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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 02:38:51 -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/Nov/22/t11957240164w1cgy9p50orenv.htm/, Retrieved Thu, 02 May 2024 15:01:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5926, Retrieved Thu, 02 May 2024 15:01:57 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

205

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-11-22 09:38:51] [c8a4a40341940b3329d625726d352171] [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	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=5926&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=5926&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5926&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	7.8102	0
1	0.507404	3.963	9.8e-05
2	0.376724	2.9423	0.0023
3	0.485455	3.7915	0.000173
4	0.521262	4.0712	6.8e-05
5	0.46693	3.6468	0.000276
6	0.561402	4.3847	2.3e-05
7	0.323254	2.5247	0.007098
8	0.421545	3.2924	0.000828
9	0.383348	2.994	0.001986
10	0.186705	1.4582	0.074956
11	0.299322	2.3378	0.011348
12	0.575948	4.4983	1.6e-05
13	0.193449	1.5109	0.06799
14	0.129333	1.0101	0.158213
15	0.148094	1.1567	0.125962
16	0.131806	1.0294	0.153669

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.507404 & 3.963 & 9.8e-05 \tabularnewline
2 & 0.376724 & 2.9423 & 0.0023 \tabularnewline
3 & 0.485455 & 3.7915 & 0.000173 \tabularnewline
4 & 0.521262 & 4.0712 & 6.8e-05 \tabularnewline
5 & 0.46693 & 3.6468 & 0.000276 \tabularnewline
6 & 0.561402 & 4.3847 & 2.3e-05 \tabularnewline
7 & 0.323254 & 2.5247 & 0.007098 \tabularnewline
8 & 0.421545 & 3.2924 & 0.000828 \tabularnewline
9 & 0.383348 & 2.994 & 0.001986 \tabularnewline
10 & 0.186705 & 1.4582 & 0.074956 \tabularnewline
11 & 0.299322 & 2.3378 & 0.011348 \tabularnewline
12 & 0.575948 & 4.4983 & 1.6e-05 \tabularnewline
13 & 0.193449 & 1.5109 & 0.06799 \tabularnewline
14 & 0.129333 & 1.0101 & 0.158213 \tabularnewline
15 & 0.148094 & 1.1567 & 0.125962 \tabularnewline
16 & 0.131806 & 1.0294 & 0.153669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5926&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]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.507404[/C][C]3.963[/C][C]9.8e-05[/C][/ROW]
[ROW][C]2[/C][C]0.376724[/C][C]2.9423[/C][C]0.0023[/C][/ROW]
[ROW][C]3[/C][C]0.485455[/C][C]3.7915[/C][C]0.000173[/C][/ROW]
[ROW][C]4[/C][C]0.521262[/C][C]4.0712[/C][C]6.8e-05[/C][/ROW]
[ROW][C]5[/C][C]0.46693[/C][C]3.6468[/C][C]0.000276[/C][/ROW]
[ROW][C]6[/C][C]0.561402[/C][C]4.3847[/C][C]2.3e-05[/C][/ROW]
[ROW][C]7[/C][C]0.323254[/C][C]2.5247[/C][C]0.007098[/C][/ROW]
[ROW][C]8[/C][C]0.421545[/C][C]3.2924[/C][C]0.000828[/C][/ROW]
[ROW][C]9[/C][C]0.383348[/C][C]2.994[/C][C]0.001986[/C][/ROW]
[ROW][C]10[/C][C]0.186705[/C][C]1.4582[/C][C]0.074956[/C][/ROW]
[ROW][C]11[/C][C]0.299322[/C][C]2.3378[/C][C]0.011348[/C][/ROW]
[ROW][C]12[/C][C]0.575948[/C][C]4.4983[/C][C]1.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.193449[/C][C]1.5109[/C][C]0.06799[/C][/ROW]
[ROW][C]14[/C][C]0.129333[/C][C]1.0101[/C][C]0.158213[/C][/ROW]
[ROW][C]15[/C][C]0.148094[/C][C]1.1567[/C][C]0.125962[/C][/ROW]
[ROW][C]16[/C][C]0.131806[/C][C]1.0294[/C][C]0.153669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5926&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5926&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	7.8102	0
1	0.507404	3.963	9.8e-05
2	0.376724	2.9423	0.0023
3	0.485455	3.7915	0.000173
4	0.521262	4.0712	6.8e-05
5	0.46693	3.6468	0.000276
6	0.561402	4.3847	2.3e-05
7	0.323254	2.5247	0.007098
8	0.421545	3.2924	0.000828
9	0.383348	2.994	0.001986
10	0.186705	1.4582	0.074956
11	0.299322	2.3378	0.011348
12	0.575948	4.4983	1.6e-05
13	0.193449	1.5109	0.06799
14	0.129333	1.0101	0.158213
15	0.148094	1.1567	0.125962
16	0.131806	1.0294	0.153669

