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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 05 Dec 2007 07:30:41 -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/05/t1196864571djzvg1z4hxibs6e.htm/, Retrieved Thu, 02 May 2024 22:49:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2477, Retrieved Thu, 02 May 2024 22:49:10 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

bridome

Estimated Impact

250

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

-       [(Partial) Autocorrelation Function] [workshop 3 correl...] [2007-12-05 14:30:41] [ff60737d3854dcb913eacf6907ce202b] [Current]
-   PD    [(Partial) Autocorrelation Function] [estimation Q1] [2007-12-06 13:09:33] [74be16979710d4c4e7c6647856088456] 

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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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2477&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]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=2477&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2477&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	10.247	0
1	-0.49172	-5.0386	0.999999
2	-0.101994	-1.0451	0.850818
3	0.319834	3.2773	0.000711
4	-0.265227	-2.7178	0.996155
5	0.036468	0.3737	0.354695
6	0.092709	0.95	0.17215
7	-0.025552	-0.2618	0.603016
8	-0.22439	-2.2993	0.988267
9	0.329465	3.376	0.000516
10	-0.182086	-1.8658	0.967572
11	-0.1012	-1.037	0.848938
12	0.358896	3.6776	0.000187
13	-0.296787	-3.0412	0.998512
14	0.080157	0.8214	0.206651
15	0.147286	1.5092	0.067121
16	-0.217216	-2.2258	0.985918
17	0.048301	0.4949	0.310839
18	0.088161	0.9034	0.184197
19	-0.07096	-0.7271	0.765616

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.247 & 0 \tabularnewline
1 & -0.49172 & -5.0386 & 0.999999 \tabularnewline
2 & -0.101994 & -1.0451 & 0.850818 \tabularnewline
3 & 0.319834 & 3.2773 & 0.000711 \tabularnewline
4 & -0.265227 & -2.7178 & 0.996155 \tabularnewline
5 & 0.036468 & 0.3737 & 0.354695 \tabularnewline
6 & 0.092709 & 0.95 & 0.17215 \tabularnewline
7 & -0.025552 & -0.2618 & 0.603016 \tabularnewline
8 & -0.22439 & -2.2993 & 0.988267 \tabularnewline
9 & 0.329465 & 3.376 & 0.000516 \tabularnewline
10 & -0.182086 & -1.8658 & 0.967572 \tabularnewline
11 & -0.1012 & -1.037 & 0.848938 \tabularnewline
12 & 0.358896 & 3.6776 & 0.000187 \tabularnewline
13 & -0.296787 & -3.0412 & 0.998512 \tabularnewline
