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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

Mon, 20 Dec 2010 17:48:08 +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/20/t1292867261ovpyp1q1jlxfqkr.htm/, Retrieved Sat, 04 May 2024 03:07:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113034, Retrieved Sat, 04 May 2024 03:07:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

167

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

-     [] [correlation betwe...] [1970-01-01 00:00:00] [1df589bc3feb749f1946d8c1ee38b85f]
- RM D  [Pearson Correlation] [correlation betwe...] [2010-12-20 15:44:31] [1df589bc3feb749f1946d8c1ee38b85f]
- RMPD    [Variance Reduction Matrix] [Paper: VRM] [2010-12-20 16:52:21] [1df589bc3feb749f1946d8c1ee38b85f]
- RMP         [(Partial) Autocorrelation Function] [paper: autocorrel...] [2010-12-20 17:48:08] [36a5183bc8f6439b2481209b0fbe6bda] [Current]
-               [(Partial) Autocorrelation Function] [paper] [2010-12-28 19:23:11] [83d13bd1a1b3e64dad996f4022b3c29f] 

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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=113034&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=113034&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113034&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	-0.214747	-2.115	0.018496
2	-0.000414	-0.0041	0.498377
3	0.003383	0.0333	0.486746
4	-0.341979	-3.3681	0.000543
5	0.088268	0.8693	0.193405
6	-0.01202	-0.1184	0.453005
7	0.14365	1.4148	0.080167
8	-0.080061	-0.7885	0.21616
9	-0.023513	-0.2316	0.408679
10	-0.035786	-0.3525	0.362632
11	-0.03373	-0.3322	0.370227
12	0.135784	1.3373	0.092123
13	-0.157992	-1.556	0.061477
14	0.052846	0.5205	0.301959
15	0.011451	0.1128	0.455217
16	-0.156136	-1.5378	0.063682
17	0.15604	1.5368	0.063798
18	0.031846	0.3136	0.377232
19	-0.067922	-0.669	0.252558
20	0.082028	0.8079	0.210567

