664[/C][C]-0.3072[/C][C]0.379865[/C][/ROW]
[ROW][C]9[/C][C]-0.005672[/C][C]-0.0439[/C][C]0.482551[/C][/ROW]
[ROW][C]10[/C][C]-0.063079[/C][C]-0.4886[/C][C]0.313451[/C][/ROW]
[ROW][C]11[/C][C]-0.040429[/C][C]-0.3132[/C][C]0.377623[/C][/ROW]
[ROW][C]12[/C][C]-0.044207[/C][C]-0.3424[/C][C]0.366615[/C][/ROW]
[ROW][C]13[/C][C]-0.012718[/C][C]-0.0985[/C][C]0.460926[/C][/ROW]
[ROW][C]14[/C][C]-0.054448[/C][C]-0.4218[/C][C]0.337355[/C][/ROW]
[ROW][C]15[/C][C]-0.032622[/C][C]-0.2527[/C][C]0.400685[/C][/ROW]
[ROW][C]16[/C][C]-0.04784[/C][C]-0.3706[/C][C]0.356133[/C][/ROW]
[ROW][C]17[/C][C]-0.005322[/C][C]-0.0412[/C][C]0.483627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115343&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115343&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
10.9579917.42060
2-0.032414-0.25110.401305
3-0.032615-0.25260.400706
4-0.04145-0.32110.374636
5-0.030935-0.23960.40572
6-0.017526-0.13580.446235
7-0.035956-0.27850.390788
8-0.039664-0.30720.379865
9-0.005672-0.04390.482551
10-0.063079-0.48860.313451
11-0.040429-0.31320.377623
12-0.044207-0.34240.366615
13-0.012718-0.09850.460926
14-0.054448-0.42180.337355
15-0.032622-0.25270.400685
16-0.04784-0.37060.356133
17-0.005322-0.04120.483627


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')