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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 11 Dec 2009 04:52:35 -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/2009/Dec/11/t1260532442raxw07qevnkmlal.htm/, Retrieved Sun, 28 Apr 2024 23:21:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66036, Retrieved Sun, 28 Apr 2024 23:21:22 +0000

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Estimated Impact

146

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [] [2009-11-27 14:46:03] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [cs.shw.ws9.v3] [2009-12-04 13:20:59] [74be16979710d4c4e7c6647856088456]
-   P         [(Partial) Autocorrelation Function] [ws9-1] [2009-12-11 11:52:35] [d41d8cd98f00b204e9800998ecf8427e] [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=66036&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=66036&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66036&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	0.847702	5.8731	0
2	0.731422	5.0674	3e-06
3	0.622	4.3093	4e-05
4	0.443948	3.0758	0.001731
5	0.219284	1.5192	0.067631
6	0.045505	0.3153	0.376962
7	-0.118714	-0.8225	0.207436
8	-0.330596	-2.2904	0.013216
9	-0.462258	-3.2026	0.001209
10	-0.563724	-3.9056	0.000147
11	-0.627341	-4.3463	3.6e-05
12	-0.693689	-4.806	8e-06
13	-0.644805	-4.4673	2.4e-05
14	-0.599227	-4.1516	6.7e-05
15	-0.52884	-3.6639	0.00031
16	-0.385506	-2.6709	0.005149
17	-0.224572	-1.5559	0.063153

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.847702 & 5.8731 & 0 \tabularnewline
2 & 0.731422 & 5.0674 & 3e-06 \tabularnewline
3 & 0.622 & 4.3093 & 4e-05 \tabularnewline
4 & 0.443948 & 3.0758 & 0.001731 \tabularnewline
5 & 0.219284 & 1.5192 & 0.067631 \tabularnewline
6 & 0.045505 & 0.3153 & 0.376962 \tabularnewline
7 & -0.118714 & -0.8225 & 0.207436 \tabularnewline
8 & -0.330596 & -2.2904 & 0.013216 \tabularnewline
9 & -0.462258 & -3.2026 & 0.001209 \tabularnewline
10 & -0.563724 & -3.9056 & 0.000147 \tabularnewline
11 & -0.627341 & -4.3463 & 3.6e-05 \tabularnewline
12 & -0.693689 & -4.806 & 8e-06 \tabularnewline
13 & -0.644805 & -4.4673 & 2.4e-05 \tabularnewline
14 & -0.599227 & -4.1516 & 6.7e-05 \tabularnewline
15 & -0.52884 & -3.6639 & 0.00031 \tabularnewline
16 & -0.385506 & -2.6709 & 0.005149 \tabularnewline
17 & -0.224572 & -1.5559 & 0.063153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66036&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]0.847702[/C][C]5.8731[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.731422[/C][C]5.0674[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.622[/C][C]4.3093[/C][C]4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.443948[/C][C]3.0758[/C][C]0.001731[/C][/ROW]
[ROW][C]5[/C][C]0.219284[/C][C]1.5192[/C][C]0.067631[/C][/ROW]
[ROW][C]6[/C][C]0.045505[/C][C]0.3153[/C][C]0.376962[/C][/ROW]
[ROW][C]7[/C][C]-0.118714[/C][C]-0.8225[/C][C]0.207436[/C][/ROW]
[ROW][C]8[/C][C]-0.330596[/C][C]-2.2904[/C][C]0.013216[/C][/ROW]
[ROW][C]9[/C][C]-0.462258[/C][C]-3.2026[/C][C]0.001209[/C][/ROW]
[ROW][C]10[/C][C]-0.563724[/C][C]-3.9056[/C][C]0.000147[/C][/ROW]
[ROW][C]11[/C][C]-0.627341[/C][C]-4.3463[/C][C]3.6e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.693689[/C][C]-4.806[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.644805[/C][C]-4.4673[/C][C]2.4e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.599227[/C][C]-4.1516[/C][C]6.7e-05[/C][/ROW]
[ROW][C]15[/C][C]-0.52884[/C][C]-3.6639[/C][C]0.00031[/C][/ROW]
[ROW][C]16[/C][C]-0.385506[/C][C]-2.6709[/C][C]0.005149[/C][/ROW]
[ROW][C]17[/C][C]-0.224572[/C][C]-1.5559[/C][C]0.063153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66036&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66036&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	0.847702	5.8731	0
2	0.731422	5.0674	3e-06
3	0.622	4.3093	4e-05
4	0.443948	3.0758	0.001731
5	0.219284	1.5192	0.067631
6	0.045505	0.3153	0.376962
7	-0.118714	-0.8225	0.207436
8	-0.330596	-2.2904	0.013216
9	-0.462258	-3.2026	0.001209
10	-0.563724	-3.9056	0.000147
11	-0.627341	-4.3463	3.6e-05
12	-0.693689	-4.806	8e-06
13	-0.644805	-4.4673	2.4e-05
14	-0.599227	-4.1516	6.7e-05
15	-0.52884	-3.6639	0.00031
16	-0.385506	-2.6709	0.005149
17	-0.224572	-1.5559	0.063153

