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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 Jan 2016 15:00:30 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/21/t1453388480z99s7bmsgapd9lk.htm/, Retrieved Mon, 29 Apr 2024 01:33:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289899, Retrieved Mon, 29 Apr 2024 01:33:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [vraag 8 examen] [2016-01-21 15:00:30] [f0540685e8d53548e4baf07e0669deea] [Current]

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Dataseries X:

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0.0013999990894105
0.0876771622176185
0.253920154859331
-0.0329407507841036
0.00427395855379008
-0.0889668134958849
-0.165281368150775
-0.33220433089751
0.219927126513421
0.236701919529402
0.234525437835356
-0.0304289243382355
0.0953913592916723
0.222671044416315
0.0914666084830592
-0.206034580848975
0.317983507811223
0.209887369047125
0.47505736015715
-0.222062521324981
0.0119408639911758
-0.172481528037084
-0.342720660187122
-0.343867756086308
0.088435724392957
0.207149951929822
0.0343760117343465
-0.301707672057424
-0.0110173444677831
-0.0691482212286872
-0.925838573157798
0.137673245546374
0.0727565374056945
0.201173883123843
0.0856783035058499
-0.109577212438584
-0.260551934204086
0.147885882041203
0.212413648519748
-0.0832851309957541
-0.115216896092894
-0.221533847078893
0.33793754507397
-0.134446101735477
0.164631582429395
0.0888222485881065
0.0469533479921545
0.241738416214495
-0.0752540261587926
-0.0299598595890917
0.225881103587503
0.0412636104361186
0.128108276344458
-0.141250457347375
0.481091241511557
-0.11016711751824
0.191801843198123
-0.066757083135655
0.0394798962983962
-0.0743907512944395
0.0864476825544102
-0.0321810065262648
0.121406171476103
-0.0784677853924106
-0.219288911182277
-0.0373619502368736
0.449190378168538
-0.083495394142657
0.104571843583723
0.564217976443139
-0.156913984252991
0.0837627464269975
0.129666943943497
-0.0279018187223396
-0.0344326851573588
-0.328655799589801
0.121385421475263
0.0494710079304724
0.428353319793773
-0.368885964978714
-0.302589451991359
-0.45541145100303
-0.0851366312257987
0.244537840690697

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289899&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289899&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289899&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.000747	-0.0068	0.497277
2	-0.014661	-0.1344	0.446716
3	-0.128078	-1.1739	0.121885
4	-0.002018	-0.0185	0.492644
5	-0.043918	-0.4025	0.344165
6	0.025726	0.2358	0.407087
7	0.095899	0.8789	0.190973
8	0.115573	1.0592	0.146262
9	0.031136	0.2854	0.388033
10	-0.079214	-0.726	0.234926
11	-0.101582	-0.931	0.177256
12	-0.073709	-0.6756	0.250589
13	-0.124543	-1.1415	0.128462
14	-0.077191	-0.7075	0.240617
15	0.045148	0.4138	0.340043
16	0.113845	1.0434	0.149876
17	-0.011835	-0.1085	0.456943
18	-0.020437	-0.1873	0.425935
19	-0.044161	-0.4047	0.343348

