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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 07:09:22 -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/04/t1196776658j635yskuv425tf9.htm/, Retrieved Thu, 02 May 2024 02:16:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2376, Retrieved Thu, 02 May 2024 02:16:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

q1 - werkloosheid < 25j

Estimated Impact

217

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

-       [(Partial) Autocorrelation Function] [estimation of ARM...] [2007-12-04 14:09:22] [ac6f409873aab27747ac7f3d36ded223] [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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2376&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2376&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2376&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	-0.031368	-0.243	0.595573
2	-0.160953	-1.2467	0.89133
3	-0.006859	-0.0531	0.521097
4	-0.051638	-0.4	0.654708
5	-0.133554	-1.0345	0.847474
6	0.132374	1.0254	0.154654
7	0.243642	1.8872	0.031984
8	-0.097313	-0.7538	0.773036
9	-0.07235	-0.5604	0.71136
10	-0.071103	-0.5508	0.70808
11	0.116475	0.9022	0.185276
12	-0.125116	-0.9691	0.831819
13	-0.059327	-0.4595	0.676249
14	0.108548	0.8408	0.201897
15	0.063085	0.4887	0.313434
16	-0.090156	-0.6983	0.756171
17	-0.026345	-0.2041	0.580503

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & -0.031368 & -0.243 & 0.595573 \tabularnewline
2 & -0.160953 & -1.2467 & 0.89133 \tabularnewline
3 & -0.006859 & -0.0531 & 0.521097 \tabularnewline
4 & -0.051638 & -0.4 & 0.654708 \tabularnewline
5 & -0.133554 & -1.0345 & 0.847474 \tabularnewline
6 & 0.132374 & 1.0254 & 0.154654 \tabularnewline
7 & 0.243642 & 1.8872 & 0.031984 \tabularnewline
8 & -0.097313 & -0.7538 & 0.773036 \tabularnewline
9 & -0.07235 & -0.5604 & 0.71136 \tabularnewline
10 & -0.071103 & -0.5508 & 0.70808 \tabularnewline
11 & 0.116475 & 0.9022 & 0.185276 \tabularnewline
12 & -0.125116 & -0.9691 & 0.831819 \tabularnewline
13 & -0.059327 & -0.4595 & 0.676249 \tabularnewline
14 & 0.108548 & 0.8408 & 0.201897 \tabularnewline
15 & 0.063085 & 0.4887 & 0.313434 \tabularnewline
16 & -0.090156 & -0.6983 & 0.756171 \tabularnewline
17 & -0.026345 & -0.2041 & 0.580503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2376&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.031368[/C][C]-0.243[/C][C]0.595573[/C][/ROW]
[ROW][C]2[/C][C]-0.160953[/C][C]-1.2467[/C][C]0.89133[/C][/ROW]
[ROW][C]3[/C][C]-0.006859[/C][C]-0.0531[/C][C]0.521097[/C][/ROW]
[ROW][C]4[/C][C]-0.051638[/C][C]-0.4[/C][C]0.654708[/C][/ROW]
[ROW][C]5[/C][C]-0.133554[/C][C]-1.0345[/C][C]0.847474[/C][/ROW]
[ROW][C]6[/C][C]0.132374[/C][C]1.0254[/C][C]0.154654[/C][/ROW]
[ROW][C]7[/C][C]0.243642[/C][C]1.8872[/C][C]0.031984[/C][/ROW]
[ROW][C]8[/C][C]-0.097313[/C][C]-0.7538[/C][C]0.773036[/C][/ROW]
[ROW][C]9[/C][C]-0.07235[/C][C]-0.5604[/C][C]0.71136[/C][/ROW]
[ROW][C]10[/C][C]-0.071103[/C][C]-0.5508[/C][C]0.70808[/C][/ROW]
[ROW][C]11[/C][C]0.116475[/C][C]0.9022[/C][C]0.185276[/C][/ROW]
[ROW][C]12[/C][C]-0.125116[/C][C]-0.9691[/C][C]0.831819[/C][/ROW]
[ROW][C]13[/C][C]-0.059327[/C][C]-0.4595[/C][C]0.676249[/C][/ROW]
[ROW][C]14[/C][C]0.108548[/C][C]0.8408[/C][C]0.201897[/C][/ROW]
[ROW][C]15[/C][C]0.063085[/C][C]0.4887[/C][C]0.313434[/C][/ROW]
[ROW][C]16[/C][C]-0.090156[/C][C]-0.6983[/C][C]0.756171[/C][/ROW]
[ROW][C]17[/C][C]-0.026345[/C][C]-0.2041[/C][C]0.580503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2376&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2376&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	7.746	0
1	-0.031368	-0.243	0.595573
2	-0.160953	-1.2467	0.89133
3	-0.006859	-0.0531	0.521097
4	-0.051638	-0.4	0.654708
5	-0.133554	-1.0345	0.847474
6	0.132374	1.0254	0.154654
7	0.243642	1.8872	0.031984
8	-0.097313	-0.7538	0.773036
9	-0.07235	-0.5604	0.71136
10	-0.071103	-0.5508	0.70808
11	0.116475	0.9022	0.185276
12	-0.125116	-0.9691	0.831819
13	-0.059327	-0.4595	0.676249
14	0.108548	0.8408	0.201897
15	0.063085	0.4887	0.313434
16	-0.090156	-0.6983	0.756171
17	-0.026345	-0.2041	0.580503