14 & 0.080157 & 0.8214 & 0.206651 \tabularnewline
15 & 0.147286 & 1.5092 & 0.067121 \tabularnewline
16 & -0.217216 & -2.2258 & 0.985918 \tabularnewline
17 & 0.048301 & 0.4949 & 0.310839 \tabularnewline
18 & 0.088161 & 0.9034 & 0.184197 \tabularnewline
19 & -0.07096 & -0.7271 & 0.765616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2477&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]10.247[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.49172[/C][C]-5.0386[/C][C]0.999999[/C][/ROW]
[ROW][C]2[/C][C]-0.101994[/C][C]-1.0451[/C][C]0.850818[/C][/ROW]
[ROW][C]3[/C][C]0.319834[/C][C]3.2773[/C][C]0.000711[/C][/ROW]
[ROW][C]4[/C][C]-0.265227[/C][C]-2.7178[/C][C]0.996155[/C][/ROW]
[ROW][C]5[/C][C]0.036468[/C][C]0.3737[/C][C]0.354695[/C][/ROW]
[ROW][C]6[/C][C]0.092709[/C][C]0.95[/C][C]0.17215[/C][/ROW]
[ROW][C]7[/C][C]-0.025552[/C][C]-0.2618[/C][C]0.603016[/C][/ROW]
[ROW][C]8[/C][C]-0.22439[/C][C]-2.2993[/C][C]0.988267[/C][/ROW]
[ROW][C]9[/C][C]0.329465[/C][C]3.376[/C][C]0.000516[/C][/ROW]
[ROW][C]10[/C][C]-0.182086[/C][C]-1.8658[/C][C]0.967572[/C][/ROW]
[ROW][C]11[/C][C]-0.1012[/C][C]-1.037[/C][C]0.848938[/C][/ROW]
[ROW][C]12[/C][C]0.358896[/C][C]3.6776[/C][C]0.000187[/C][/ROW]
[ROW][C]13[/C][C]-0.296787[/C][C]-3.0412[/C][C]0.998512[/C][/ROW]
[ROW][C]14[/C][C]0.080157[/C][C]0.8214[/C][C]0.206651[/C][/ROW]
[ROW][C]15[/C][C]0.147286[/C][C]1.5092[/C][C]0.067121[/C][/ROW]
[ROW][C]16[/C][C]-0.217216[/C][C]-2.2258[/C][C]0.985918[/C][/ROW]
[ROW][C]17[/C][C]0.048301[/C][C]0.4949[/C][C]0.310839[/C][/ROW]
[ROW][C]18[/C][C]0.088161[/C][C]0.9034[/C][C]0.184197[/C][/ROW]
[ROW][C]19[/C][C]-0.07096[/C][C]-0.7271[/C][C]0.765616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2477&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2477&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	10.247	0
1	-0.49172	-5.0386	0.999999
2	-0.101994	-1.0451	0.850818
3	0.319834	3.2773	0.000711
4	-0.265227	-2.7178	0.996155
5	0.036468	0.3737	0.354695
6	0.092709	0.95	0.17215
7	-0.025552	-0.2618	0.603016
8	-0.22439	-2.2993	0.988267
9	0.329465	3.376	0.000516
10	-0.182086	-1.8658	0.967572
11	-0.1012	-1.037	0.848938
12	0.358896	3.6776	0.000187
13	-0.296787	-3.0412	0.998512
14	0.080157	0.8214	0.206651
15	0.147286	1.5092	0.067121
16	-0.217216	-2.2258	0.985918
17	0.048301	0.4949	0.310839
18	0.088161	0.9034	0.184197
19	-0.07096	-0.7271	0.765616

