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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 07 Dec 2008 09:31:47 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/07/t12286675443nkt3zeu3a27o1c.htm/, Retrieved Sun, 19 May 2024 09:19:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30149, Retrieved Sun, 19 May 2024 09:19:04 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

169

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

-     [(Partial) Autocorrelation Function] [Paper: autocorrel...] [2008-12-07 16:29:33] [57850c80fd59ccfb28f882be994e814e]
-   P     [(Partial) Autocorrelation Function] [Paper: autocorrel...] [2008-12-07 16:31:47] [0831954c833179c36e9320daee0825b5] [Current]
-   P       [(Partial) Autocorrelation Function] [Paper: autocorrel...] [2008-12-07 16:35:18] [57850c80fd59ccfb28f882be994e814e] 

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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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30149&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30149&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30149&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.618216	5.1724	1e-06
2	0.474218	3.9676	8.7e-05
3	0.544136	4.5526	1.1e-05
4	0.599519	5.0159	2e-06
5	0.524804	4.3908	2e-05
6	0.557471	4.6641	7e-06
7	0.428535	3.5854	0.000309
8	0.493686	4.1305	4.9e-05
9	0.409971	3.4301	0.000508
10	0.280574	2.3475	0.010868
11	0.368158	3.0802	0.001478
12	0.573238	4.7961	4e-06
13	0.273734	2.2902	0.012513
14	0.203294	1.7009	0.046702
15	0.211741	1.7716	0.040411
16	0.252512	2.1127	0.019099
17	0.223181	1.8673	0.033026
18	0.20911	1.7495	0.04229

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.618216 & 5.1724 & 1e-06 \tabularnewline
2 & 0.474218 & 3.9676 & 8.7e-05 \tabularnewline
3 & 0.544136 & 4.5526 & 1.1e-05 \tabularnewline
4 & 0.599519 & 5.0159 & 2e-06 \tabularnewline
5 & 0.524804 & 4.3908 & 2e-05 \tabularnewline
6 & 0.557471 & 4.6641 & 7e-06 \tabularnewline
7 & 0.428535 & 3.5854 & 0.000309 \tabularnewline
8 & 0.493686 & 4.1305 & 4.9e-05 \tabularnewline
9 & 0.409971 & 3.4301 & 0.000508 \tabularnewline
10 & 0.280574 & 2.3475 & 0.010868 \tabularnewline
11 & 0.368158 & 3.0802 & 0.001478 \tabularnewline
12 & 0.573238 & 4.7961 & 4e-06 \tabularnewline
13 & 0.273734 & 2.2902 & 0.012513 \tabularnewline
14 & 0.203294 & 1.7009 & 0.046702 \tabularnewline
15 & 0.211741 & 1.7716 & 0.040411 \tabularnewline
16 & 0.252512 & 2.1127 & 0.019099 \tabularnewline
17 & 0.223181 & 1.8673 & 0.033026 \tabularnewline
18 & 0.20911 & 1.7495 & 0.04229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30149&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]0.618216[/C][C]5.1724[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.474218[/C][C]3.9676[/C][C]8.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.544136[/C][C]4.5526[/C][C]1.1e-05[/C][/ROW]
[ROW][C]4[/C][C]0.599519[/C][C]5.0159[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.524804[/C][C]4.3908[/C][C]2e-05[/C][/ROW]
[ROW][C]6[/C][C]0.557471[/C][C]4.6641[/C][C]7e-06[/C][/ROW]
[ROW][C]7[/C][C]0.428535[/C][C]3.5854[/C][C]0.000309[/C][/ROW]
[ROW][C]8[/C][C]0.493686[/C][C]4.1305[/C][C]4.9e-05[/C][/ROW]
[ROW][C]9[/C][C]0.409971[/C][C]3.4301[/C][C]0.000508[/C][/ROW]
[ROW][C]10[/C][C]0.280574[/C][C]2.3475[/C][C]0.010868[/C][/ROW]
[ROW][C]11[/C][C]0.368158[/C][C]3.0802[/C][C]0.001478[/C][/ROW]
[ROW][C]12[/C][C]0.573238[/C][C]4.7961[/C][C]4e-06[/C][/ROW]
[ROW][C]13[/C][C]0.273734[/C][C]2.2902[/C][C]0.012513[/C][/ROW]
[ROW][C]14[/C][C]0.203294[/C][C]1.7009[/C][C]0.046702[/C][/ROW]
[ROW][C]15[/C][C]0.211741[/C][C]1.7716[/C][C]0.040411[/C][/ROW]
[ROW][C]16[/C][C]0.252512[/C][C]2.1127[/C][C]0.019099[/C][/ROW]
[ROW][C]17[/C][C]0.223181[/C][C]1.8673[/C][C]0.033026[/C][/ROW]
[ROW][C]18[/C][C]0.20911[/C][C]1.7495[/C][C]0.04229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30149&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30149&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	0.618216	5.1724	1e-06
2	0.474218	3.9676	8.7e-05
3	0.544136	4.5526	1.1e-05
4	0.599519	5.0159	2e-06
5	0.524804	4.3908	2e-05
6	0.557471	4.6641	7e-06
7	0.428535	3.5854	0.000309
8	0.493686	4.1305	4.9e-05
9	0.409971	3.4301	0.000508
10	0.280574	2.3475	0.010868
11	0.368158	3.0802	0.001478
12	0.573238	4.7961	4e-06
13	0.273734	2.2902	0.012513
14	0.203294	1.7009	0.046702
15	0.211741	1.7716	0.040411
16	0.252512	2.1127	0.019099
17	0.223181	1.8673	0.033026
18	0.20911	1.7495	0.04229