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.847702	5.8731	0
2	0.045566	0.3157	0.376803
3	-0.02992	-0.2073	0.418328
4	-0.305869	-2.1191	0.01964
5	-0.36671	-2.5406	0.007177
6	-0.082882	-0.5742	0.284248
7	-0.052429	-0.3632	0.35901
8	-0.275637	-1.9097	0.031081
9	-0.016365	-0.1134	0.455101
10	-0.117644	-0.8151	0.209532
11	0.032151	0.2227	0.412338
12	-0.204821	-1.419	0.081174
13	0.116789	0.8091	0.211215
14	-0.117586	-0.8147	0.209646
15	0.014452	0.1001	0.460329
16	0.093845	0.6502	0.259339
17	0.062279	0.4315	0.334024

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.847702 & 5.8731 & 0 \tabularnewline
2 & 0.045566 & 0.3157 & 0.376803 \tabularnewline
3 & -0.02992 & -0.2073 & 0.418328 \tabularnewline
4 & -0.305869 & -2.1191 & 0.01964 \tabularnewline
5 & -0.36671 & -2.5406 & 0.007177 \tabularnewline
6 & -0.082882 & -0.5742 & 0.284248 \tabularnewline
7 & -0.052429 & -0.3632 & 0.35901 \tabularnewline
8 & -0.275637 & -1.9097 & 0.031081 \tabularnewline
9 & -0.016365 & -0.1134 & 0.455101 \tabularnewline
10 & -0.117644 & -0.8151 & 0.209532 \tabularnewline
11 & 0.032151 & 0.2227 & 0.412338 \tabularnewline
12 & -0.204821 & -1.419 & 0.081174 \tabularnewline
13 & 0.116789 & 0.8091 & 0.211215 \tabularnewline
14 & -0.117586 & -0.8147 & 0.209646 \tabularnewline
15 & 0.014452 & 0.1001 & 0.460329 \tabularnewline
16 & 0.093845 & 0.6502 & 0.259339 \tabularnewline
17 & 0.062279 & 0.4315 & 0.334024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66036&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]0.847702[/C][C]5.8731[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.045566[/C][C]0.3157[/C][C]0.376803[/C][/ROW]
[ROW][C]3[/C][C]-0.02992[/C][C]-0.2073[/C][C]0.418328[/C][/ROW]
[ROW][C]4[/C][C]-0.305869[/C][C]-2.1191[/C][C]0.01964[/C][/ROW]
[ROW][C]5[/C][C]-0.36671[/C][C]-2.5406[/C][C]0.007177[/C][/ROW]
[ROW][C]6[/C][C]-0.082882[/C][C]-0.5742[/C][C]0.284248[/C][/ROW]
[ROW][C]7[/C][C]-0.052429[/C][C]-0.3632[/C][C]0.35901[/C][/ROW]
[ROW][C]8[/C][C]-0.275637[/C][C]-1.9097[/C][C]0.031081[/C][/ROW]
[ROW][C]9[/C][C]-0.016365[/C][C]-0.1134[/C][C]0.455101[/C][/ROW]
[ROW][C]10[/C][C]-0.117644[/C][C]-0.8151[/C][C]0.209532[/C][/ROW]
[ROW][C]11[/C][C]0.032151[/C][C]0.2227[/C][C]0.412338[/C][/ROW]
[ROW][C]12[/C][C]-0.204821[/C][C]-1.419[/C][C]0.081174[/C][/ROW]
[ROW][C]13[/C][C]0.116789[/C][C]0.8091[/C][C]0.211215[/C][/ROW]
[ROW][C]14[/C][C]-0.117586[/C][C]-0.8147[/C][C]0.209646[/C][/ROW]
[ROW][C]15[/C][C]0.014452[/C][C]0.1001[/C][C]0.460329[/C][/ROW]
[ROW][C]16[/C][C]0.093845[/C][C]0.6502[/C][C]0.259339[/C][/ROW]
[ROW][C]17[/C][C]0.062279[/C][C]0.4315[/C][C]0.334024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66036&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66036&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	0.847702	5.8731	0
2	0.045566	0.3157	0.376803
3	-0.02992	-0.2073	0.418328
4	-0.305869	-2.1191	0.01964
5	-0.36671	-2.5406	0.007177
6	-0.082882	-0.5742	0.284248
7	-0.052429	-0.3632	0.35901
8	-0.275637	-1.9097	0.031081
9	-0.016365	-0.1134	0.455101
10	-0.117644	-0.8151	0.209532
11	0.032151	0.2227	0.412338
12	-0.204821	-1.419	0.081174
13	0.116789	0.8091	0.211215
14	-0.117586	-0.8147	0.209646
15	0.014452	0.1001	0.460329
16	0.093845	0.6502	0.259339
17	0.062279	0.4315	0.334024

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 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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