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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 12:43:06 -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/t1195760102rhv6skw4qe7n8ds.htm/, Retrieved Thu, 02 May 2024 21:29:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6094, Retrieved Thu, 02 May 2024 21:29:26 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

174

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

-       [(Partial) Autocorrelation Function] [Ws9Q2AFCE] [2007-11-22 19:43:06] [142ab5472309a9ae9a3b52678758dc4a] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6094&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]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=6094&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6094&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.73553	5.6974	0
2	0.395337	3.0623	0.001643
3	-0.016964	-0.1314	0.552052
4	-0.427668	-3.3127	0.999215
5	-0.722535	-5.5967	1
6	-0.789226	-6.1133	1
7	-0.676324	-5.2388	0.999999
8	-0.35126	-2.7208	0.995746
9	0.045738	0.3543	0.362184
10	0.385269	2.9843	0.002054
11	0.623374	4.8286	5e-06
12	0.765686	5.931	0
13	0.56979	4.4136	2.2e-05
14	0.306125	2.3712	0.010478
15	-0.033	-0.2556	0.60044
16	-0.334113	-2.588	0.993955

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.73553 & 5.6974 & 0 \tabularnewline
2 & 0.395337 & 3.0623 & 0.001643 \tabularnewline
3 & -0.016964 & -0.1314 & 0.552052 \tabularnewline
4 & -0.427668 & -3.3127 & 0.999215 \tabularnewline
5 & -0.722535 & -5.5967 & 1 \tabularnewline
6 & -0.789226 & -6.1133 & 1 \tabularnewline
7 & -0.676324 & -5.2388 & 0.999999 \tabularnewline
8 & -0.35126 & -2.7208 & 0.995746 \tabularnewline
9 & 0.045738 & 0.3543 & 0.362184 \tabularnewline
10 & 0.385269 & 2.9843 & 0.002054 \tabularnewline
11 & 0.623374 & 4.8286 & 5e-06 \tabularnewline
12 & 0.765686 & 5.931 & 0 \tabularnewline
13 & 0.56979 & 4.4136 & 2.2e-05 \tabularnewline
14 & 0.306125 & 2.3712 & 0.010478 \tabularnewline
15 & -0.033 & -0.2556 & 0.60044 \tabularnewline
16 & -0.334113 & -2.588 & 0.993955 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6094&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]0.73553[/C][C]5.6974[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.395337[/C][C]3.0623[/C][C]0.001643[/C][/ROW]
[ROW][C]3[/C][C]-0.016964[/C][C]-0.1314[/C][C]0.552052[/C][/ROW]
[ROW][C]4[/C][C]-0.427668[/C][C]-3.3127[/C][C]0.999215[/C][/ROW]
[ROW][C]5[/C][C]-0.722535[/C][C]-5.5967[/C][C]1[/C][/ROW]
[ROW][C]6[/C][C]-0.789226[/C][C]-6.1133[/C][C]1[/C][/ROW]
[ROW][C]7[/C][C]-0.676324[/C][C]-5.2388[/C][C]0.999999[/C][/ROW]
[ROW][C]8[/C][C]-0.35126[/C][C]-2.7208[/C][C]0.995746[/C][/ROW]
[ROW][C]9[/C][C]0.045738[/C][C]0.3543[/C][C]0.362184[/C][/ROW]
[ROW][C]10[/C][C]0.385269[/C][C]2.9843[/C][C]0.002054[/C][/ROW]
[ROW][C]11[/C][C]0.623374[/C][C]4.8286[/C][C]5e-06[/C][/ROW]
[ROW][C]12[/C][C]0.765686[/C][C]5.931[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.56979[/C][C]4.4136[/C][C]2.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.306125[/C][C]2.3712[/C][C]0.010478[/C][/ROW]
[ROW][C]15[/C][C]-0.033[/C][C]-0.2556[/C][C]0.60044[/C][/ROW]
[ROW][C]16[/C][C]-0.334113[/C][C]-2.588[/C][C]0.993955[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6094&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6094&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	0.73553	5.6974	0
2	0.395337	3.0623	0.001643
3	-0.016964	-0.1314	0.552052
4	-0.427668	-3.3127	0.999215
5	-0.722535	-5.5967	1
6	-0.789226	-6.1133	1
7	-0.676324	-5.2388	0.999999
8	-0.35126	-2.7208	0.995746
9	0.045738	0.3543	0.362184
10	0.385269	2.9843	0.002054
11	0.623374	4.8286	5e-06
12	0.765686	5.931	0
13	0.56979	4.4136	2.2e-05
14	0.306125	2.3712	0.010478
15	-0.033	-0.2556	0.60044
16	-0.334113	-2.588	0.993955

