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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

Tue, 21 Dec 2010 17:16:30 +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/2010/Dec/21/t12929517219vbhwqog1u2sdmm.htm/, Retrieved Sat, 11 May 2024 04:42:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113765, Retrieved Sat, 11 May 2024 04:42:40 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

144

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [Unemployment] [2010-11-30 13:37:23] [b98453cac15ba1066b407e146608df68]
- RMPD    [(Partial) Autocorrelation Function] [Goudprijs-ACF] [2010-12-20 12:17:14] [d672a41e0af7ff107c03f1d65e47fd32]
-   PD        [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-12-21 17:16:30] [c6b3e187a4a1689d42fffda4bc860ab5] [Current]
-   P           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-12-21 17:26:04] [c2a9e95daa10045f9fd6252038bcb219] 
-   P           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-12-21 18:10:50] [c2a9e95daa10045f9fd6252038bcb219] 
-   P             [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-12-21 18:16:23] [c2a9e95daa10045f9fd6252038bcb219] 

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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	'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=113765&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=113765&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113765&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.117449	1.3391	0.091433
2	-0.161636	-1.8429	0.033808
3	0.080328	0.9159	0.180714
4	0.074291	0.847	0.199264
5	-0.079816	-0.91	0.182242
6	0.006419	0.0732	0.470883
7	0.084176	0.9598	0.16948
8	-0.043173	-0.4922	0.311687
9	0.041252	0.4703	0.319448
10	-0.062054	-0.7075	0.240252
11	0.065097	0.7422	0.229647
12	0.107108	1.2212	0.112107
13	0.032456	0.3701	0.355973
14	-0.051004	-0.5815	0.280942
15	0.151989	1.7329	0.042739
16	0.139775	1.5937	0.056718
17	-0.119604	-1.3637	0.087509
18	-0.084392	-0.9622	0.168863
19	-0.040726	-0.4644	0.321586
20	0.058761	0.67	0.252028
21	-0.015776	-0.1799	0.428764

