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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 14:33:49 +0000

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/2010/Dec/03/t1291386742rg4pujix7xk6rco.htm/, Retrieved Wed, 08 May 2024 00:34:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104826, Retrieved Wed, 08 May 2024 00:34:39 +0000

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User-defined keywords

Estimated Impact

132

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] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-   PD    [(Partial) Autocorrelation Function] [Stationarity in t...] [2010-12-03 14:19:39] [aeb27d5c05332f2e597ad139ee63fbe4]
-   P         [(Partial) Autocorrelation Function] [Stationarity in t...] [2010-12-03 14:33:49] [18ef3d986e8801a4b28404e69e5bf56b] [Current]
-   P           [(Partial) Autocorrelation Function] [Stationarity in t...] [2010-12-03 14:41:54] [aeb27d5c05332f2e597ad139ee63fbe4] 

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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=104826&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=104826&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104826&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	0.94835	9.5779	0
2	0.891116	8.9998	0
3	0.829464	8.3772	0
4	0.765458	7.7307	0
5	0.716736	7.2387	0
6	0.679696	6.8646	0
7	0.671632	6.7832	0
8	0.675606	6.8233	0
9	0.687548	6.9439	0
10	0.704042	7.1105	0
11	0.710396	7.1747	0
12	0.700591	7.0756	0
13	0.65538	6.619	0
14	0.590115	5.9599	0
15	0.521812	5.27	0
16	0.451841	4.5634	7e-06
17	0.399066	4.0304	5.4e-05
18	0.364419	3.6805	0.000187
19	0.346289	3.4973	0.000349
20	0.34307	3.4648	0.000389

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.94835 & 9.5779 & 0 \tabularnewline
2 & 0.891116 & 8.9998 & 0 \tabularnewline
3 & 0.829464 & 8.3772 & 0 \tabularnewline
4 & 0.765458 & 7.7307 & 0 \tabularnewline
5 & 0.716736 & 7.2387 & 0 \tabularnewline
6 & 0.679696 & 6.8646 & 0 \tabularnewline
7 & 0.671632 & 6.7832 & 0 \tabularnewline
8 & 0.675606 & 6.8233 & 0 \tabularnewline
9 & 0.687548 & 6.9439 & 0 \tabularnewline
10 & 0.704042 & 7.1105 & 0 \tabularnewline
11 & 0.710396 & 7.1747 & 0 \tabularnewline
12 & 0.700591 & 7.0756 & 0 \tabularnewline
13 & 0.65538 & 6.619 & 0 \tabularnewline
14 & 0.590115 & 5.9599 & 0 \tabularnewline
15 & 0.521812 & 5.27 & 0 \tabularnewline
16 & 0.451841 & 4.5634 & 7e-06 \tabularnewline
17 & 0.399066 & 4.0304 & 5.4e-05 \tabularnewline
18 & 0.364419 & 3.6805 & 0.000187 \tabularnewline
19 & 0.346289 & 3.4973 & 0.000349 \tabularnewline
20 & 0.34307 & 3.4648 & 0.000389 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104826&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]0.94835[/C][C]9.5779[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.891116[/C][C]8.9998[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.829464[/C][C]8.3772[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.765458[/C][C]7.7307[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.716736[/C][C]7.2387[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.679696[/C][C]6.8646[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.671632[/C][C]6.7832[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.675606[/C][C]6.8233[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.687548[/C][C]6.9439[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.704042[/C][C]7.1105[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.710396[/C][C]7.1747[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.700591[/C][C]7.0756[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.65538[/C][C]6.619[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.590115[/C][C]5.9599[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.521812[/C][C]5.27[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.451841[/C][C]4.5634[/C][C]7e-06[/C][/ROW]
[ROW][C]17[/C][C]0.399066[/C][C]4.0304[/C][C]5.4e-05[/C][/ROW]
[ROW][C]18[/C][C]0.364419[/C][C]3.6805[/C][C]0.000187[/C][/ROW]
[ROW][C]19[/C][C]0.346289[/C][C]3.4973[/C][C]0.000349[/C][/ROW]
[ROW][C]20[/C][C]0.34307[/C][C]3.4648[/C][C]0.000389[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104826&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104826&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	0.94835	9.5779	0
2	0.891116	8.9998	0
3	0.829464	8.3772	0
4	0.765458	7.7307	0
5	0.716736	7.2387	0
6	0.679696	6.8646	0
7	0.671632	6.7832	0
8	0.675606	6.8233	0
9	0.687548	6.9439	0
10	0.704042	7.1105	0
11	0.710396	7.1747	0
12	0.700591	7.0756	0
13	0.65538	6.619	0
14	0.590115	5.9599	0
15	0.521812	5.27	0
16	0.451841	4.5634	7e-06
17	0.399066	4.0304	5.4e-05
18	0.364419	3.6805	0.000187
19	0.346289	3.4973	0.000349
20	0.34307	3.4648	0.000389