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.618216	5.1724	1e-06
2	0.148956	1.2463	0.108412
3	0.33529	2.8052	0.003252
4	0.272562	2.2804	0.012816
5	0.078616	0.6577	0.256429
6	0.227547	1.9038	0.030524
7	-0.186271	-1.5585	0.061817
8	0.200368	1.6764	0.04906
9	-0.232394	-1.9443	0.027937
10	-0.22411	-1.875	0.032479
11	0.193961	1.6228	0.054565
12	0.318734	2.6667	0.004753
13	-0.368531	-3.0833	0.001464
14	0.010383	0.0869	0.465513
15	-0.175301	-1.4667	0.073472
16	0.004364	0.0365	0.485491
17	0.002327	0.0195	0.492262
18	-0.033937	-0.2839	0.388648

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.618216 & 5.1724 & 1e-06 \tabularnewline
2 & 0.148956 & 1.2463 & 0.108412 \tabularnewline
3 & 0.33529 & 2.8052 & 0.003252 \tabularnewline
4 & 0.272562 & 2.2804 & 0.012816 \tabularnewline
5 & 0.078616 & 0.6577 & 0.256429 \tabularnewline
6 & 0.227547 & 1.9038 & 0.030524 \tabularnewline
7 & -0.186271 & -1.5585 & 0.061817 \tabularnewline
8 & 0.200368 & 1.6764 & 0.04906 \tabularnewline
9 & -0.232394 & -1.9443 & 0.027937 \tabularnewline
10 & -0.22411 & -1.875 & 0.032479 \tabularnewline
11 & 0.193961 & 1.6228 & 0.054565 \tabularnewline
12 & 0.318734 & 2.6667 & 0.004753 \tabularnewline
13 & -0.368531 & -3.0833 & 0.001464 \tabularnewline
14 & 0.010383 & 0.0869 & 0.465513 \tabularnewline
15 & -0.175301 & -1.4667 & 0.073472 \tabularnewline
16 & 0.004364 & 0.0365 & 0.485491 \tabularnewline
17 & 0.002327 & 0.0195 & 0.492262 \tabularnewline
18 & -0.033937 & -0.2839 & 0.388648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30149&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]0.618216[/C][C]5.1724[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.148956[/C][C]1.2463[/C][C]0.108412[/C][/ROW]
[ROW][C]3[/C][C]0.33529[/C][C]2.8052[/C][C]0.003252[/C][/ROW]
[ROW][C]4[/C][C]0.272562[/C][C]2.2804[/C][C]0.012816[/C][/ROW]
[ROW][C]5[/C][C]0.078616[/C][C]0.6577[/C][C]0.256429[/C][/ROW]
[ROW][C]6[/C][C]0.227547[/C][C]1.9038[/C][C]0.030524[/C][/ROW]
[ROW][C]7[/C][C]-0.186271[/C][C]-1.5585[/C][C]0.061817[/C][/ROW]
[ROW][C]8[/C][C]0.200368[/C][C]1.6764[/C][C]0.04906[/C][/ROW]
[ROW][C]9[/C][C]-0.232394[/C][C]-1.9443[/C][C]0.027937[/C][/ROW]
[ROW][C]10[/C][C]-0.22411[/C][C]-1.875[/C][C]0.032479[/C][/ROW]
[ROW][C]11[/C][C]0.193961[/C][C]1.6228[/C][C]0.054565[/C][/ROW]
[ROW][C]12[/C][C]0.318734[/C][C]2.6667[/C][C]0.004753[/C][/ROW]
[ROW][C]13[/C][C]-0.368531[/C][C]-3.0833[/C][C]0.001464[/C][/ROW]
[ROW][C]14[/C][C]0.010383[/C][C]0.0869[/C][C]0.465513[/C][/ROW]
[ROW][C]15[/C][C]-0.175301[/C][C]-1.4667[/C][C]0.073472[/C][/ROW]
[ROW][C]16[/C][C]0.004364[/C][C]0.0365[/C][C]0.485491[/C][/ROW]
[ROW][C]17[/C][C]0.002327[/C][C]0.0195[/C][C]0.492262[/C][/ROW]
[ROW][C]18[/C][C]-0.033937[/C][C]-0.2839[/C][C]0.388648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30149&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30149&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	0.618216	5.1724	1e-06
2	0.148956	1.2463	0.108412
3	0.33529	2.8052	0.003252
4	0.272562	2.2804	0.012816
5	0.078616	0.6577	0.256429
6	0.227547	1.9038	0.030524
7	-0.186271	-1.5585	0.061817
8	0.200368	1.6764	0.04906
9	-0.232394	-1.9443	0.027937
10	-0.22411	-1.875	0.032479
11	0.193961	1.6228	0.054565
12	0.318734	2.6667	0.004753
13	-0.368531	-3.0833	0.001464
14	0.010383	0.0869	0.465513
15	-0.175301	-1.4667	0.073472
16	0.004364	0.0365	0.485491
17	0.002327	0.0195	0.492262
18	-0.033937	-0.2839	0.388648

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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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Figures (Output of Computation)

Input Parameters & R Code