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.117449 & 1.3391 & 0.091433 \tabularnewline
2 & -0.161636 & -1.8429 & 0.033808 \tabularnewline
3 & 0.080328 & 0.9159 & 0.180714 \tabularnewline
4 & 0.074291 & 0.847 & 0.199264 \tabularnewline
5 & -0.079816 & -0.91 & 0.182242 \tabularnewline
6 & 0.006419 & 0.0732 & 0.470883 \tabularnewline
7 & 0.084176 & 0.9598 & 0.16948 \tabularnewline
8 & -0.043173 & -0.4922 & 0.311687 \tabularnewline
9 & 0.041252 & 0.4703 & 0.319448 \tabularnewline
10 & -0.062054 & -0.7075 & 0.240252 \tabularnewline
11 & 0.065097 & 0.7422 & 0.229647 \tabularnewline
12 & 0.107108 & 1.2212 & 0.112107 \tabularnewline
13 & 0.032456 & 0.3701 & 0.355973 \tabularnewline
14 & -0.051004 & -0.5815 & 0.280942 \tabularnewline
15 & 0.151989 & 1.7329 & 0.042739 \tabularnewline
16 & 0.139775 & 1.5937 & 0.056718 \tabularnewline
17 & -0.119604 & -1.3637 & 0.087509 \tabularnewline
18 & -0.084392 & -0.9622 & 0.168863 \tabularnewline
19 & -0.040726 & -0.4644 & 0.321586 \tabularnewline
20 & 0.058761 & 0.67 & 0.252028 \tabularnewline
21 & -0.015776 & -0.1799 & 0.428764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113765&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]0.117449[/C][C]1.3391[/C][C]0.091433[/C][/ROW]
[ROW][C]2[/C][C]-0.161636[/C][C]-1.8429[/C][C]0.033808[/C][/ROW]
[ROW][C]3[/C][C]0.080328[/C][C]0.9159[/C][C]0.180714[/C][/ROW]
[ROW][C]4[/C][C]0.074291[/C][C]0.847[/C][C]0.199264[/C][/ROW]
[ROW][C]5[/C][C]-0.079816[/C][C]-0.91[/C][C]0.182242[/C][/ROW]
[ROW][C]6[/C][C]0.006419[/C][C]0.0732[/C][C]0.470883[/C][/ROW]
[ROW][C]7[/C][C]0.084176[/C][C]0.9598[/C][C]0.16948[/C][/ROW]
[ROW][C]8[/C][C]-0.043173[/C][C]-0.4922[/C][C]0.311687[/C][/ROW]
[ROW][C]9[/C][C]0.041252[/C][C]0.4703[/C][C]0.319448[/C][/ROW]
[ROW][C]10[/C][C]-0.062054[/C][C]-0.7075[/C][C]0.240252[/C][/ROW]
[ROW][C]11[/C][C]0.065097[/C][C]0.7422[/C][C]0.229647[/C][/ROW]
[ROW][C]12[/C][C]0.107108[/C][C]1.2212[/C][C]0.112107[/C][/ROW]
[ROW][C]13[/C][C]0.032456[/C][C]0.3701[/C][C]0.355973[/C][/ROW]
[ROW][C]14[/C][C]-0.051004[/C][C]-0.5815[/C][C]0.280942[/C][/ROW]
[ROW][C]15[/C][C]0.151989[/C][C]1.7329[/C][C]0.042739[/C][/ROW]
[ROW][C]16[/C][C]0.139775[/C][C]1.5937[/C][C]0.056718[/C][/ROW]
[ROW][C]17[/C][C]-0.119604[/C][C]-1.3637[/C][C]0.087509[/C][/ROW]
[ROW][C]18[/C][C]-0.084392[/C][C]-0.9622[/C][C]0.168863[/C][/ROW]
[ROW][C]19[/C][C]-0.040726[/C][C]-0.4644[/C][C]0.321586[/C][/ROW]
[ROW][C]20[/C][C]0.058761[/C][C]0.67[/C][C]0.252028[/C][/ROW]
[ROW][C]21[/C][C]-0.015776[/C][C]-0.1799[/C][C]0.428764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113765&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113765&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	0.117449	1.3391	0.091433
2	-0.161636	-1.8429	0.033808
3	0.080328	0.9159	0.180714
4	0.074291	0.847	0.199264
5	-0.079816	-0.91	0.182242
6	0.006419	0.0732	0.470883
7	0.084176	0.9598	0.16948
8	-0.043173	-0.4922	0.311687
9	0.041252	0.4703	0.319448
10	-0.062054	-0.7075	0.240252
11	0.065097	0.7422	0.229647
12	0.107108	1.2212	0.112107
13	0.032456	0.3701	0.355973
14	-0.051004	-0.5815	0.280942
15	0.151989	1.7329	0.042739
16	0.139775	1.5937	0.056718
17	-0.119604	-1.3637	0.087509
18	-0.084392	-0.9622	0.168863
19	-0.040726	-0.4644	0.321586
20	0.058761	0.67	0.252028
21	-0.015776	-0.1799	0.428764

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.117449	1.3391	0.091433
2	-0.177884	-2.0282	0.022292
3	0.129404	1.4754	0.071257
4	0.015425	0.1759	0.430334
5	-0.061216	-0.698	0.243222
6	0.037391	0.4263	0.335287
7	0.045212	0.5155	0.303542
8	-0.047807	-0.5451	0.293316
9	0.087733	1.0003	0.15951
10	-0.127062	-1.4487	0.074911
11	0.133475	1.5218	0.065238
12	0.050965	0.5811	0.281092
13	0.037714	0.43	0.333952
14	-0.03497	-0.3987	0.345375
15	0.165328	1.885	0.030829
16	0.06122	0.698	0.243206
17	-0.069511	-0.7925	0.214744
18	-0.077867	-0.8878	0.188139
19	-0.084788	-0.9667	0.167738
20	0.078027	0.8896	0.18765
21	-0.013189	-0.1504	0.440349

