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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 13:37:51 +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/t1293197807qo3xqdbcz1v2b8b.htm/, Retrieved Tue, 30 Apr 2024 03:55:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114944, Retrieved Tue, 30 Apr 2024 03:55:45 +0000

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Original text written by user:

Prijsverandering in België. d=1

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Cross Correlation Function] [Q7 - zonder trans...] [2008-12-01 20:04:13] [299afd6311e4c20059ea2f05c8dd029d]
F RM D    [Variance Reduction Matrix] [Q8] [2008-12-01 20:20:44] [299afd6311e4c20059ea2f05c8dd029d]
F    D      [Variance Reduction Matrix] [Q8 - 2] [2008-12-01 20:25:07] [299afd6311e4c20059ea2f05c8dd029d]
F RM D        [Standard Deviation-Mean Plot] [Deel 2: Step 1] [2008-12-08 20:09:35] [299afd6311e4c20059ea2f05c8dd029d]
-    D          [Standard Deviation-Mean Plot] [Totale Uitvoer - SMP] [2008-12-17 15:57:12] [299afd6311e4c20059ea2f05c8dd029d]
- RMPD              [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-12-24 13:37:51] [fba9c6aa004af59d8497d682e70ddad5] [Current]

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Dataseries X:

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Histogram

Boxplots

3.4
3.4
3.4
-3.5
-3.5
-3.5
-8.3
-8.3
-8.3
-16.7
-16.7
-16.7
-11.6
-11.6
-11.6
-8.4
-8.4
-8.4
-8.6
-8.6
-8.6
0.6
0.6
0.6
-1.5
-1.5
-1.5
9.3
9.3
9.3
2.0
2.0
2.0
-5.5
-5.5
-5.5
4.0
4.0
4.0
-0.5
-0.5
-0.5
10.9
10.9
10.9
19.4
19.4
19.4
13.9
13.9
13.9
10.6
10.6
10.6
4.8
4.8
4.8
4.7
4.7
4.7
-3.9
-3.9
-3.9
-0.2
-0.2
-0.2

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114944&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114944&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114944&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.000209	-0.0017	0.49933
2	-0.000212	-0.0017	0.49932
3	-0.134261	-1.0824	0.141527
4	-3.6e-05	-3e-04	0.499886
5	-3.9e-05	-3e-04	0.499876
6	0.098454	0.7938	0.215112
7	0.000722	0.0058	0.497687
8	0.000719	0.0058	0.497697
9	0.015422	0.1243	0.450718
10	0.001199	0.0097	0.496159
11	0.001196	0.0096	0.496169
12	-0.439915	-3.5467	0.000365
13	0.001229	0.0099	0.496061
14	0.001226	0.0099	0.496071
15	0.112226	0.9048	0.184457
16	0.001226	0.0099	0.496073
17	0.001222	0.0099	0.496083
18	-0.243504	-1.9632	0.026952