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.507404	3.963	9.8e-05
1	0.160618	1.2545	0.10723
2	0.336623	2.6291	0.005409
3	0.254827	1.9903	0.025524
4	0.151996	1.1871	0.11989
5	0.316042	2.4684	0.008196
6	-0.239393	-1.8697	0.966838
7	0.195371	1.5259	0.066102
8	-0.200461	-1.5657	0.938698
9	-0.343267	-2.681	0.995286
10	0.151936	1.1867	0.119982
11	0.37413	2.9221	0.002435
12	-0.304113	-2.3752	0.989651
13	-0.075083	-0.5864	0.720121
14	-0.154256	-1.2048	0.883529
15	-0.170347	-1.3304	0.905839
16	-0.106379	-0.8308	0.795349

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.507404 & 3.963 & 9.8e-05 \tabularnewline
1 & 0.160618 & 1.2545 & 0.10723 \tabularnewline
2 & 0.336623 & 2.6291 & 0.005409 \tabularnewline
3 & 0.254827 & 1.9903 & 0.025524 \tabularnewline
4 & 0.151996 & 1.1871 & 0.11989 \tabularnewline
5 & 0.316042 & 2.4684 & 0.008196 \tabularnewline
6 & -0.239393 & -1.8697 & 0.966838 \tabularnewline
7 & 0.195371 & 1.5259 & 0.066102 \tabularnewline
8 & -0.200461 & -1.5657 & 0.938698 \tabularnewline
9 & -0.343267 & -2.681 & 0.995286 \tabularnewline
10 & 0.151936 & 1.1867 & 0.119982 \tabularnewline
11 & 0.37413 & 2.9221 & 0.002435 \tabularnewline
12 & -0.304113 & -2.3752 & 0.989651 \tabularnewline
13 & -0.075083 & -0.5864 & 0.720121 \tabularnewline
14 & -0.154256 & -1.2048 & 0.883529 \tabularnewline
15 & -0.170347 & -1.3304 & 0.905839 \tabularnewline
16 & -0.106379 & -0.8308 & 0.795349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5926&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]0.507404[/C][C]3.963[/C][C]9.8e-05[/C][/ROW]
[ROW][C]1[/C][C]0.160618[/C][C]1.2545[/C][C]0.10723[/C][/ROW]
[ROW][C]2[/C][C]0.336623[/C][C]2.6291[/C][C]0.005409[/C][/ROW]
[ROW][C]3[/C][C]0.254827[/C][C]1.9903[/C][C]0.025524[/C][/ROW]
[ROW][C]4[/C][C]0.151996[/C][C]1.1871[/C][C]0.11989[/C][/ROW]
[ROW][C]5[/C][C]0.316042[/C][C]2.4684[/C][C]0.008196[/C][/ROW]
[ROW][C]6[/C][C]-0.239393[/C][C]-1.8697[/C][C]0.966838[/C][/ROW]
[ROW][C]7[/C][C]0.195371[/C][C]1.5259[/C][C]0.066102[/C][/ROW]
[ROW][C]8[/C][C]-0.200461[/C][C]-1.5657[/C][C]0.938698[/C][/ROW]
[ROW][C]9[/C][C]-0.343267[/C][C]-2.681[/C][C]0.995286[/C][/ROW]
[ROW][C]10[/C][C]0.151936[/C][C]1.1867[/C][C]0.119982[/C][/ROW]
[ROW][C]11[/C][C]0.37413[/C][C]2.9221[/C][C]0.002435[/C][/ROW]
[ROW][C]12[/C][C]-0.304113[/C][C]-2.3752[/C][C]0.989651[/C][/ROW]
[ROW][C]13[/C][C]-0.075083[/C][C]-0.5864[/C][C]0.720121[/C][/ROW]
[ROW][C]14[/C][C]-0.154256[/C][C]-1.2048[/C][C]0.883529[/C][/ROW]
[ROW][C]15[/C][C]-0.170347[/C][C]-1.3304[/C][C]0.905839[/C][/ROW]
[ROW][C]16[/C][C]-0.106379[/C][C]-0.8308[/C][C]0.795349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5926&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5926&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	0.507404	3.963	9.8e-05
1	0.160618	1.2545	0.10723
2	0.336623	2.6291	0.005409
3	0.254827	1.9903	0.025524
4	0.151996	1.1871	0.11989
5	0.316042	2.4684	0.008196
6	-0.239393	-1.8697	0.966838
7	0.195371	1.5259	0.066102
8	-0.200461	-1.5657	0.938698
9	-0.343267	-2.681	0.995286
10	0.151936	1.1867	0.119982
11	0.37413	2.9221	0.002435
12	-0.304113	-2.3752	0.989651
13	-0.075083	-0.5864	0.720121
14	-0.154256	-1.2048	0.883529
15	-0.170347	-1.3304	0.905839
16	-0.106379	-0.8308	0.795349

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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