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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 17 Aug 2014 18:13:10 +0100

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/2014/Aug/17/t1408295661wpymjjolii09pn6.htm/, Retrieved Thu, 16 May 2024 13:17:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235624, Retrieved Thu, 16 May 2024 13:17:22 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Stefaan Segers

Estimated Impact

109

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

-       [(Partial) Autocorrelation Function] [Tijdreeks A - Sta...] [2014-08-17 17:13:10] [92f35a2db74bf110e350beffc19b3da6] [Current]
- R P     [(Partial) Autocorrelation Function] [Tijdreeks A - Sta...] [2014-08-17 17:15:53] [40556739fb744d7815ea48083fb3e63a] 
- R P       [(Partial) Autocorrelation Function] [Tijdreeks A - Sta...] [2014-08-17 17:34:53] [40556739fb744d7815ea48083fb3e63a] 
- RMP         [Standard Deviation Plot] [Tijdreeks A - Sta...] [2014-08-17 17:45:48] [40556739fb744d7815ea48083fb3e63a] 
- RMP         [Standard Deviation-Mean Plot] [Tijdreeks A- stap 26] [2014-08-17 18:24:16] [40556739fb744d7815ea48083fb3e63a] 
- RMP         [Classical Decomposition] [Tijdreeks A - Sta...] [2014-08-17 18:54:33] [40556739fb744d7815ea48083fb3e63a] 
- RMP         [Exponential Smoothing] [Tijdreeks A - Sta...] [2014-08-17 19:39:55] [40556739fb744d7815ea48083fb3e63a] 
- RMPD        [Univariate Data Series] [Tijdreeks B - Stap 1] [2014-08-17 20:05:47] [f85cc8f00ef4b762f0a6fdfddc793773] 
- RMPD        [Univariate Data Series] [Tijdreeks B - Sta...] [2014-08-17 20:10:51] [f85cc8f00ef4b762f0a6fdfddc793773] 
- RM            [Histogram] [Tijdreeks B - Stap 2] [2014-08-17 20:17:22] [f85cc8f00ef4b762f0a6fdfddc793773] 
- RM            [Kernel Density Estimation] [Tijdreeks B - Stap 4] [2014-08-17 20:21:46] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Notched Boxplots] [Tijdreeks B - Stap 5] [2014-08-17 20:35:46] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Harrell-Davis Quantiles] [Tijdreeks B - Stap 6] [2014-08-17 20:39:34] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Harrell-Davis Quantiles] [Tijdreeks B - Stap 7] [2014-08-17 20:49:25] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Central Tendency] [Tijdreeks B - Stap 9] [2014-08-17 21:08:15] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Mean versus Median] [Tijdreeks B - Sta...] [2014-08-17 23:19:38] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Mean Plot] [Tijdreeks B - sta...] [2014-08-17 23:29:01] [40556739fb744d7815ea48083fb3e63a] 
- RM            [(Partial) Autocorrelation Function] [Tijdreeks B - Sta...] [2014-08-17 23:44:18] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Variability] [Tijdreeks B - Sta...] [2014-08-18 00:08:25] [40556739fb744d7815ea48083fb3e63a] 
- RM            [Standard Deviation-Mean Plot] [Tijdreeks B - Sta...] [2014-08-18 00:19:52] [40556739fb744d7815ea48083fb3e63a] 

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Dataseries X:

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Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235624&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235624&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235624&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.948779	10.3934	0
2	0.87943	9.6337	0
3	0.814489	8.9223	0
4	0.759704	8.3221	0
5	0.719598	7.8828	0
6	0.693055	7.592	0
7	0.678784	7.4357	0
8	0.669116	7.3298	0
9	0.66172	7.2488	0
10	0.658522	7.2137	0
11	0.657279	7.2001	0
12	0.641909	7.0318	0
13	0.596164	6.5306	0
14	0.534544	5.8556	0
15	0.47584	5.2126	0
16	0.427375	4.6817	4e-06
17	0.39507	4.3278	1.6e-05
18	0.373093	4.087	4e-05
19	0.364498	3.9929	5.6e-05
20	0.359273	3.9356	7e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948779 & 10.3934 & 0 \tabularnewline
2 & 0.87943 & 9.6337 & 0 \tabularnewline
3 & 0.814489 & 8.9223 & 0 \tabularnewline
4 & 0.759704 & 8.3221 & 0 \tabularnewline
5 & 0.719598 & 7.8828 & 0 \tabularnewline
6 & 0.693055 & 7.592 & 0 \tabularnewline
7 & 0.678784 & 7.4357 & 0 \tabularnewline
8 & 0.669116 & 7.3298 & 0 \tabularnewline
9 & 0.66172 & 7.2488 & 0 \tabularnewline
10 & 0.658522 & 7.2137 & 0 \tabularnewline
11 & 0.657279 & 7.2001 & 0 \tabularnewline
12 & 0.641909 & 7.0318 & 0 \tabularnewline
13 & 0.596164 & 6.5306 & 0 \tabularnewline
14 & 0.534544 & 5.8556 & 0 \tabularnewline
15 & 0.47584 & 5.2126 & 0 \tabularnewline
16 & 0.427375 & 4.6817 & 4e-06 \tabularnewline
17 & 0.39507 & 4.3278 & 1.6e-05 \tabularnewline
18 & 0.373093 & 4.087 & 4e-05 \tabularnewline
19 & 0.364498 & 3.9929 & 5.6e-05 \tabularnewline
20 & 0.359273 & 3.9356 & 7e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235624&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]0.948779[/C][C]10.3934[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.87943[/C][C]9.6337[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.814489[/C][C]8.9223[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.759704[/C][C]8.3221[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.719598[/C][C]7.8828[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.693055[/C][C]7.592[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.678784[/C][C]7.4357[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.669116[/C][C]7.3298[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.66172[/C][C]7.2488[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.658522[/C][C]7.2137[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.657279[/C][C]7.2001[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.641909[/C][C]7.0318[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.596164[/C][C]6.5306[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.534544[/C][C]5.8556[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.47584[/C][C]5.2126[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.427375[/C][C]4.6817[/C][C]4e-06[/C][/ROW]
[ROW][C]17[/C][C]0.39507[/C][C]4.3278[/C][C]1.6e-05[/C][/ROW]
[ROW][C]18[/C][C]0.373093[/C][C]4.087[/C][C]4e-05[/C][/ROW]
[ROW][C]19[/C][C]0.364498[/C][C]3.9929[/C][C]5.6e-05[/C][/ROW]
[ROW][C]20[/C][C]0.359273[/C][C]3.9356[/C][C]7e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235624&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235624&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	0.948779	10.3934	0
2	0.87943	9.6337	0
3	0.814489	8.9223	0
4	0.759704	8.3221	0
5	0.719598	7.8828	0
6	0.693055	7.592	0
7	0.678784	7.4357	0
8	0.669116	7.3298	0
9	0.66172	7.2488	0
10	0.658522	7.2137	0
11	0.657279	7.2001	0
12	0.641909	7.0318	0
13	0.596164	6.5306	0
14	0.534544	5.8556	0
15	0.47584	5.2126	0
16	0.427375	4.6817	4e-06
17	0.39507	4.3278	1.6e-05
18	0.373093	4.087	4e-05
19	0.364498	3.9929	5.6e-05
20	0.359273	3.9356	7e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.948779	10.3934	0
2	-0.207885	-2.2773	0.012271
3	0.040676	0.4456	0.328349
4	0.048477	0.531	0.298187
5	0.091779	1.0054	0.158366
6	0.079397	0.8698	0.193086
7	0.090851	0.9952	0.160816
8	0.031369	0.3436	0.365862
9	0.047957	0.5253	0.300156
10	0.077319	0.847	0.199343
11	0.05078	0.5563	0.289531
12	-0.114158	-1.2505	0.106768
13	-0.251562	-2.7557	0.003385
14	-0.099168	-1.0863	0.139756
15	0.007517	0.0823	0.467256
16	0.006777	0.0742	0.470471
17	0.040226	0.4407	0.330129
18	-0.030356	-0.3325	0.370034
19	0.069832	0.765	0.222894
20	0.004931	0.054	0.478506