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.000209 & -0.0017 & 0.49933 \tabularnewline
2 & -0.000212 & -0.0017 & 0.49932 \tabularnewline
3 & -0.134261 & -1.0824 & 0.141527 \tabularnewline
4 & -3.6e-05 & -3e-04 & 0.499886 \tabularnewline
5 & -3.9e-05 & -3e-04 & 0.499876 \tabularnewline
6 & 0.098454 & 0.7938 & 0.215112 \tabularnewline
7 & 0.000722 & 0.0058 & 0.497687 \tabularnewline
8 & 0.000719 & 0.0058 & 0.497697 \tabularnewline
9 & 0.015422 & 0.1243 & 0.450718 \tabularnewline
10 & 0.001199 & 0.0097 & 0.496159 \tabularnewline
11 & 0.001196 & 0.0096 & 0.496169 \tabularnewline
12 & -0.439915 & -3.5467 & 0.000365 \tabularnewline
13 & 0.001229 & 0.0099 & 0.496061 \tabularnewline
14 & 0.001226 & 0.0099 & 0.496071 \tabularnewline
15 & 0.112226 & 0.9048 & 0.184457 \tabularnewline
16 & 0.001226 & 0.0099 & 0.496073 \tabularnewline
17 & 0.001222 & 0.0099 & 0.496083 \tabularnewline
18 & -0.243504 & -1.9632 & 0.026952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114944&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]-0.000209[/C][C]-0.0017[/C][C]0.49933[/C][/ROW]
[ROW][C]2[/C][C]-0.000212[/C][C]-0.0017[/C][C]0.49932[/C][/ROW]
[ROW][C]3[/C][C]-0.134261[/C][C]-1.0824[/C][C]0.141527[/C][/ROW]
[ROW][C]4[/C][C]-3.6e-05[/C][C]-3e-04[/C][C]0.499886[/C][/ROW]
[ROW][C]5[/C][C]-3.9e-05[/C][C]-3e-04[/C][C]0.499876[/C][/ROW]
[ROW][C]6[/C][C]0.098454[/C][C]0.7938[/C][C]0.215112[/C][/ROW]
[ROW][C]7[/C][C]0.000722[/C][C]0.0058[/C][C]0.497687[/C][/ROW]
[ROW][C]8[/C][C]0.000719[/C][C]0.0058[/C][C]0.497697[/C][/ROW]
[ROW][C]9[/C][C]0.015422[/C][C]0.1243[/C][C]0.450718[/C][/ROW]
[ROW][C]10[/C][C]0.001199[/C][C]0.0097[/C][C]0.496159[/C][/ROW]
[ROW][C]11[/C][C]0.001196[/C][C]0.0096[/C][C]0.496169[/C][/ROW]
[ROW][C]12[/C][C]-0.439915[/C][C]-3.5467[/C][C]0.000365[/C][/ROW]
[ROW][C]13[/C][C]0.001229[/C][C]0.0099[/C][C]0.496061[/C][/ROW]
[ROW][C]14[/C][C]0.001226[/C][C]0.0099[/C][C]0.496071[/C][/ROW]
[ROW][C]15[/C][C]0.112226[/C][C]0.9048[/C][C]0.184457[/C][/ROW]
[ROW][C]16[/C][C]0.001226[/C][C]0.0099[/C][C]0.496073[/C][/ROW]
[ROW][C]17[/C][C]0.001222[/C][C]0.0099[/C][C]0.496083[/C][/ROW]
[ROW][C]18[/C][C]-0.243504[/C][C]-1.9632[/C][C]0.026952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114944&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114944&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	-0.000209	-0.0017	0.49933
2	-0.000212	-0.0017	0.49932
3	-0.134261	-1.0824	0.141527
4	-3.6e-05	-3e-04	0.499886
5	-3.9e-05	-3e-04	0.499876
6	0.098454	0.7938	0.215112
7	0.000722	0.0058	0.497687
8	0.000719	0.0058	0.497697
9	0.015422	0.1243	0.450718
10	0.001199	0.0097	0.496159
11	0.001196	0.0096	0.496169
12	-0.439915	-3.5467	0.000365
13	0.001229	0.0099	0.496061
14	0.001226	0.0099	0.496071
15	0.112226	0.9048	0.184457
16	0.001226	0.0099	0.496073
17	0.001222	0.0099	0.496083
18	-0.243504	-1.9632	0.026952

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.000209	-0.0017	0.49933
2	-0.000212	-0.0017	0.499319
3	-0.134261	-1.0824	0.141527
4	-9.7e-05	-8e-04	0.499688
5	-0.000101	-8e-04	0.499675
6	0.081904	0.6603	0.255687
7	0.000767	0.0062	0.497542
8	0.000764	0.0062	0.497552
9	0.039528	0.3187	0.375495
10	0.001448	0.0117	0.495361
11	0.001445	0.0117	0.495369
12	-0.453042	-3.6525	0.00026
13	0.00176	0.0142	0.49436
14	0.001751	0.0141	0.49439
15	0.00443	0.0357	0.485811
16	0.001704	0.0137	0.494542
17	0.001693	0.0136	0.494576
18	-0.168764	-1.3606	0.089166