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.73553	5.6974	0
1	-0.317362	-2.4583	0.991568
2	-0.403618	-3.1264	0.998636
3	-0.421614	-3.2658	0.999097
4	-0.36748	-2.8465	0.996979
5	-0.163209	-1.2642	0.894478
6	-0.211195	-1.6359	0.946453
7	0.027032	0.2094	0.417428
8	0.007388	0.0572	0.477277
9	-0.109021	-0.8445	0.79912
10	-0.036075	-0.2794	0.609565
11	0.305641	2.3675	0.010576
12	-0.286349	-2.218	0.984826
13	0.10409	0.8063	0.211633
14	0.021609	0.1674	0.433816
15	0.165227	1.2798	0.102764
16	-0.00516	-0.04	0.515875

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.73553 & 5.6974 & 0 \tabularnewline
1 & -0.317362 & -2.4583 & 0.991568 \tabularnewline
2 & -0.403618 & -3.1264 & 0.998636 \tabularnewline
3 & -0.421614 & -3.2658 & 0.999097 \tabularnewline
4 & -0.36748 & -2.8465 & 0.996979 \tabularnewline
5 & -0.163209 & -1.2642 & 0.894478 \tabularnewline
6 & -0.211195 & -1.6359 & 0.946453 \tabularnewline
7 & 0.027032 & 0.2094 & 0.417428 \tabularnewline
8 & 0.007388 & 0.0572 & 0.477277 \tabularnewline
9 & -0.109021 & -0.8445 & 0.79912 \tabularnewline
10 & -0.036075 & -0.2794 & 0.609565 \tabularnewline
11 & 0.305641 & 2.3675 & 0.010576 \tabularnewline
12 & -0.286349 & -2.218 & 0.984826 \tabularnewline
13 & 0.10409 & 0.8063 & 0.211633 \tabularnewline
14 & 0.021609 & 0.1674 & 0.433816 \tabularnewline
15 & 0.165227 & 1.2798 & 0.102764 \tabularnewline
16 & -0.00516 & -0.04 & 0.515875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6094&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]0.73553[/C][C]5.6974[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.317362[/C][C]-2.4583[/C][C]0.991568[/C][/ROW]
[ROW][C]2[/C][C]-0.403618[/C][C]-3.1264[/C][C]0.998636[/C][/ROW]
[ROW][C]3[/C][C]-0.421614[/C][C]-3.2658[/C][C]0.999097[/C][/ROW]
[ROW][C]4[/C][C]-0.36748[/C][C]-2.8465[/C][C]0.996979[/C][/ROW]
[ROW][C]5[/C][C]-0.163209[/C][C]-1.2642[/C][C]0.894478[/C][/ROW]
[ROW][C]6[/C][C]-0.211195[/C][C]-1.6359[/C][C]0.946453[/C][/ROW]
[ROW][C]7[/C][C]0.027032[/C][C]0.2094[/C][C]0.417428[/C][/ROW]
[ROW][C]8[/C][C]0.007388[/C][C]0.0572[/C][C]0.477277[/C][/ROW]
[ROW][C]9[/C][C]-0.109021[/C][C]-0.8445[/C][C]0.79912[/C][/ROW]
[ROW][C]10[/C][C]-0.036075[/C][C]-0.2794[/C][C]0.609565[/C][/ROW]
[ROW][C]11[/C][C]0.305641[/C][C]2.3675[/C][C]0.010576[/C][/ROW]
[ROW][C]12[/C][C]-0.286349[/C][C]-2.218[/C][C]0.984826[/C][/ROW]
[ROW][C]13[/C][C]0.10409[/C][C]0.8063[/C][C]0.211633[/C][/ROW]
[ROW][C]14[/C][C]0.021609[/C][C]0.1674[/C][C]0.433816[/C][/ROW]
[ROW][C]15[/C][C]0.165227[/C][C]1.2798[/C][C]0.102764[/C][/ROW]
[ROW][C]16[/C][C]-0.00516[/C][C]-0.04[/C][C]0.515875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6094&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6094&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	0.73553	5.6974	0
1	-0.317362	-2.4583	0.991568
2	-0.403618	-3.1264	0.998636
3	-0.421614	-3.2658	0.999097
4	-0.36748	-2.8465	0.996979
5	-0.163209	-1.2642	0.894478
6	-0.211195	-1.6359	0.946453
7	0.027032	0.2094	0.417428
8	0.007388	0.0572	0.477277
9	-0.109021	-0.8445	0.79912
10	-0.036075	-0.2794	0.609565
11	0.305641	2.3675	0.010576
12	-0.286349	-2.218	0.984826
13	0.10409	0.8063	0.211633
14	0.021609	0.1674	0.433816
15	0.165227	1.2798	0.102764
16	-0.00516	-0.04	0.515875

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.5 ; 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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Input Parameters & R Code