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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 computationTue, 15 Mar 2016 22:15:59 +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/15/t1458080258cn8pi12lnforofs.htm/, Retrieved Tue, 30 Apr 2024 11:25:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294128, Retrieved Tue, 30 Apr 2024 11:25:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79

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] [Opgave 7 eigen reeks] [2016-03-15 22:15:59] [0996086de175370e0a22efa864593ca4] [Current]
- R PD    [(Partial) Autocorrelation Function] [Opgave 7 eigen re...] [2016-05-28 17:39:01] [29ab9c45344d5c037bf74b62f65f8e78]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
91,27
91,51
91,78
91,83
92,01
92,1
92,35
92,46
93,08
93,38
93,46
93,58
93,74
94,18
94,43
94,53
94,66
94,8
95,04
95,29
95,42
95,64
95,82
96,01
96,16
96,4
96,87
97
97,26
97,42
97,64
97,93
98,1
98,29
98,42
98,49
98,67
99,1
99,37
99,54
99,58
99,77
100,06
100,26
100,57
100,94
101,03
101,12
101,26
101,94
102,26
102,51
102,61
102,76
103,04
103,22
103,47
103,64
103,76
103,85

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' @ 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294128&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294128&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294128&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' @ fisher.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.950877.36540
20.9009866.9790
30.8511536.5930
40.8002756.19890
50.749595.80630
60.6976275.40381e-06
70.6465735.00833e-06
80.5943824.60411.1e-05
90.5448414.22034.2e-05
100.4969983.84970.000145
110.44973.48340.000465
120.405753.14290.0013
130.3612312.79810.003451
140.3180942.46390.008313
150.2752832.13230.018541
160.2338261.81120.037557
170.1934911.49880.069588

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95087 & 7.3654 & 0 \tabularnewline
2 & 0.900986 & 6.979 & 0 \tabularnewline
3 & 0.851153 & 6.593 & 0 \tabularnewline
4 & 0.800275 & 6.1989 & 0 \tabularnewline
5 & 0.74959 & 5.8063 & 0 \tabularnewline
6 & 0.697627 & 5.4038 & 1e-06 \tabularnewline
7 & 0.646573 & 5.0083 & 3e-06 \tabularnewline
8 & 0.594382 & 4.6041 & 1.1e-05 \tabularnewline
9 & 0.544841 & 4.2203 & 4.2e-05 \tabularnewline
10 & 0.496998 & 3.8497 & 0.000145 \tabularnewline
11 & 0.4497 & 3.4834 & 0.000465 \tabularnewline
12 & 0.40575 & 3.1429 & 0.0013 \tabularnewline
13 & 0.361231 & 2.7981 & 0.003451 \tabularnewline
14 & 0.318094 & 2.4639 & 0.008313 \tabularnewline
15 & 0.275283 & 2.1323 & 0.018541 \tabularnewline
16 & 0.233826 & 1.8112 & 0.037557 \tabularnewline
17 & 0.193491 & 1.4988 & 0.069588 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294128&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]0.95087[/C][C]7.3654[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.900986[/C][C]6.979[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.851153[/C][C]6.593[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.800275[/C][C]6.1989[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.74959[/C][C]5.8063[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.697627[/C][C]5.4038[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.646573[/C][C]5.0083[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.594382[/C][C]4.6041[/C][C]1.1e-05[/C][/ROW]
[ROW][C]9[/C][C]0.544841[/C][C]4.2203[/C][C]4.2e-05[/C][/ROW]
[ROW][C]10[/C][C]0.496998[/C][C]3.8497[/C][C]0.000145[/C][/ROW]
[ROW][C]11[/C][C]0.4497[/C][C]3.4834[/C][C]0.000465[/C][/ROW]
[ROW][C]12[/C][C]0.40575[/C][C]3.1429[/C][C]0.0013[/C][/ROW]
[ROW][C]13[/C][C]0.361231[/C][C]2.7981[/C][C]0.003451[/C][/ROW]
[ROW][C]14[/C][C]0.318094[/C][C]2.4639[/C][C]0.008313[/C][/ROW]
[ROW][C]15[/C][C]0.275283[/C][C]2.1323[/C][C]0.018541[/C][/ROW]
[ROW][C]16[/C][C]0.233826[/C][C]1.8112[/C][C]0.037557[/C][/ROW]
[ROW][C]17[/C][C]0.193491[/C][C]1.4988[/C][C]0.069588[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294128&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294128&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
10.950877.36540
20.9009866.9790
30.8511536.5930
40.8002756.19890
50.749595.80630
60.6976275.40381e-06
70.6465735.00833e-06
80.5943824.60411.1e-05
90.5448414.22034.2e-05
100.4969983.84970.000145
110.44973.48340.000465
120.405753.14290.0013
130.3612312.79810.003451
140.3180942.46390.008313
150.2752832.13230.018541
160.2338261.81120.037557
170.1934911.49880.069588