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.49172	-5.0386	0.999999
1	-0.453413	-4.6461	0.999995
2	0.039828	0.4081	0.342011
3	-0.110054	-1.1277	0.868996
4	-0.091117	-0.9337	0.823692
5	-0.075728	-0.776	0.780249
6	0.085608	0.8772	0.191185
7	-0.302523	-3.0999	0.998758
8	0.076824	0.7872	0.216464
9	-0.088483	-0.9067	0.816673
10	-0.080619	-0.8261	0.794689
11	0.13876	1.4219	0.079015
12	0.046428	0.4757	0.317624
13	0.067444	0.6911	0.245514
14	0.127118	1.3026	0.097786
15	-0.036159	-0.3705	0.644129
16	-0.019083	-0.1955	0.577326
17	-0.050555	-0.518	0.697239
18	0.03843	0.3938	0.347266
19	-0.085198	-0.873	0.807678

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.49172 & -5.0386 & 0.999999 \tabularnewline
1 & -0.453413 & -4.6461 & 0.999995 \tabularnewline
2 & 0.039828 & 0.4081 & 0.342011 \tabularnewline
3 & -0.110054 & -1.1277 & 0.868996 \tabularnewline
4 & -0.091117 & -0.9337 & 0.823692 \tabularnewline
5 & -0.075728 & -0.776 & 0.780249 \tabularnewline
6 & 0.085608 & 0.8772 & 0.191185 \tabularnewline
7 & -0.302523 & -3.0999 & 0.998758 \tabularnewline
8 & 0.076824 & 0.7872 & 0.216464 \tabularnewline
9 & -0.088483 & -0.9067 & 0.816673 \tabularnewline
10 & -0.080619 & -0.8261 & 0.794689 \tabularnewline
11 & 0.13876 & 1.4219 & 0.079015 \tabularnewline
12 & 0.046428 & 0.4757 & 0.317624 \tabularnewline
13 & 0.067444 & 0.6911 & 0.245514 \tabularnewline
14 & 0.127118 & 1.3026 & 0.097786 \tabularnewline
15 & -0.036159 & -0.3705 & 0.644129 \tabularnewline
16 & -0.019083 & -0.1955 & 0.577326 \tabularnewline
17 & -0.050555 & -0.518 & 0.697239 \tabularnewline
18 & 0.03843 & 0.3938 & 0.347266 \tabularnewline
19 & -0.085198 & -0.873 & 0.807678 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2477&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]-0.49172[/C][C]-5.0386[/C][C]0.999999[/C][/ROW]
[ROW][C]1[/C][C]-0.453413[/C][C]-4.6461[/C][C]0.999995[/C][/ROW]
[ROW][C]2[/C][C]0.039828[/C][C]0.4081[/C][C]0.342011[/C][/ROW]
[ROW][C]3[/C][C]-0.110054[/C][C]-1.1277[/C][C]0.868996[/C][/ROW]
[ROW][C]4[/C][C]-0.091117[/C][C]-0.9337[/C][C]0.823692[/C][/ROW]
[ROW][C]5[/C][C]-0.075728[/C][C]-0.776[/C][C]0.780249[/C][/ROW]
[ROW][C]6[/C][C]0.085608[/C][C]0.8772[/C][C]0.191185[/C][/ROW]
[ROW][C]7[/C][C]-0.302523[/C][C]-3.0999[/C][C]0.998758[/C][/ROW]
[ROW][C]8[/C][C]0.076824[/C][C]0.7872[/C][C]0.216464[/C][/ROW]
[ROW][C]9[/C][C]-0.088483[/C][C]-0.9067[/C][C]0.816673[/C][/ROW]
[ROW][C]10[/C][C]-0.080619[/C][C]-0.8261[/C][C]0.794689[/C][/ROW]
[ROW][C]11[/C][C]0.13876[/C][C]1.4219[/C][C]0.079015[/C][/ROW]
[ROW][C]12[/C][C]0.046428[/C][C]0.4757[/C][C]0.317624[/C][/ROW]
[ROW][C]13[/C][C]0.067444[/C][C]0.6911[/C][C]0.245514[/C][/ROW]
[ROW][C]14[/C][C]0.127118[/C][C]1.3026[/C][C]0.097786[/C][/ROW]
[ROW][C]15[/C][C]-0.036159[/C][C]-0.3705[/C][C]0.644129[/C][/ROW]
[ROW][C]16[/C][C]-0.019083[/C][C]-0.1955[/C][C]0.577326[/C][/ROW]
[ROW][C]17[/C][C]-0.050555[/C][C]-0.518[/C][C]0.697239[/C][/ROW]
[ROW][C]18[/C][C]0.03843[/C][C]0.3938[/C][C]0.347266[/C][/ROW]
[ROW][C]19[/C][C]-0.085198[/C][C]-0.873[/C][C]0.807678[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2477&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2477&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	-0.49172	-5.0386	0.999999
1	-0.453413	-4.6461	0.999995
2	0.039828	0.4081	0.342011
3	-0.110054	-1.1277	0.868996
4	-0.091117	-0.9337	0.823692
5	-0.075728	-0.776	0.780249
6	0.085608	0.8772	0.191185
7	-0.302523	-3.0999	0.998758
8	0.076824	0.7872	0.216464
9	-0.088483	-0.9067	0.816673
10	-0.080619	-0.8261	0.794689
11	0.13876	1.4219	0.079015
12	0.046428	0.4757	0.317624
13	0.067444	0.6911	0.245514
14	0.127118	1.3026	0.097786
15	-0.036159	-0.3705	0.644129
16	-0.019083	-0.1955	0.577326
17	-0.050555	-0.518	0.697239
18	0.03843	0.3938	0.347266
19	-0.085198	-0.873	0.807678

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code