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.000747 & -0.0068 & 0.497277 \tabularnewline
2 & -0.014661 & -0.1344 & 0.446716 \tabularnewline
3 & -0.128078 & -1.1739 & 0.121885 \tabularnewline
4 & -0.002018 & -0.0185 & 0.492644 \tabularnewline
5 & -0.043918 & -0.4025 & 0.344165 \tabularnewline
6 & 0.025726 & 0.2358 & 0.407087 \tabularnewline
7 & 0.095899 & 0.8789 & 0.190973 \tabularnewline
8 & 0.115573 & 1.0592 & 0.146262 \tabularnewline
9 & 0.031136 & 0.2854 & 0.388033 \tabularnewline
10 & -0.079214 & -0.726 & 0.234926 \tabularnewline
11 & -0.101582 & -0.931 & 0.177256 \tabularnewline
12 & -0.073709 & -0.6756 & 0.250589 \tabularnewline
13 & -0.124543 & -1.1415 & 0.128462 \tabularnewline
14 & -0.077191 & -0.7075 & 0.240617 \tabularnewline
15 & 0.045148 & 0.4138 & 0.340043 \tabularnewline
16 & 0.113845 & 1.0434 & 0.149876 \tabularnewline
17 & -0.011835 & -0.1085 & 0.456943 \tabularnewline
18 & -0.020437 & -0.1873 & 0.425935 \tabularnewline
19 & -0.044161 & -0.4047 & 0.343348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289899&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]-0.000747[/C][C]-0.0068[/C][C]0.497277[/C][/ROW]
[ROW][C]2[/C][C]-0.014661[/C][C]-0.1344[/C][C]0.446716[/C][/ROW]
[ROW][C]3[/C][C]-0.128078[/C][C]-1.1739[/C][C]0.121885[/C][/ROW]
[ROW][C]4[/C][C]-0.002018[/C][C]-0.0185[/C][C]0.492644[/C][/ROW]
[ROW][C]5[/C][C]-0.043918[/C][C]-0.4025[/C][C]0.344165[/C][/ROW]
[ROW][C]6[/C][C]0.025726[/C][C]0.2358[/C][C]0.407087[/C][/ROW]
[ROW][C]7[/C][C]0.095899[/C][C]0.8789[/C][C]0.190973[/C][/ROW]
[ROW][C]8[/C][C]0.115573[/C][C]1.0592[/C][C]0.146262[/C][/ROW]
[ROW][C]9[/C][C]0.031136[/C][C]0.2854[/C][C]0.388033[/C][/ROW]
[ROW][C]10[/C][C]-0.079214[/C][C]-0.726[/C][C]0.234926[/C][/ROW]
[ROW][C]11[/C][C]-0.101582[/C][C]-0.931[/C][C]0.177256[/C][/ROW]
[ROW][C]12[/C][C]-0.073709[/C][C]-0.6756[/C][C]0.250589[/C][/ROW]
[ROW][C]13[/C][C]-0.124543[/C][C]-1.1415[/C][C]0.128462[/C][/ROW]
[ROW][C]14[/C][C]-0.077191[/C][C]-0.7075[/C][C]0.240617[/C][/ROW]
[ROW][C]15[/C][C]0.045148[/C][C]0.4138[/C][C]0.340043[/C][/ROW]
[ROW][C]16[/C][C]0.113845[/C][C]1.0434[/C][C]0.149876[/C][/ROW]
[ROW][C]17[/C][C]-0.011835[/C][C]-0.1085[/C][C]0.456943[/C][/ROW]
[ROW][C]18[/C][C]-0.020437[/C][C]-0.1873[/C][C]0.425935[/C][/ROW]
[ROW][C]19[/C][C]-0.044161[/C][C]-0.4047[/C][C]0.343348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289899&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289899&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.000747	-0.0068	0.497277
2	-0.014661	-0.1344	0.446716
3	-0.128078	-1.1739	0.121885
4	-0.002018	-0.0185	0.492644
5	-0.043918	-0.4025	0.344165
6	0.025726	0.2358	0.407087
7	0.095899	0.8789	0.190973
8	0.115573	1.0592	0.146262
9	0.031136	0.2854	0.388033
10	-0.079214	-0.726	0.234926
11	-0.101582	-0.931	0.177256
12	-0.073709	-0.6756	0.250589
13	-0.124543	-1.1415	0.128462
14	-0.077191	-0.7075	0.240617
15	0.045148	0.4138	0.340043
16	0.113845	1.0434	0.149876
17	-0.011835	-0.1085	0.456943
18	-0.020437	-0.1873	0.425935
19	-0.044161	-0.4047	0.343348

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.000747	-0.0068	0.497277
2	-0.014661	-0.1344	0.446714
3	-0.128128	-1.1743	0.121794
4	-0.002713	-0.0249	0.490112
5	-0.048507	-0.4446	0.328887
6	0.009139	0.0838	0.466724
7	0.095562	0.8758	0.191807
8	0.108038	0.9902	0.162463
9	0.042448	0.389	0.349115
10	-0.054273	-0.4974	0.310096
11	-0.077048	-0.7062	0.241023
12	-0.067413	-0.6179	0.269172
13	-0.149881	-1.3737	0.086598
14	-0.12669	-1.1611	0.124439
15	-0.011114	-0.1019	0.459554
16	0.064827	0.5941	0.277004
17	-0.015889	-0.1456	0.442284
18	0.023332	0.2138	0.415595
19	0.021073	0.1931	0.42366