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.950877.36540
2-0.033047-0.2560.399419
3-0.025654-0.19870.421579
4-0.037847-0.29320.385205
5-0.02609-0.20210.420263
6-0.042396-0.32840.371877
7-0.020792-0.16110.436295
8-0.043156-0.33430.369664
9-0.004399-0.03410.486466
10-0.014925-0.11560.454174
11-0.025963-0.20110.420647
120.0016280.01260.49499
13-0.037855-0.29320.385181
14-0.019201-0.14870.441134
15-0.030435-0.23570.407215
16-0.020022-0.15510.438635
17-0.023446-0.18160.42825

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95087 & 7.3654 & 0 \tabularnewline
2 & -0.033047 & -0.256 & 0.399419 \tabularnewline
3 & -0.025654 & -0.1987 & 0.421579 \tabularnewline
4 & -0.037847 & -0.2932 & 0.385205 \tabularnewline
5 & -0.02609 & -0.2021 & 0.420263 \tabularnewline
6 & -0.042396 & -0.3284 & 0.371877 \tabularnewline
7 & -0.020792 & -0.1611 & 0.436295 \tabularnewline
8 & -0.043156 & -0.3343 & 0.369664 \tabularnewline
9 & -0.004399 & -0.0341 & 0.486466 \tabularnewline
10 & -0.014925 & -0.1156 & 0.454174 \tabularnewline
11 & -0.025963 & -0.2011 & 0.420647 \tabularnewline
12 & 0.001628 & 0.0126 & 0.49499 \tabularnewline
13 & -0.037855 & -0.2932 & 0.385181 \tabularnewline
14 & -0.019201 & -0.1487 & 0.441134 \tabularnewline
15 & -0.030435 & -0.2357 & 0.407215 \tabularnewline
16 & -0.020022 & -0.1551 & 0.438635 \tabularnewline
17 & -0.023446 & -0.1816 & 0.42825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294128&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]0.95087[/C][C]7.3654[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.033047[/C][C]-0.256[/C][C]0.399419[/C][/ROW]
[ROW][C]3[/C][C]-0.025654[/C][C]-0.1987[/C][C]0.421579[/C][/ROW]
[ROW][C]4[/C][C]-0.037847[/C][C]-0.2932[/C][C]0.385205[/C][/ROW]
[ROW][C]5[/C][C]-0.02609[/C][C]-0.2021[/C][C]0.420263[/C][/ROW]
[ROW][C]6[/C][C]-0.042396[/C][C]-0.3284[/C][C]0.371877[/C][/ROW]
[ROW][C]7[/C][C]-0.020792[/C][C]-0.1611[/C][C]0.436295[/C][/ROW]
[ROW][C]8[/C][C]-0.043156[/C][C]-0.3343[/C][C]0.369664[/C][/ROW]
[ROW][C]9[/C][C]-0.004399[/C][C]-0.0341[/C][C]0.486466[/C][/ROW]
[ROW][C]10[/C][C]-0.014925[/C][C]-0.1156[/C][C]0.454174[/C][/ROW]
[ROW][C]11[/C][C]-0.025963[/C][C]-0.2011[/C][C]0.420647[/C][/ROW]
[ROW][C]12[/C][C]0.001628[/C][C]0.0126[/C][C]0.49499[/C][/ROW]
[ROW][C]13[/C][C]-0.037855[/C][C]-0.2932[/C][C]0.385181[/C][/ROW]
[ROW][C]14[/C][C]-0.019201[/C][C]-0.1487[/C][C]0.441134[/C][/ROW]
[ROW][C]15[/C][C]-0.030435[/C][C]-0.2357[/C][C]0.407215[/C][/ROW]
[ROW][C]16[/C][C]-0.020022[/C][C]-0.1551[/C][C]0.438635[/C][/ROW]
[ROW][C]17[/C][C]-0.023446[/C][C]-0.1816[/C][C]0.42825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294128&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294128&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
10.950877.36540
2-0.033047-0.2560.399419
3-0.025654-0.19870.421579
4-0.037847-0.29320.385205
5-0.02609-0.20210.420263
6-0.042396-0.32840.371877
7-0.020792-0.16110.436295
8-0.043156-0.33430.369664
9-0.004399-0.03410.486466
10-0.014925-0.11560.454174
11-0.025963-0.20110.420647
120.0016280.01260.49499
13-0.037855-0.29320.385181
14-0.019201-0.14870.441134
15-0.030435-0.23570.407215
16-0.020022-0.15510.438635
17-0.023446-0.18160.42825


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')