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.000209 & -0.0017 & 0.49933 \tabularnewline
2 & -0.000212 & -0.0017 & 0.499319 \tabularnewline
3 & -0.134261 & -1.0824 & 0.141527 \tabularnewline
4 & -9.7e-05 & -8e-04 & 0.499688 \tabularnewline
5 & -0.000101 & -8e-04 & 0.499675 \tabularnewline
6 & 0.081904 & 0.6603 & 0.255687 \tabularnewline
7 & 0.000767 & 0.0062 & 0.497542 \tabularnewline
8 & 0.000764 & 0.0062 & 0.497552 \tabularnewline
9 & 0.039528 & 0.3187 & 0.375495 \tabularnewline
10 & 0.001448 & 0.0117 & 0.495361 \tabularnewline
11 & 0.001445 & 0.0117 & 0.495369 \tabularnewline
12 & -0.453042 & -3.6525 & 0.00026 \tabularnewline
13 & 0.00176 & 0.0142 & 0.49436 \tabularnewline
14 & 0.001751 & 0.0141 & 0.49439 \tabularnewline
15 & 0.00443 & 0.0357 & 0.485811 \tabularnewline
16 & 0.001704 & 0.0137 & 0.494542 \tabularnewline
17 & 0.001693 & 0.0136 & 0.494576 \tabularnewline
18 & -0.168764 & -1.3606 & 0.089166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114944&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]-0.000209[/C][C]-0.0017[/C][C]0.49933[/C][/ROW]
[ROW][C]2[/C][C]-0.000212[/C][C]-0.0017[/C][C]0.499319[/C][/ROW]
[ROW][C]3[/C][C]-0.134261[/C][C]-1.0824[/C][C]0.141527[/C][/ROW]
[ROW][C]4[/C][C]-9.7e-05[/C][C]-8e-04[/C][C]0.499688[/C][/ROW]
[ROW][C]5[/C][C]-0.000101[/C][C]-8e-04[/C][C]0.499675[/C][/ROW]
[ROW][C]6[/C][C]0.081904[/C][C]0.6603[/C][C]0.255687[/C][/ROW]
[ROW][C]7[/C][C]0.000767[/C][C]0.0062[/C][C]0.497542[/C][/ROW]
[ROW][C]8[/C][C]0.000764[/C][C]0.0062[/C][C]0.497552[/C][/ROW]
[ROW][C]9[/C][C]0.039528[/C][C]0.3187[/C][C]0.375495[/C][/ROW]
[ROW][C]10[/C][C]0.001448[/C][C]0.0117[/C][C]0.495361[/C][/ROW]
[ROW][C]11[/C][C]0.001445[/C][C]0.0117[/C][C]0.495369[/C][/ROW]
[ROW][C]12[/C][C]-0.453042[/C][C]-3.6525[/C][C]0.00026[/C][/ROW]
[ROW][C]13[/C][C]0.00176[/C][C]0.0142[/C][C]0.49436[/C][/ROW]
[ROW][C]14[/C][C]0.001751[/C][C]0.0141[/C][C]0.49439[/C][/ROW]
[ROW][C]15[/C][C]0.00443[/C][C]0.0357[/C][C]0.485811[/C][/ROW]
[ROW][C]16[/C][C]0.001704[/C][C]0.0137[/C][C]0.494542[/C][/ROW]
[ROW][C]17[/C][C]0.001693[/C][C]0.0136[/C][C]0.494576[/C][/ROW]
[ROW][C]18[/C][C]-0.168764[/C][C]-1.3606[/C][C]0.089166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114944&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114944&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	-0.000209	-0.0017	0.49933
2	-0.000212	-0.0017	0.499319
3	-0.134261	-1.0824	0.141527
4	-9.7e-05	-8e-04	0.499688
5	-0.000101	-8e-04	0.499675
6	0.081904	0.6603	0.255687
7	0.000767	0.0062	0.497542
8	0.000764	0.0062	0.497552
9	0.039528	0.3187	0.375495
10	0.001448	0.0117	0.495361
11	0.001445	0.0117	0.495369
12	-0.453042	-3.6525	0.00026
13	0.00176	0.0142	0.49436
14	0.001751	0.0141	0.49439
15	0.00443	0.0357	0.485811
16	0.001704	0.0137	0.494542
17	0.001693	0.0136	0.494576
18	-0.168764	-1.3606	0.089166

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