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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 27 Dec 2009 08:37:59 -0700

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/2009/Dec/27/t12619283795ahci88nf7fjrfq.htm/, Retrieved Thu, 02 May 2024 21:47:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70915, Retrieved Thu, 02 May 2024 21:47:55 +0000

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Estimated Impact

144

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

-     [Central Tendency] [test 3] [2007-10-13 09:57:27] [74be16979710d4c4e7c6647856088456]
- RMPD  [Standard Deviation-Mean Plot] [paper standard de...] [2008-12-10 13:47:28] [11edab5c4db3615abbf782b1c6e7cacf]
- RMPD      [(Partial) Autocorrelation Function] [paper diff3ACF WLH] [2009-12-27 15:37:59] [1b03feaac1d41902024770a37504c07f] [Current]

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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	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=70915&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=70915&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70915&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	0.073365	0.434	0.333464
2	-0.114973	-0.6802	0.250429
3	-0.441705	-2.6132	0.006567
4	-0.333143	-1.9709	0.028342
5	-0.028047	-0.1659	0.434585
6	0.268225	1.5868	0.060771
7	0.331048	1.9585	0.029089
8	-0.074313	-0.4396	0.331449
9	-0.189078	-1.1186	0.135465
10	-0.191116	-1.1307	0.132944
11	0.216943	1.2834	0.103884
12	0.002228	0.0132	0.494778
13	0.185431	1.097	0.140061
14	-0.043541	-0.2576	0.399116
15	-0.253685	-1.5008	0.071185
16	0.02041	0.1207	0.452291
17	-0.000577	-0.0034	0.498647

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.073365 & 0.434 & 0.333464 \tabularnewline
2 & -0.114973 & -0.6802 & 0.250429 \tabularnewline
3 & -0.441705 & -2.6132 & 0.006567 \tabularnewline
4 & -0.333143 & -1.9709 & 0.028342 \tabularnewline
5 & -0.028047 & -0.1659 & 0.434585 \tabularnewline
6 & 0.268225 & 1.5868 & 0.060771 \tabularnewline
7 & 0.331048 & 1.9585 & 0.029089 \tabularnewline
8 & -0.074313 & -0.4396 & 0.331449 \tabularnewline
9 & -0.189078 & -1.1186 & 0.135465 \tabularnewline
10 & -0.191116 & -1.1307 & 0.132944 \tabularnewline
11 & 0.216943 & 1.2834 & 0.103884 \tabularnewline
12 & 0.002228 & 0.0132 & 0.494778 \tabularnewline
13 & 0.185431 & 1.097 & 0.140061 \tabularnewline
14 & -0.043541 & -0.2576 & 0.399116 \tabularnewline
15 & -0.253685 & -1.5008 & 0.071185 \tabularnewline
16 & 0.02041 & 0.1207 & 0.452291 \tabularnewline
17 & -0.000577 & -0.0034 & 0.498647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70915&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]0.073365[/C][C]0.434[/C][C]0.333464[/C][/ROW]
[ROW][C]2[/C][C]-0.114973[/C][C]-0.6802[/C][C]0.250429[/C][/ROW]
[ROW][C]3[/C][C]-0.441705[/C][C]-2.6132[/C][C]0.006567[/C][/ROW]
[ROW][C]4[/C][C]-0.333143[/C][C]-1.9709[/C][C]0.028342[/C][/ROW]
[ROW][C]5[/C][C]-0.028047[/C][C]-0.1659[/C][C]0.434585[/C][/ROW]
[ROW][C]6[/C][C]0.268225[/C][C]1.5868[/C][C]0.060771[/C][/ROW]
[ROW][C]7[/C][C]0.331048[/C][C]1.9585[/C][C]0.029089[/C][/ROW]
[ROW][C]8[/C][C]-0.074313[/C][C]-0.4396[/C][C]0.331449[/C][/ROW]
[ROW][C]9[/C][C]-0.189078[/C][C]-1.1186[/C][C]0.135465[/C][/ROW]
[ROW][C]10[/C][C]-0.191116[/C][C]-1.1307[/C][C]0.132944[/C][/ROW]
[ROW][C]11[/C][C]0.216943[/C][C]1.2834[/C][C]0.103884[/C][/ROW]
[ROW][C]12[/C][C]0.002228[/C][C]0.0132[/C][C]0.494778[/C][/ROW]
[ROW][C]13[/C][C]0.185431[/C][C]1.097[/C][C]0.140061[/C][/ROW]
[ROW][C]14[/C][C]-0.043541[/C][C]-0.2576[/C][C]0.399116[/C][/ROW]
[ROW][C]15[/C][C]-0.253685[/C][C]-1.5008[/C][C]0.071185[/C][/ROW]
[ROW][C]16[/C][C]0.02041[/C][C]0.1207[/C][C]0.452291[/C][/ROW]
[ROW][C]17[/C][C]-0.000577[/C][C]-0.0034[/C][C]0.498647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70915&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70915&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	0.073365	0.434	0.333464
2	-0.114973	-0.6802	0.250429
3	-0.441705	-2.6132	0.006567
4	-0.333143	-1.9709	0.028342
5	-0.028047	-0.1659	0.434585
6	0.268225	1.5868	0.060771
7	0.331048	1.9585	0.029089
8	-0.074313	-0.4396	0.331449
9	-0.189078	-1.1186	0.135465
10	-0.191116	-1.1307	0.132944
11	0.216943	1.2834	0.103884
12	0.002228	0.0132	0.494778
13	0.185431	1.097	0.140061
14	-0.043541	-0.2576	0.399116
15	-0.253685	-1.5008	0.071185
16	0.02041	0.1207	0.452291
17	-0.000577	-0.0034	0.498647

