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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

Fri, 24 Dec 2010 15:15:06 +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/24/t12932035651mdt3t0uvfftdmm.htm/, Retrieved Tue, 30 Apr 2024 00:15:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115089, Retrieved Tue, 30 Apr 2024 00:15:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

126

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

-       [(Partial) Autocorrelation Function] [paperACF_WERK] [2010-12-24 15:15:06] [13dfa60174f50d862e8699db2153bfc5] [Current]
-   P     [(Partial) Autocorrelation Function] [paperACF_werk] [2010-12-24 15:18:03] [7e261c986c934df955dd3ac53e9d45c6] 

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Histogram

Boxplots

6.7
6.7
6.5
6.3
6.3
6.3
6.5
6.6
6.5
6.3
6.3
6.5
7
7.1
7.3
7.3
7.4
7.4
7.3
7.4
7.5
7.7
7.7
7.7
7.7
7.7
7.8
8
8.1
8.1
8.2
8.2
8.2
8.1
8.1
8.2
8.3
8.3
8.4
8.5
8.5
8.4
8
7.9
8.1
8.5
8.8
8.8
8.6
8.3
8.3
8.3
8.4
8.4
8.5
8.6
8.6
8.6
8.6
8.6
8.5
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.4
8.2
8
8
8
8
7.9
7.9
7.8
7.8
8
7.8
7.4
7.2
7
7
7.2
7.2
7.2
7
6.9
6.8
6.8
6.8
6.9
7.2
7.2
7.2
7.1
7.2
7.3
7.5
7.6
7.7
7.7
7.7
7.8
8
8.1
8.1
8
8.1
8.2
8.3
8.4
8.4
8.4
8.5
8.5
8.6
8.6
8.5
8.5

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115089&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115089&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115089&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.964637	10.611	0
2	0.910221	10.0124	0
3	0.849591	9.3455	0
4	0.797725	8.775	0
5	0.757275	8.33	0
6	0.715222	7.8674	0
7	0.668698	7.3557	0
8	0.612361	6.736	0
9	0.545893	6.0048	0
10	0.47129	5.1842	0
11	0.397241	4.3697	1.3e-05
12	0.326557	3.5921	0.000238
13	0.266836	2.9352	0.001995
14	0.209036	2.2994	0.011598
15	0.155293	1.7082	0.045079
16	0.101748	1.1192	0.13263
17	0.052852	0.5814	0.281036
18	0.006468	0.0711	0.471699
19	-0.042568	-0.4682	0.320224
20	-0.093048	-1.0235	0.15405

