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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 11 Dec 2007 11:57:37 -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/2007/Dec/11/t1197398575mq8c49s02ehw81m.htm/, Retrieved Sun, 28 Apr 2024 21:58:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3145, Retrieved Sun, 28 Apr 2024 21:58:37 +0000

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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)

-       [(Partial) Autocorrelation Function] [Inducing stationa...] [2007-12-11 18:57:37] [578856645eee7b4b8f74dcf589866e9b] [Current]

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Summary of compuational 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 compuational 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=3145&T=0

[TABLE]
[ROW][C]Summary of compuational 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=3145&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3145&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 compuational 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
0	1	8.4853	0
1	0.964763	8.1863	0
2	0.922188	7.825	0
3	0.883541	7.4971	0
4	0.844726	7.1677	0
5	0.79975	6.7861	0
6	0.752359	6.384	0
7	0.709408	6.0195	0
8	0.668878	5.6756	0
9	0.632071	5.3633	0
10	0.593334	5.0346	2e-06
11	0.550053	4.6674	7e-06
12	0.503015	4.2682	3e-05
13	0.457646	3.8833	0.000113
14	0.411765	3.4939	0.000409
15	0.363996	3.0886	0.001428
16	0.316792	2.6881	0.004461
17	0.275826	2.3405	0.011017

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.964763 & 8.1863 & 0 \tabularnewline
2 & 0.922188 & 7.825 & 0 \tabularnewline
3 & 0.883541 & 7.4971 & 0 \tabularnewline
4 & 0.844726 & 7.1677 & 0 \tabularnewline
5 & 0.79975 & 6.7861 & 0 \tabularnewline
6 & 0.752359 & 6.384 & 0 \tabularnewline
7 & 0.709408 & 6.0195 & 0 \tabularnewline
8 & 0.668878 & 5.6756 & 0 \tabularnewline
9 & 0.632071 & 5.3633 & 0 \tabularnewline
10 & 0.593334 & 5.0346 & 2e-06 \tabularnewline
11 & 0.550053 & 4.6674 & 7e-06 \tabularnewline
12 & 0.503015 & 4.2682 & 3e-05 \tabularnewline
13 & 0.457646 & 3.8833 & 0.000113 \tabularnewline
14 & 0.411765 & 3.4939 & 0.000409 \tabularnewline
15 & 0.363996 & 3.0886 & 0.001428 \tabularnewline
16 & 0.316792 & 2.6881 & 0.004461 \tabularnewline
17 & 0.275826 & 2.3405 & 0.011017 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3145&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]0[/C][C]1[/C][C]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.964763[/C][C]8.1863[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.922188[/C][C]7.825[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.883541[/C][C]7.4971[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.844726[/C][C]7.1677[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.79975[/C][C]6.7861[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.752359[/C][C]6.384[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.709408[/C][C]6.0195[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.668878[/C][C]5.6756[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.632071[/C][C]5.3633[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.593334[/C][C]5.0346[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.550053[/C][C]4.6674[/C][C]7e-06[/C][/ROW]
[ROW][C]12[/C][C]0.503015[/C][C]4.2682[/C][C]3e-05[/C][/ROW]
[ROW][C]13[/C][C]0.457646[/C][C]3.8833[/C][C]0.000113[/C][/ROW]
[ROW][C]14[/C][C]0.411765[/C][C]3.4939[/C][C]0.000409[/C][/ROW]
[ROW][C]15[/C][C]0.363996[/C][C]3.0886[/C][C]0.001428[/C][/ROW]
[ROW][C]16[/C][C]0.316792[/C][C]2.6881[/C][C]0.004461[/C][/ROW]
[ROW][C]17[/C][C]0.275826[/C][C]2.3405[/C][C]0.011017[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3145&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3145&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
0	1	8.4853	0
1	0.964763	8.1863	0
2	0.922188	7.825	0
3	0.883541	7.4971	0
4	0.844726	7.1677	0
5	0.79975	6.7861	0
6	0.752359	6.384	0
7	0.709408	6.0195	0
8	0.668878	5.6756	0
9	0.632071	5.3633	0
10	0.593334	5.0346	2e-06
11	0.550053	4.6674	7e-06
12	0.503015	4.2682	3e-05
13	0.457646	3.8833	0.000113
14	0.411765	3.4939	0.000409
15	0.363996	3.0886	0.001428
16	0.316792	2.6881	0.004461
17	0.275826	2.3405	0.011017