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.214747 & -2.115 & 0.018496 \tabularnewline
2 & -0.000414 & -0.0041 & 0.498377 \tabularnewline
3 & 0.003383 & 0.0333 & 0.486746 \tabularnewline
4 & -0.341979 & -3.3681 & 0.000543 \tabularnewline
5 & 0.088268 & 0.8693 & 0.193405 \tabularnewline
6 & -0.01202 & -0.1184 & 0.453005 \tabularnewline
7 & 0.14365 & 1.4148 & 0.080167 \tabularnewline
8 & -0.080061 & -0.7885 & 0.21616 \tabularnewline
9 & -0.023513 & -0.2316 & 0.408679 \tabularnewline
10 & -0.035786 & -0.3525 & 0.362632 \tabularnewline
11 & -0.03373 & -0.3322 & 0.370227 \tabularnewline
12 & 0.135784 & 1.3373 & 0.092123 \tabularnewline
13 & -0.157992 & -1.556 & 0.061477 \tabularnewline
14 & 0.052846 & 0.5205 & 0.301959 \tabularnewline
15 & 0.011451 & 0.1128 & 0.455217 \tabularnewline
16 & -0.156136 & -1.5378 & 0.063682 \tabularnewline
17 & 0.15604 & 1.5368 & 0.063798 \tabularnewline
18 & 0.031846 & 0.3136 & 0.377232 \tabularnewline
19 & -0.067922 & -0.669 & 0.252558 \tabularnewline
20 & 0.082028 & 0.8079 & 0.210567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113034&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]-0.214747[/C][C]-2.115[/C][C]0.018496[/C][/ROW]
[ROW][C]2[/C][C]-0.000414[/C][C]-0.0041[/C][C]0.498377[/C][/ROW]
[ROW][C]3[/C][C]0.003383[/C][C]0.0333[/C][C]0.486746[/C][/ROW]
[ROW][C]4[/C][C]-0.341979[/C][C]-3.3681[/C][C]0.000543[/C][/ROW]
[ROW][C]5[/C][C]0.088268[/C][C]0.8693[/C][C]0.193405[/C][/ROW]
[ROW][C]6[/C][C]-0.01202[/C][C]-0.1184[/C][C]0.453005[/C][/ROW]
[ROW][C]7[/C][C]0.14365[/C][C]1.4148[/C][C]0.080167[/C][/ROW]
[ROW][C]8[/C][C]-0.080061[/C][C]-0.7885[/C][C]0.21616[/C][/ROW]
[ROW][C]9[/C][C]-0.023513[/C][C]-0.2316[/C][C]0.408679[/C][/ROW]
[ROW][C]10[/C][C]-0.035786[/C][C]-0.3525[/C][C]0.362632[/C][/ROW]
[ROW][C]11[/C][C]-0.03373[/C][C]-0.3322[/C][C]0.370227[/C][/ROW]
[ROW][C]12[/C][C]0.135784[/C][C]1.3373[/C][C]0.092123[/C][/ROW]
[ROW][C]13[/C][C]-0.157992[/C][C]-1.556[/C][C]0.061477[/C][/ROW]
[ROW][C]14[/C][C]0.052846[/C][C]0.5205[/C][C]0.301959[/C][/ROW]
[ROW][C]15[/C][C]0.011451[/C][C]0.1128[/C][C]0.455217[/C][/ROW]
[ROW][C]16[/C][C]-0.156136[/C][C]-1.5378[/C][C]0.063682[/C][/ROW]
[ROW][C]17[/C][C]0.15604[/C][C]1.5368[/C][C]0.063798[/C][/ROW]
[ROW][C]18[/C][C]0.031846[/C][C]0.3136[/C][C]0.377232[/C][/ROW]
[ROW][C]19[/C][C]-0.067922[/C][C]-0.669[/C][C]0.252558[/C][/ROW]
[ROW][C]20[/C][C]0.082028[/C][C]0.8079[/C][C]0.210567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113034&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113034&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	-0.214747	-2.115	0.018496
2	-0.000414	-0.0041	0.498377
3	0.003383	0.0333	0.486746
4	-0.341979	-3.3681	0.000543
5	0.088268	0.8693	0.193405
6	-0.01202	-0.1184	0.453005
7	0.14365	1.4148	0.080167
8	-0.080061	-0.7885	0.21616
9	-0.023513	-0.2316	0.408679
10	-0.035786	-0.3525	0.362632
11	-0.03373	-0.3322	0.370227
12	0.135784	1.3373	0.092123
13	-0.157992	-1.556	0.061477
14	0.052846	0.5205	0.301959
15	0.011451	0.1128	0.455217
16	-0.156136	-1.5378	0.063682
17	0.15604	1.5368	0.063798
18	0.031846	0.3136	0.377232
19	-0.067922	-0.669	0.252558
20	0.082028	0.8079	0.210567

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.214747	-2.115	0.018496
2	-0.04878	-0.4804	0.316003
3	-0.007551	-0.0744	0.470433
4	-0.360312	-3.5487	0.000299
5	-0.080904	-0.7968	0.213752
6	-0.039445	-0.3885	0.349255
7	0.131205	1.2922	0.099676
8	-0.1707	-1.6812	0.047971
9	-0.076263	-0.7511	0.227203
10	-0.074143	-0.7302	0.233507
11	0.036471	0.3592	0.360114
12	0.051325	0.5055	0.307179
13	-0.187894	-1.8505	0.033639
14	-0.086335	-0.8503	0.198626
15	0.044803	0.4413	0.330004
16	-0.116798	-1.1503	0.126418
17	-0.030212	-0.2976	0.38334
18	0.038091	0.3752	0.354183
19	-0.076582	-0.7542	0.226265
20	0.022941	0.2259	0.410861