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.000747 & -0.0068 & 0.497277 \tabularnewline
2 & -0.014661 & -0.1344 & 0.446714 \tabularnewline
3 & -0.128128 & -1.1743 & 0.121794 \tabularnewline
4 & -0.002713 & -0.0249 & 0.490112 \tabularnewline
5 & -0.048507 & -0.4446 & 0.328887 \tabularnewline
6 & 0.009139 & 0.0838 & 0.466724 \tabularnewline
7 & 0.095562 & 0.8758 & 0.191807 \tabularnewline
8 & 0.108038 & 0.9902 & 0.162463 \tabularnewline
9 & 0.042448 & 0.389 & 0.349115 \tabularnewline
10 & -0.054273 & -0.4974 & 0.310096 \tabularnewline
11 & -0.077048 & -0.7062 & 0.241023 \tabularnewline
12 & -0.067413 & -0.6179 & 0.269172 \tabularnewline
13 & -0.149881 & -1.3737 & 0.086598 \tabularnewline
14 & -0.12669 & -1.1611 & 0.124439 \tabularnewline
15 & -0.011114 & -0.1019 & 0.459554 \tabularnewline
16 & 0.064827 & 0.5941 & 0.277004 \tabularnewline
17 & -0.015889 & -0.1456 & 0.442284 \tabularnewline
18 & 0.023332 & 0.2138 & 0.415595 \tabularnewline
19 & 0.021073 & 0.1931 & 0.42366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289899&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]-0.000747[/C][C]-0.0068[/C][C]0.497277[/C][/ROW]
[ROW][C]2[/C][C]-0.014661[/C][C]-0.1344[/C][C]0.446714[/C][/ROW]
[ROW][C]3[/C][C]-0.128128[/C][C]-1.1743[/C][C]0.121794[/C][/ROW]
[ROW][C]4[/C][C]-0.002713[/C][C]-0.0249[/C][C]0.490112[/C][/ROW]
[ROW][C]5[/C][C]-0.048507[/C][C]-0.4446[/C][C]0.328887[/C][/ROW]
[ROW][C]6[/C][C]0.009139[/C][C]0.0838[/C][C]0.466724[/C][/ROW]
[ROW][C]7[/C][C]0.095562[/C][C]0.8758[/C][C]0.191807[/C][/ROW]
[ROW][C]8[/C][C]0.108038[/C][C]0.9902[/C][C]0.162463[/C][/ROW]
[ROW][C]9[/C][C]0.042448[/C][C]0.389[/C][C]0.349115[/C][/ROW]
[ROW][C]10[/C][C]-0.054273[/C][C]-0.4974[/C][C]0.310096[/C][/ROW]
[ROW][C]11[/C][C]-0.077048[/C][C]-0.7062[/C][C]0.241023[/C][/ROW]
[ROW][C]12[/C][C]-0.067413[/C][C]-0.6179[/C][C]0.269172[/C][/ROW]
[ROW][C]13[/C][C]-0.149881[/C][C]-1.3737[/C][C]0.086598[/C][/ROW]
[ROW][C]14[/C][C]-0.12669[/C][C]-1.1611[/C][C]0.124439[/C][/ROW]
[ROW][C]15[/C][C]-0.011114[/C][C]-0.1019[/C][C]0.459554[/C][/ROW]
[ROW][C]16[/C][C]0.064827[/C][C]0.5941[/C][C]0.277004[/C][/ROW]
[ROW][C]17[/C][C]-0.015889[/C][C]-0.1456[/C][C]0.442284[/C][/ROW]
[ROW][C]18[/C][C]0.023332[/C][C]0.2138[/C][C]0.415595[/C][/ROW]
[ROW][C]19[/C][C]0.021073[/C][C]0.1931[/C][C]0.42366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289899&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289899&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.000747	-0.0068	0.497277
2	-0.014661	-0.1344	0.446714
3	-0.128128	-1.1743	0.121794
4	-0.002713	-0.0249	0.490112
5	-0.048507	-0.4446	0.328887
6	0.009139	0.0838	0.466724
7	0.095562	0.8758	0.191807
8	0.108038	0.9902	0.162463
9	0.042448	0.389	0.349115
10	-0.054273	-0.4974	0.310096
11	-0.077048	-0.7062	0.241023
12	-0.067413	-0.6179	0.269172
13	-0.149881	-1.3737	0.086598
14	-0.12669	-1.1611	0.124439
15	-0.011114	-0.1019	0.459554
16	0.064827	0.5941	0.277004
17	-0.015889	-0.1456	0.442284
18	0.023332	0.2138	0.415595
19	0.021073	0.1931	0.42366

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code