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964637 & 10.611 & 0 \tabularnewline
2 & 0.910221 & 10.0124 & 0 \tabularnewline
3 & 0.849591 & 9.3455 & 0 \tabularnewline
4 & 0.797725 & 8.775 & 0 \tabularnewline
5 & 0.757275 & 8.33 & 0 \tabularnewline
6 & 0.715222 & 7.8674 & 0 \tabularnewline
7 & 0.668698 & 7.3557 & 0 \tabularnewline
8 & 0.612361 & 6.736 & 0 \tabularnewline
9 & 0.545893 & 6.0048 & 0 \tabularnewline
10 & 0.47129 & 5.1842 & 0 \tabularnewline
11 & 0.397241 & 4.3697 & 1.3e-05 \tabularnewline
12 & 0.326557 & 3.5921 & 0.000238 \tabularnewline
13 & 0.266836 & 2.9352 & 0.001995 \tabularnewline
14 & 0.209036 & 2.2994 & 0.011598 \tabularnewline
15 & 0.155293 & 1.7082 & 0.045079 \tabularnewline
16 & 0.101748 & 1.1192 & 0.13263 \tabularnewline
17 & 0.052852 & 0.5814 & 0.281036 \tabularnewline
18 & 0.006468 & 0.0711 & 0.471699 \tabularnewline
19 & -0.042568 & -0.4682 & 0.320224 \tabularnewline
20 & -0.093048 & -1.0235 & 0.15405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115089&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]0.964637[/C][C]10.611[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.910221[/C][C]10.0124[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.849591[/C][C]9.3455[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.797725[/C][C]8.775[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.757275[/C][C]8.33[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.715222[/C][C]7.8674[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.668698[/C][C]7.3557[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.612361[/C][C]6.736[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.545893[/C][C]6.0048[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.47129[/C][C]5.1842[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.397241[/C][C]4.3697[/C][C]1.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.326557[/C][C]3.5921[/C][C]0.000238[/C][/ROW]
[ROW][C]13[/C][C]0.266836[/C][C]2.9352[/C][C]0.001995[/C][/ROW]
[ROW][C]14[/C][C]0.209036[/C][C]2.2994[/C][C]0.011598[/C][/ROW]
[ROW][C]15[/C][C]0.155293[/C][C]1.7082[/C][C]0.045079[/C][/ROW]
[ROW][C]16[/C][C]0.101748[/C][C]1.1192[/C][C]0.13263[/C][/ROW]
[ROW][C]17[/C][C]0.052852[/C][C]0.5814[/C][C]0.281036[/C][/ROW]
[ROW][C]18[/C][C]0.006468[/C][C]0.0711[/C][C]0.471699[/C][/ROW]
[ROW][C]19[/C][C]-0.042568[/C][C]-0.4682[/C][C]0.320224[/C][/ROW]
[ROW][C]20[/C][C]-0.093048[/C][C]-1.0235[/C][C]0.15405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115089&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115089&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	0.964637	10.611	0
2	0.910221	10.0124	0
3	0.849591	9.3455	0
4	0.797725	8.775	0
5	0.757275	8.33	0
6	0.715222	7.8674	0
7	0.668698	7.3557	0
8	0.612361	6.736	0
9	0.545893	6.0048	0
10	0.47129	5.1842	0
11	0.397241	4.3697	1.3e-05
12	0.326557	3.5921	0.000238
13	0.266836	2.9352	0.001995
14	0.209036	2.2994	0.011598
15	0.155293	1.7082	0.045079
16	0.101748	1.1192	0.13263
17	0.052852	0.5814	0.281036
18	0.006468	0.0711	0.471699
19	-0.042568	-0.4682	0.320224
20	-0.093048	-1.0235	0.15405

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964637	10.611	0
2	-0.292259	-3.2149	0.000837
3	-0.049283	-0.5421	0.294367
4	0.134671	1.4814	0.070552
5	0.076192	0.8381	0.201809
6	-0.147187	-1.6191	0.05402
7	-0.064061	-0.7047	0.241183
8	-0.103577	-1.1393	0.128404
9	-0.130279	-1.4331	0.077209
10	-0.13315	-1.4647	0.072805
11	-0.006569	-0.0723	0.471258
12	-0.046447	-0.5109	0.305169
13	0.065662	0.7223	0.235758
14	-0.093895	-1.0328	0.151868
15	0.044459	0.4891	0.312845
16	-0.013572	-0.1493	0.440787
17	0.074031	0.8143	0.208526
18	-0.05068	-0.5575	0.289114
19	-0.097871	-1.0766	0.141903
20	-0.072389	-0.7963	0.213716