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.214747 & -2.115 & 0.018496 \tabularnewline
2 & -0.04878 & -0.4804 & 0.316003 \tabularnewline
3 & -0.007551 & -0.0744 & 0.470433 \tabularnewline
4 & -0.360312 & -3.5487 & 0.000299 \tabularnewline
5 & -0.080904 & -0.7968 & 0.213752 \tabularnewline
6 & -0.039445 & -0.3885 & 0.349255 \tabularnewline
7 & 0.131205 & 1.2922 & 0.099676 \tabularnewline
8 & -0.1707 & -1.6812 & 0.047971 \tabularnewline
9 & -0.076263 & -0.7511 & 0.227203 \tabularnewline
10 & -0.074143 & -0.7302 & 0.233507 \tabularnewline
11 & 0.036471 & 0.3592 & 0.360114 \tabularnewline
12 & 0.051325 & 0.5055 & 0.307179 \tabularnewline
13 & -0.187894 & -1.8505 & 0.033639 \tabularnewline
14 & -0.086335 & -0.8503 & 0.198626 \tabularnewline
15 & 0.044803 & 0.4413 & 0.330004 \tabularnewline
16 & -0.116798 & -1.1503 & 0.126418 \tabularnewline
17 & -0.030212 & -0.2976 & 0.38334 \tabularnewline
18 & 0.038091 & 0.3752 & 0.354183 \tabularnewline
19 & -0.076582 & -0.7542 & 0.226265 \tabularnewline
20 & 0.022941 & 0.2259 & 0.410861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113034&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]-0.214747[/C][C]-2.115[/C][C]0.018496[/C][/ROW]
[ROW][C]2[/C][C]-0.04878[/C][C]-0.4804[/C][C]0.316003[/C][/ROW]
[ROW][C]3[/C][C]-0.007551[/C][C]-0.0744[/C][C]0.470433[/C][/ROW]
[ROW][C]4[/C][C]-0.360312[/C][C]-3.5487[/C][C]0.000299[/C][/ROW]
[ROW][C]5[/C][C]-0.080904[/C][C]-0.7968[/C][C]0.213752[/C][/ROW]
[ROW][C]6[/C][C]-0.039445[/C][C]-0.3885[/C][C]0.349255[/C][/ROW]
[ROW][C]7[/C][C]0.131205[/C][C]1.2922[/C][C]0.099676[/C][/ROW]
[ROW][C]8[/C][C]-0.1707[/C][C]-1.6812[/C][C]0.047971[/C][/ROW]
[ROW][C]9[/C][C]-0.076263[/C][C]-0.7511[/C][C]0.227203[/C][/ROW]
[ROW][C]10[/C][C]-0.074143[/C][C]-0.7302[/C][C]0.233507[/C][/ROW]
[ROW][C]11[/C][C]0.036471[/C][C]0.3592[/C][C]0.360114[/C][/ROW]
[ROW][C]12[/C][C]0.051325[/C][C]0.5055[/C][C]0.307179[/C][/ROW]
[ROW][C]13[/C][C]-0.187894[/C][C]-1.8505[/C][C]0.033639[/C][/ROW]
[ROW][C]14[/C][C]-0.086335[/C][C]-0.8503[/C][C]0.198626[/C][/ROW]
[ROW][C]15[/C][C]0.044803[/C][C]0.4413[/C][C]0.330004[/C][/ROW]
[ROW][C]16[/C][C]-0.116798[/C][C]-1.1503[/C][C]0.126418[/C][/ROW]
[ROW][C]17[/C][C]-0.030212[/C][C]-0.2976[/C][C]0.38334[/C][/ROW]
[ROW][C]18[/C][C]0.038091[/C][C]0.3752[/C][C]0.354183[/C][/ROW]
[ROW][C]19[/C][C]-0.076582[/C][C]-0.7542[/C][C]0.226265[/C][/ROW]
[ROW][C]20[/C][C]0.022941[/C][C]0.2259[/C][C]0.410861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113034&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113034&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	-0.214747	-2.115	0.018496
2	-0.04878	-0.4804	0.316003
3	-0.007551	-0.0744	0.470433
4	-0.360312	-3.5487	0.000299
5	-0.080904	-0.7968	0.213752
6	-0.039445	-0.3885	0.349255
7	0.131205	1.2922	0.099676
8	-0.1707	-1.6812	0.047971
9	-0.076263	-0.7511	0.227203
10	-0.074143	-0.7302	0.233507
11	0.036471	0.3592	0.360114
12	0.051325	0.5055	0.307179
13	-0.187894	-1.8505	0.033639
14	-0.086335	-0.8503	0.198626
15	0.044803	0.4413	0.330004
16	-0.116798	-1.1503	0.126418
17	-0.030212	-0.2976	0.38334
18	0.038091	0.3752	0.354183
19	-0.076582	-0.7542	0.226265
20	0.022941	0.2259	0.410861

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 = 2 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 4 ; 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