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948779 & 10.3934 & 0 \tabularnewline
2 & -0.207885 & -2.2773 & 0.012271 \tabularnewline
3 & 0.040676 & 0.4456 & 0.328349 \tabularnewline
4 & 0.048477 & 0.531 & 0.298187 \tabularnewline
5 & 0.091779 & 1.0054 & 0.158366 \tabularnewline
6 & 0.079397 & 0.8698 & 0.193086 \tabularnewline
7 & 0.090851 & 0.9952 & 0.160816 \tabularnewline
8 & 0.031369 & 0.3436 & 0.365862 \tabularnewline
9 & 0.047957 & 0.5253 & 0.300156 \tabularnewline
10 & 0.077319 & 0.847 & 0.199343 \tabularnewline
11 & 0.05078 & 0.5563 & 0.289531 \tabularnewline
12 & -0.114158 & -1.2505 & 0.106768 \tabularnewline
13 & -0.251562 & -2.7557 & 0.003385 \tabularnewline
14 & -0.099168 & -1.0863 & 0.139756 \tabularnewline
15 & 0.007517 & 0.0823 & 0.467256 \tabularnewline
16 & 0.006777 & 0.0742 & 0.470471 \tabularnewline
17 & 0.040226 & 0.4407 & 0.330129 \tabularnewline
18 & -0.030356 & -0.3325 & 0.370034 \tabularnewline
19 & 0.069832 & 0.765 & 0.222894 \tabularnewline
20 & 0.004931 & 0.054 & 0.478506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235624&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]0.948779[/C][C]10.3934[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.207885[/C][C]-2.2773[/C][C]0.012271[/C][/ROW]
[ROW][C]3[/C][C]0.040676[/C][C]0.4456[/C][C]0.328349[/C][/ROW]
[ROW][C]4[/C][C]0.048477[/C][C]0.531[/C][C]0.298187[/C][/ROW]
[ROW][C]5[/C][C]0.091779[/C][C]1.0054[/C][C]0.158366[/C][/ROW]
[ROW][C]6[/C][C]0.079397[/C][C]0.8698[/C][C]0.193086[/C][/ROW]
[ROW][C]7[/C][C]0.090851[/C][C]0.9952[/C][C]0.160816[/C][/ROW]
[ROW][C]8[/C][C]0.031369[/C][C]0.3436[/C][C]0.365862[/C][/ROW]
[ROW][C]9[/C][C]0.047957[/C][C]0.5253[/C][C]0.300156[/C][/ROW]
[ROW][C]10[/C][C]0.077319[/C][C]0.847[/C][C]0.199343[/C][/ROW]
[ROW][C]11[/C][C]0.05078[/C][C]0.5563[/C][C]0.289531[/C][/ROW]
[ROW][C]12[/C][C]-0.114158[/C][C]-1.2505[/C][C]0.106768[/C][/ROW]
[ROW][C]13[/C][C]-0.251562[/C][C]-2.7557[/C][C]0.003385[/C][/ROW]
[ROW][C]14[/C][C]-0.099168[/C][C]-1.0863[/C][C]0.139756[/C][/ROW]
[ROW][C]15[/C][C]0.007517[/C][C]0.0823[/C][C]0.467256[/C][/ROW]
[ROW][C]16[/C][C]0.006777[/C][C]0.0742[/C][C]0.470471[/C][/ROW]
[ROW][C]17[/C][C]0.040226[/C][C]0.4407[/C][C]0.330129[/C][/ROW]
[ROW][C]18[/C][C]-0.030356[/C][C]-0.3325[/C][C]0.370034[/C][/ROW]
[ROW][C]19[/C][C]0.069832[/C][C]0.765[/C][C]0.222894[/C][/ROW]
[ROW][C]20[/C][C]0.004931[/C][C]0.054[/C][C]0.478506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235624&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235624&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	0.948779	10.3934	0
2	-0.207885	-2.2773	0.012271
3	0.040676	0.4456	0.328349
4	0.048477	0.531	0.298187
5	0.091779	1.0054	0.158366
6	0.079397	0.8698	0.193086
7	0.090851	0.9952	0.160816
8	0.031369	0.3436	0.365862
9	0.047957	0.5253	0.300156
10	0.077319	0.847	0.199343
11	0.05078	0.5563	0.289531
12	-0.114158	-1.2505	0.106768
13	-0.251562	-2.7557	0.003385
14	-0.099168	-1.0863	0.139756
15	0.007517	0.0823	0.467256
16	0.006777	0.0742	0.470471
17	0.040226	0.4407	0.330129
18	-0.030356	-0.3325	0.370034
19	0.069832	0.765	0.222894
20	0.004931	0.054	0.478506

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)
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