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964637 & 10.611 & 0 \tabularnewline
2 & -0.292259 & -3.2149 & 0.000837 \tabularnewline
3 & -0.049283 & -0.5421 & 0.294367 \tabularnewline
4 & 0.134671 & 1.4814 & 0.070552 \tabularnewline
5 & 0.076192 & 0.8381 & 0.201809 \tabularnewline
6 & -0.147187 & -1.6191 & 0.05402 \tabularnewline
7 & -0.064061 & -0.7047 & 0.241183 \tabularnewline
8 & -0.103577 & -1.1393 & 0.128404 \tabularnewline
9 & -0.130279 & -1.4331 & 0.077209 \tabularnewline
10 & -0.13315 & -1.4647 & 0.072805 \tabularnewline
11 & -0.006569 & -0.0723 & 0.471258 \tabularnewline
12 & -0.046447 & -0.5109 & 0.305169 \tabularnewline
13 & 0.065662 & 0.7223 & 0.235758 \tabularnewline
14 & -0.093895 & -1.0328 & 0.151868 \tabularnewline
15 & 0.044459 & 0.4891 & 0.312845 \tabularnewline
16 & -0.013572 & -0.1493 & 0.440787 \tabularnewline
17 & 0.074031 & 0.8143 & 0.208526 \tabularnewline
18 & -0.05068 & -0.5575 & 0.289114 \tabularnewline
19 & -0.097871 & -1.0766 & 0.141903 \tabularnewline
20 & -0.072389 & -0.7963 & 0.213716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115089&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]0.964637[/C][C]10.611[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.292259[/C][C]-3.2149[/C][C]0.000837[/C][/ROW]
[ROW][C]3[/C][C]-0.049283[/C][C]-0.5421[/C][C]0.294367[/C][/ROW]
[ROW][C]4[/C][C]0.134671[/C][C]1.4814[/C][C]0.070552[/C][/ROW]
[ROW][C]5[/C][C]0.076192[/C][C]0.8381[/C][C]0.201809[/C][/ROW]
[ROW][C]6[/C][C]-0.147187[/C][C]-1.6191[/C][C]0.05402[/C][/ROW]
[ROW][C]7[/C][C]-0.064061[/C][C]-0.7047[/C][C]0.241183[/C][/ROW]
[ROW][C]8[/C][C]-0.103577[/C][C]-1.1393[/C][C]0.128404[/C][/ROW]
[ROW][C]9[/C][C]-0.130279[/C][C]-1.4331[/C][C]0.077209[/C][/ROW]
[ROW][C]10[/C][C]-0.13315[/C][C]-1.4647[/C][C]0.072805[/C][/ROW]
[ROW][C]11[/C][C]-0.006569[/C][C]-0.0723[/C][C]0.471258[/C][/ROW]
[ROW][C]12[/C][C]-0.046447[/C][C]-0.5109[/C][C]0.305169[/C][/ROW]
[ROW][C]13[/C][C]0.065662[/C][C]0.7223[/C][C]0.235758[/C][/ROW]
[ROW][C]14[/C][C]-0.093895[/C][C]-1.0328[/C][C]0.151868[/C][/ROW]
[ROW][C]15[/C][C]0.044459[/C][C]0.4891[/C][C]0.312845[/C][/ROW]
[ROW][C]16[/C][C]-0.013572[/C][C]-0.1493[/C][C]0.440787[/C][/ROW]
[ROW][C]17[/C][C]0.074031[/C][C]0.8143[/C][C]0.208526[/C][/ROW]
[ROW][C]18[/C][C]-0.05068[/C][C]-0.5575[/C][C]0.289114[/C][/ROW]
[ROW][C]19[/C][C]-0.097871[/C][C]-1.0766[/C][C]0.141903[/C][/ROW]
[ROW][C]20[/C][C]-0.072389[/C][C]-0.7963[/C][C]0.213716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115089&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115089&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	0.964637	10.611	0
2	-0.292259	-3.2149	0.000837
3	-0.049283	-0.5421	0.294367
4	0.134671	1.4814	0.070552
5	0.076192	0.8381	0.201809
6	-0.147187	-1.6191	0.05402
7	-0.064061	-0.7047	0.241183
8	-0.103577	-1.1393	0.128404
9	-0.130279	-1.4331	0.077209
10	-0.13315	-1.4647	0.072805
11	-0.006569	-0.0723	0.471258
12	-0.046447	-0.5109	0.305169
13	0.065662	0.7223	0.235758
14	-0.093895	-1.0328	0.151868
15	0.044459	0.4891	0.312845
16	-0.013572	-0.1493	0.440787
17	0.074031	0.8143	0.208526
18	-0.05068	-0.5575	0.289114
19	-0.097871	-1.0766	0.141903
20	-0.072389	-0.7963	0.213716

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