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.117449 & 1.3391 & 0.091433 \tabularnewline
2 & -0.177884 & -2.0282 & 0.022292 \tabularnewline
3 & 0.129404 & 1.4754 & 0.071257 \tabularnewline
4 & 0.015425 & 0.1759 & 0.430334 \tabularnewline
5 & -0.061216 & -0.698 & 0.243222 \tabularnewline
6 & 0.037391 & 0.4263 & 0.335287 \tabularnewline
7 & 0.045212 & 0.5155 & 0.303542 \tabularnewline
8 & -0.047807 & -0.5451 & 0.293316 \tabularnewline
9 & 0.087733 & 1.0003 & 0.15951 \tabularnewline
10 & -0.127062 & -1.4487 & 0.074911 \tabularnewline
11 & 0.133475 & 1.5218 & 0.065238 \tabularnewline
12 & 0.050965 & 0.5811 & 0.281092 \tabularnewline
13 & 0.037714 & 0.43 & 0.333952 \tabularnewline
14 & -0.03497 & -0.3987 & 0.345375 \tabularnewline
15 & 0.165328 & 1.885 & 0.030829 \tabularnewline
16 & 0.06122 & 0.698 & 0.243206 \tabularnewline
17 & -0.069511 & -0.7925 & 0.214744 \tabularnewline
18 & -0.077867 & -0.8878 & 0.188139 \tabularnewline
19 & -0.084788 & -0.9667 & 0.167738 \tabularnewline
20 & 0.078027 & 0.8896 & 0.18765 \tabularnewline
21 & -0.013189 & -0.1504 & 0.440349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113765&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]0.117449[/C][C]1.3391[/C][C]0.091433[/C][/ROW]
[ROW][C]2[/C][C]-0.177884[/C][C]-2.0282[/C][C]0.022292[/C][/ROW]
[ROW][C]3[/C][C]0.129404[/C][C]1.4754[/C][C]0.071257[/C][/ROW]
[ROW][C]4[/C][C]0.015425[/C][C]0.1759[/C][C]0.430334[/C][/ROW]
[ROW][C]5[/C][C]-0.061216[/C][C]-0.698[/C][C]0.243222[/C][/ROW]
[ROW][C]6[/C][C]0.037391[/C][C]0.4263[/C][C]0.335287[/C][/ROW]
[ROW][C]7[/C][C]0.045212[/C][C]0.5155[/C][C]0.303542[/C][/ROW]
[ROW][C]8[/C][C]-0.047807[/C][C]-0.5451[/C][C]0.293316[/C][/ROW]
[ROW][C]9[/C][C]0.087733[/C][C]1.0003[/C][C]0.15951[/C][/ROW]
[ROW][C]10[/C][C]-0.127062[/C][C]-1.4487[/C][C]0.074911[/C][/ROW]
[ROW][C]11[/C][C]0.133475[/C][C]1.5218[/C][C]0.065238[/C][/ROW]
[ROW][C]12[/C][C]0.050965[/C][C]0.5811[/C][C]0.281092[/C][/ROW]
[ROW][C]13[/C][C]0.037714[/C][C]0.43[/C][C]0.333952[/C][/ROW]
[ROW][C]14[/C][C]-0.03497[/C][C]-0.3987[/C][C]0.345375[/C][/ROW]
[ROW][C]15[/C][C]0.165328[/C][C]1.885[/C][C]0.030829[/C][/ROW]
[ROW][C]16[/C][C]0.06122[/C][C]0.698[/C][C]0.243206[/C][/ROW]
[ROW][C]17[/C][C]-0.069511[/C][C]-0.7925[/C][C]0.214744[/C][/ROW]
[ROW][C]18[/C][C]-0.077867[/C][C]-0.8878[/C][C]0.188139[/C][/ROW]
[ROW][C]19[/C][C]-0.084788[/C][C]-0.9667[/C][C]0.167738[/C][/ROW]
[ROW][C]20[/C][C]0.078027[/C][C]0.8896[/C][C]0.18765[/C][/ROW]
[ROW][C]21[/C][C]-0.013189[/C][C]-0.1504[/C][C]0.440349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113765&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113765&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	0.117449	1.3391	0.091433
2	-0.177884	-2.0282	0.022292
3	0.129404	1.4754	0.071257
4	0.015425	0.1759	0.430334
5	-0.061216	-0.698	0.243222
6	0.037391	0.4263	0.335287
7	0.045212	0.5155	0.303542
8	-0.047807	-0.5451	0.293316
9	0.087733	1.0003	0.15951
10	-0.127062	-1.4487	0.074911
11	0.133475	1.5218	0.065238
12	0.050965	0.5811	0.281092
13	0.037714	0.43	0.333952
14	-0.03497	-0.3987	0.345375
15	0.165328	1.885	0.030829
16	0.06122	0.698	0.243206
17	-0.069511	-0.7925	0.214744
18	-0.077867	-0.8878	0.188139
19	-0.084788	-0.9667	0.167738
20	0.078027	0.8896	0.18765
21	-0.013189	-0.1504	0.440349

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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