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.031368	-0.243	0.595573
1	-0.162096	-1.2556	0.892934
2	-0.018309	-0.1418	0.556152
3	-0.08091	-0.6267	0.733393
4	-0.147888	-1.1455	0.871732
5	0.10276	0.796	0.214592
6	0.21768	1.6861	0.048481
7	-0.052837	-0.4093	0.658102
8	-0.02304	-0.1785	0.570521
9	-0.099349	-0.7696	0.777708
10	0.166985	1.2935	0.100404
11	-0.122818	-0.9513	0.827377
12	-0.130335	-1.0096	0.841623
13	0.025175	0.195	0.423025
14	0.10843	0.8399	0.20215
15	-0.025877	-0.2004	0.579095
16	-0.07351	-0.5694	0.714396
17	-0.076213	-0.5903	0.72141

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.031368 & -0.243 & 0.595573 \tabularnewline
1 & -0.162096 & -1.2556 & 0.892934 \tabularnewline
2 & -0.018309 & -0.1418 & 0.556152 \tabularnewline
3 & -0.08091 & -0.6267 & 0.733393 \tabularnewline
4 & -0.147888 & -1.1455 & 0.871732 \tabularnewline
5 & 0.10276 & 0.796 & 0.214592 \tabularnewline
6 & 0.21768 & 1.6861 & 0.048481 \tabularnewline
7 & -0.052837 & -0.4093 & 0.658102 \tabularnewline
8 & -0.02304 & -0.1785 & 0.570521 \tabularnewline
9 & -0.099349 & -0.7696 & 0.777708 \tabularnewline
10 & 0.166985 & 1.2935 & 0.100404 \tabularnewline
11 & -0.122818 & -0.9513 & 0.827377 \tabularnewline
12 & -0.130335 & -1.0096 & 0.841623 \tabularnewline
13 & 0.025175 & 0.195 & 0.423025 \tabularnewline
14 & 0.10843 & 0.8399 & 0.20215 \tabularnewline
15 & -0.025877 & -0.2004 & 0.579095 \tabularnewline
16 & -0.07351 & -0.5694 & 0.714396 \tabularnewline
17 & -0.076213 & -0.5903 & 0.72141 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2376&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]-0.031368[/C][C]-0.243[/C][C]0.595573[/C][/ROW]
[ROW][C]1[/C][C]-0.162096[/C][C]-1.2556[/C][C]0.892934[/C][/ROW]
[ROW][C]2[/C][C]-0.018309[/C][C]-0.1418[/C][C]0.556152[/C][/ROW]
[ROW][C]3[/C][C]-0.08091[/C][C]-0.6267[/C][C]0.733393[/C][/ROW]
[ROW][C]4[/C][C]-0.147888[/C][C]-1.1455[/C][C]0.871732[/C][/ROW]
[ROW][C]5[/C][C]0.10276[/C][C]0.796[/C][C]0.214592[/C][/ROW]
[ROW][C]6[/C][C]0.21768[/C][C]1.6861[/C][C]0.048481[/C][/ROW]
[ROW][C]7[/C][C]-0.052837[/C][C]-0.4093[/C][C]0.658102[/C][/ROW]
[ROW][C]8[/C][C]-0.02304[/C][C]-0.1785[/C][C]0.570521[/C][/ROW]
[ROW][C]9[/C][C]-0.099349[/C][C]-0.7696[/C][C]0.777708[/C][/ROW]
[ROW][C]10[/C][C]0.166985[/C][C]1.2935[/C][C]0.100404[/C][/ROW]
[ROW][C]11[/C][C]-0.122818[/C][C]-0.9513[/C][C]0.827377[/C][/ROW]
[ROW][C]12[/C][C]-0.130335[/C][C]-1.0096[/C][C]0.841623[/C][/ROW]
[ROW][C]13[/C][C]0.025175[/C][C]0.195[/C][C]0.423025[/C][/ROW]
[ROW][C]14[/C][C]0.10843[/C][C]0.8399[/C][C]0.20215[/C][/ROW]
[ROW][C]15[/C][C]-0.025877[/C][C]-0.2004[/C][C]0.579095[/C][/ROW]
[ROW][C]16[/C][C]-0.07351[/C][C]-0.5694[/C][C]0.714396[/C][/ROW]
[ROW][C]17[/C][C]-0.076213[/C][C]-0.5903[/C][C]0.72141[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2376&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2376&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	-0.031368	-0.243	0.595573
1	-0.162096	-1.2556	0.892934
2	-0.018309	-0.1418	0.556152
3	-0.08091	-0.6267	0.733393
4	-0.147888	-1.1455	0.871732
5	0.10276	0.796	0.214592
6	0.21768	1.6861	0.048481
7	-0.052837	-0.4093	0.658102
8	-0.02304	-0.1785	0.570521
9	-0.099349	-0.7696	0.777708
10	0.166985	1.2935	0.100404
11	-0.122818	-0.9513	0.827377
12	-0.130335	-1.0096	0.841623
13	0.025175	0.195	0.423025
14	0.10843	0.8399	0.20215
15	-0.025877	-0.2004	0.579095
16	-0.07351	-0.5694	0.714396
17	-0.076213	-0.5903	0.72141

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; 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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