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.964763	8.1863	0
1	-0.123929	-1.0516	0.851743
2	0.046226	0.3922	0.34802
3	-0.03629	-0.3079	0.620487
4	-0.105963	-0.8991	0.814209
5	-0.042989	-0.3648	0.641825
6	0.034117	0.2895	0.386517
7	-0.005135	-0.0436	0.517318
8	0.039811	0.3378	0.368247
9	-0.056713	-0.4812	0.684092
10	-0.089026	-0.7554	0.773768
11	-0.082681	-0.7016	0.757395
12	-0.009643	-0.0818	0.532492
13	-0.044796	-0.3801	0.647507
14	-0.035046	-0.2974	0.61648
15	-0.012259	-0.104	0.541279
16	0.047982	0.4071	0.342556
17	-0.004018	-0.0341	0.513552

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.964763 & 8.1863 & 0 \tabularnewline
1 & -0.123929 & -1.0516 & 0.851743 \tabularnewline
2 & 0.046226 & 0.3922 & 0.34802 \tabularnewline
3 & -0.03629 & -0.3079 & 0.620487 \tabularnewline
4 & -0.105963 & -0.8991 & 0.814209 \tabularnewline
5 & -0.042989 & -0.3648 & 0.641825 \tabularnewline
6 & 0.034117 & 0.2895 & 0.386517 \tabularnewline
7 & -0.005135 & -0.0436 & 0.517318 \tabularnewline
8 & 0.039811 & 0.3378 & 0.368247 \tabularnewline
9 & -0.056713 & -0.4812 & 0.684092 \tabularnewline
10 & -0.089026 & -0.7554 & 0.773768 \tabularnewline
11 & -0.082681 & -0.7016 & 0.757395 \tabularnewline
12 & -0.009643 & -0.0818 & 0.532492 \tabularnewline
13 & -0.044796 & -0.3801 & 0.647507 \tabularnewline
14 & -0.035046 & -0.2974 & 0.61648 \tabularnewline
15 & -0.012259 & -0.104 & 0.541279 \tabularnewline
16 & 0.047982 & 0.4071 & 0.342556 \tabularnewline
17 & -0.004018 & -0.0341 & 0.513552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3145&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]0[/C][C]0.964763[/C][C]8.1863[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.123929[/C][C]-1.0516[/C][C]0.851743[/C][/ROW]
[ROW][C]2[/C][C]0.046226[/C][C]0.3922[/C][C]0.34802[/C][/ROW]
[ROW][C]3[/C][C]-0.03629[/C][C]-0.3079[/C][C]0.620487[/C][/ROW]
[ROW][C]4[/C][C]-0.105963[/C][C]-0.8991[/C][C]0.814209[/C][/ROW]
[ROW][C]5[/C][C]-0.042989[/C][C]-0.3648[/C][C]0.641825[/C][/ROW]
[ROW][C]6[/C][C]0.034117[/C][C]0.2895[/C][C]0.386517[/C][/ROW]
[ROW][C]7[/C][C]-0.005135[/C][C]-0.0436[/C][C]0.517318[/C][/ROW]
[ROW][C]8[/C][C]0.039811[/C][C]0.3378[/C][C]0.368247[/C][/ROW]
[ROW][C]9[/C][C]-0.056713[/C][C]-0.4812[/C][C]0.684092[/C][/ROW]
[ROW][C]10[/C][C]-0.089026[/C][C]-0.7554[/C][C]0.773768[/C][/ROW]
[ROW][C]11[/C][C]-0.082681[/C][C]-0.7016[/C][C]0.757395[/C][/ROW]
[ROW][C]12[/C][C]-0.009643[/C][C]-0.0818[/C][C]0.532492[/C][/ROW]
[ROW][C]13[/C][C]-0.044796[/C][C]-0.3801[/C][C]0.647507[/C][/ROW]
[ROW][C]14[/C][C]-0.035046[/C][C]-0.2974[/C][C]0.61648[/C][/ROW]
[ROW][C]15[/C][C]-0.012259[/C][C]-0.104[/C][C]0.541279[/C][/ROW]
[ROW][C]16[/C][C]0.047982[/C][C]0.4071[/C][C]0.342556[/C][/ROW]
[ROW][C]17[/C][C]-0.004018[/C][C]-0.0341[/C][C]0.513552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3145&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3145&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
0	0.964763	8.1863	0
1	-0.123929	-1.0516	0.851743
2	0.046226	0.3922	0.34802
3	-0.03629	-0.3079	0.620487
4	-0.105963	-0.8991	0.814209
5	-0.042989	-0.3648	0.641825
6	0.034117	0.2895	0.386517
7	-0.005135	-0.0436	0.517318
8	0.039811	0.3378	0.368247
9	-0.056713	-0.4812	0.684092
10	-0.089026	-0.7554	0.773768
11	-0.082681	-0.7016	0.757395
12	-0.009643	-0.0818	0.532492
13	-0.044796	-0.3801	0.647507
14	-0.035046	-0.2974	0.61648
15	-0.012259	-0.104	0.541279
16	0.047982	0.4071	0.342556
17	-0.004018	-0.0341	0.513552

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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Dataset

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Figures (Output of Computation)

Input Parameters & R Code