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.073365	0.434	0.333464
2	-0.121007	-0.7159	0.239405
3	-0.431988	-2.5557	0.007549
4	-0.373876	-2.2119	0.016798
5	-0.211002	-1.2483	0.110103
6	-0.051713	-0.3059	0.380732
7	0.036895	0.2183	0.414242
8	-0.290107	-1.7163	0.047474
9	-0.247729	-1.4656	0.075844
10	-0.129322	-0.7651	0.224677
11	0.298602	1.7666	0.043012
12	-0.196531	-1.1627	0.126411
13	-0.064259	-0.3802	0.353062
14	0.076277	0.4513	0.327292
15	-0.063756	-0.3772	0.354156
16	0.236597	1.3997	0.085198
17	-0.062382	-0.3691	0.357154

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.073365 & 0.434 & 0.333464 \tabularnewline
2 & -0.121007 & -0.7159 & 0.239405 \tabularnewline
3 & -0.431988 & -2.5557 & 0.007549 \tabularnewline
4 & -0.373876 & -2.2119 & 0.016798 \tabularnewline
5 & -0.211002 & -1.2483 & 0.110103 \tabularnewline
6 & -0.051713 & -0.3059 & 0.380732 \tabularnewline
7 & 0.036895 & 0.2183 & 0.414242 \tabularnewline
8 & -0.290107 & -1.7163 & 0.047474 \tabularnewline
9 & -0.247729 & -1.4656 & 0.075844 \tabularnewline
10 & -0.129322 & -0.7651 & 0.224677 \tabularnewline
11 & 0.298602 & 1.7666 & 0.043012 \tabularnewline
12 & -0.196531 & -1.1627 & 0.126411 \tabularnewline
13 & -0.064259 & -0.3802 & 0.353062 \tabularnewline
14 & 0.076277 & 0.4513 & 0.327292 \tabularnewline
15 & -0.063756 & -0.3772 & 0.354156 \tabularnewline
16 & 0.236597 & 1.3997 & 0.085198 \tabularnewline
17 & -0.062382 & -0.3691 & 0.357154 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70915&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]0.073365[/C][C]0.434[/C][C]0.333464[/C][/ROW]
[ROW][C]2[/C][C]-0.121007[/C][C]-0.7159[/C][C]0.239405[/C][/ROW]
[ROW][C]3[/C][C]-0.431988[/C][C]-2.5557[/C][C]0.007549[/C][/ROW]
[ROW][C]4[/C][C]-0.373876[/C][C]-2.2119[/C][C]0.016798[/C][/ROW]
[ROW][C]5[/C][C]-0.211002[/C][C]-1.2483[/C][C]0.110103[/C][/ROW]
[ROW][C]6[/C][C]-0.051713[/C][C]-0.3059[/C][C]0.380732[/C][/ROW]
[ROW][C]7[/C][C]0.036895[/C][C]0.2183[/C][C]0.414242[/C][/ROW]
[ROW][C]8[/C][C]-0.290107[/C][C]-1.7163[/C][C]0.047474[/C][/ROW]
[ROW][C]9[/C][C]-0.247729[/C][C]-1.4656[/C][C]0.075844[/C][/ROW]
[ROW][C]10[/C][C]-0.129322[/C][C]-0.7651[/C][C]0.224677[/C][/ROW]
[ROW][C]11[/C][C]0.298602[/C][C]1.7666[/C][C]0.043012[/C][/ROW]
[ROW][C]12[/C][C]-0.196531[/C][C]-1.1627[/C][C]0.126411[/C][/ROW]
[ROW][C]13[/C][C]-0.064259[/C][C]-0.3802[/C][C]0.353062[/C][/ROW]
[ROW][C]14[/C][C]0.076277[/C][C]0.4513[/C][C]0.327292[/C][/ROW]
[ROW][C]15[/C][C]-0.063756[/C][C]-0.3772[/C][C]0.354156[/C][/ROW]
[ROW][C]16[/C][C]0.236597[/C][C]1.3997[/C][C]0.085198[/C][/ROW]
[ROW][C]17[/C][C]-0.062382[/C][C]-0.3691[/C][C]0.357154[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70915&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70915&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	0.073365	0.434	0.333464
2	-0.121007	-0.7159	0.239405
3	-0.431988	-2.5557	0.007549
4	-0.373876	-2.2119	0.016798
5	-0.211002	-1.2483	0.110103
6	-0.051713	-0.3059	0.380732
7	0.036895	0.2183	0.414242
8	-0.290107	-1.7163	0.047474
9	-0.247729	-1.4656	0.075844
10	-0.129322	-0.7651	0.224677
11	0.298602	1.7666	0.043012
12	-0.196531	-1.1627	0.126411
13	-0.064259	-0.3802	0.353062
14	0.076277	0.4513	0.327292
15	-0.063756	-0.3772	0.354156
16	0.236597	1.3997	0.085198
17	-0.062382	-0.3691	0.357154

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code