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.94835	9.5779	0
2	-0.082003	-0.8282	0.204747
3	-0.071624	-0.7234	0.235556
4	-0.053213	-0.5374	0.296074
5	0.121455	1.2266	0.111392
6	0.076951	0.7772	0.219429
7	0.251325	2.5383	0.006326
8	0.083232	0.8406	0.201268
9	0.076351	0.7711	0.221213
10	0.056686	0.5725	0.28412
11	-0.0228	-0.2303	0.409171
12	-0.094063	-0.95	0.17218
13	-0.281325	-2.8412	0.002713
14	-0.182624	-1.8444	0.034013
15	-0.041416	-0.4183	0.338311
16	-0.047341	-0.4781	0.316792
17	0.054957	0.555	0.290043
18	0.043823	0.4426	0.329501
19	-0.018621	-0.1881	0.4256
20	-0.00349	-0.0352	0.485976

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.94835 & 9.5779 & 0 \tabularnewline
2 & -0.082003 & -0.8282 & 0.204747 \tabularnewline
3 & -0.071624 & -0.7234 & 0.235556 \tabularnewline
4 & -0.053213 & -0.5374 & 0.296074 \tabularnewline
5 & 0.121455 & 1.2266 & 0.111392 \tabularnewline
6 & 0.076951 & 0.7772 & 0.219429 \tabularnewline
7 & 0.251325 & 2.5383 & 0.006326 \tabularnewline
8 & 0.083232 & 0.8406 & 0.201268 \tabularnewline
9 & 0.076351 & 0.7711 & 0.221213 \tabularnewline
10 & 0.056686 & 0.5725 & 0.28412 \tabularnewline
11 & -0.0228 & -0.2303 & 0.409171 \tabularnewline
12 & -0.094063 & -0.95 & 0.17218 \tabularnewline
13 & -0.281325 & -2.8412 & 0.002713 \tabularnewline
14 & -0.182624 & -1.8444 & 0.034013 \tabularnewline
15 & -0.041416 & -0.4183 & 0.338311 \tabularnewline
16 & -0.047341 & -0.4781 & 0.316792 \tabularnewline
17 & 0.054957 & 0.555 & 0.290043 \tabularnewline
18 & 0.043823 & 0.4426 & 0.329501 \tabularnewline
19 & -0.018621 & -0.1881 & 0.4256 \tabularnewline
20 & -0.00349 & -0.0352 & 0.485976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104826&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]0.94835[/C][C]9.5779[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.082003[/C][C]-0.8282[/C][C]0.204747[/C][/ROW]
[ROW][C]3[/C][C]-0.071624[/C][C]-0.7234[/C][C]0.235556[/C][/ROW]
[ROW][C]4[/C][C]-0.053213[/C][C]-0.5374[/C][C]0.296074[/C][/ROW]
[ROW][C]5[/C][C]0.121455[/C][C]1.2266[/C][C]0.111392[/C][/ROW]
[ROW][C]6[/C][C]0.076951[/C][C]0.7772[/C][C]0.219429[/C][/ROW]
[ROW][C]7[/C][C]0.251325[/C][C]2.5383[/C][C]0.006326[/C][/ROW]
[ROW][C]8[/C][C]0.083232[/C][C]0.8406[/C][C]0.201268[/C][/ROW]
[ROW][C]9[/C][C]0.076351[/C][C]0.7711[/C][C]0.221213[/C][/ROW]
[ROW][C]10[/C][C]0.056686[/C][C]0.5725[/C][C]0.28412[/C][/ROW]
[ROW][C]11[/C][C]-0.0228[/C][C]-0.2303[/C][C]0.409171[/C][/ROW]
[ROW][C]12[/C][C]-0.094063[/C][C]-0.95[/C][C]0.17218[/C][/ROW]
[ROW][C]13[/C][C]-0.281325[/C][C]-2.8412[/C][C]0.002713[/C][/ROW]
[ROW][C]14[/C][C]-0.182624[/C][C]-1.8444[/C][C]0.034013[/C][/ROW]
[ROW][C]15[/C][C]-0.041416[/C][C]-0.4183[/C][C]0.338311[/C][/ROW]
[ROW][C]16[/C][C]-0.047341[/C][C]-0.4781[/C][C]0.316792[/C][/ROW]
[ROW][C]17[/C][C]0.054957[/C][C]0.555[/C][C]0.290043[/C][/ROW]
[ROW][C]18[/C][C]0.043823[/C][C]0.4426[/C][C]0.329501[/C][/ROW]
[ROW][C]19[/C][C]-0.018621[/C][C]-0.1881[/C][C]0.4256[/C][/ROW]
[ROW][C]20[/C][C]-0.00349[/C][C]-0.0352[/C][C]0.485976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104826&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104826&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	0.94835	9.5779	0
2	-0.082003	-0.8282	0.204747
3	-0.071624	-0.7234	0.235556
4	-0.053213	-0.5374	0.296074
5	0.121455	1.2266	0.111392
6	0.076951	0.7772	0.219429
7	0.251325	2.5383	0.006326
8	0.083232	0.8406	0.201268
9	0.076351	0.7711	0.221213
10	0.056686	0.5725	0.28412
11	-0.0228	-0.2303	0.409171
12	-0.094063	-0.95	0.17218
13	-0.281325	-2.8412	0.002713
14	-0.182624	-1.8444	0.034013
15	-0.041416	-0.4183	0.338311
16	-0.047341	-0.4781	0.316792
17	0.054957	0.555	0.290043
18	0.043823	0.4426	0.329501
19	-0.018621	-0.1881	0.4256
20	-0.00349	-0.0352	0.485976

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code