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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 14:08:49 -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/16/t1197838350wbmciq98fwz255e.htm/, Retrieved Thu, 02 May 2024 07:13:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4267, Retrieved Thu, 02 May 2024 07:13:03 +0000

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Estimated Impact

180

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

-       [(Partial) Autocorrelation Function] [] [2007-12-16 21:08:49] [ba3202e2798d2e4685d19d988e9c69df] [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=4267&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=4267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4267&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	8.4853	0
1	0.732888	6.2188	0
2	0.372233	3.1585	0.001159
3	0.008928	0.0758	0.469911
4	-0.325973	-2.766	0.996397
5	-0.564911	-4.7934	0.999996
6	-0.634608	-5.3848	1
7	-0.443835	-3.7661	0.999832
8	-0.210363	-1.785	0.960762
9	0.097424	0.8267	0.205577
10	0.378044	3.2078	0.000999
11	0.64011	5.4315	0
12	0.727173	6.1703	0
13	0.489141	4.1505	4.5e-05
14	0.203361	1.7256	0.044357
15	-0.109023	-0.9251	0.820997
16	-0.3788	-3.2142	0.999021
17	-0.55654	-4.7224	0.999994

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.732888 & 6.2188 & 0 \tabularnewline
2 & 0.372233 & 3.1585 & 0.001159 \tabularnewline
3 & 0.008928 & 0.0758 & 0.469911 \tabularnewline
4 & -0.325973 & -2.766 & 0.996397 \tabularnewline
5 & -0.564911 & -4.7934 & 0.999996 \tabularnewline
6 & -0.634608 & -5.3848 & 1 \tabularnewline
7 & -0.443835 & -3.7661 & 0.999832 \tabularnewline
8 & -0.210363 & -1.785 & 0.960762 \tabularnewline
9 & 0.097424 & 0.8267 & 0.205577 \tabularnewline
10 & 0.378044 & 3.2078 & 0.000999 \tabularnewline
11 & 0.64011 & 5.4315 & 0 \tabularnewline
12 & 0.727173 & 6.1703 & 0 \tabularnewline
13 & 0.489141 & 4.1505 & 4.5e-05 \tabularnewline
14 & 0.203361 & 1.7256 & 0.044357 \tabularnewline
15 & -0.109023 & -0.9251 & 0.820997 \tabularnewline
16 & -0.3788 & -3.2142 & 0.999021 \tabularnewline
17 & -0.55654 & -4.7224 & 0.999994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4267&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.732888[/C][C]6.2188[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.372233[/C][C]3.1585[/C][C]0.001159[/C][/ROW]
[ROW][C]3[/C][C]0.008928[/C][C]0.0758[/C][C]0.469911[/C][/ROW]
[ROW][C]4[/C][C]-0.325973[/C][C]-2.766[/C][C]0.996397[/C][/ROW]
[ROW][C]5[/C][C]-0.564911[/C][C]-4.7934[/C][C]0.999996[/C][/ROW]
[ROW][C]6[/C][C]-0.634608[/C][C]-5.3848[/C][C]1[/C][/ROW]
[ROW][C]7[/C][C]-0.443835[/C][C]-3.7661[/C][C]0.999832[/C][/ROW]
[ROW][C]8[/C][C]-0.210363[/C][C]-1.785[/C][C]0.960762[/C][/ROW]
[ROW][C]9[/C][C]0.097424[/C][C]0.8267[/C][C]0.205577[/C][/ROW]
[ROW][C]10[/C][C]0.378044[/C][C]3.2078[/C][C]0.000999[/C][/ROW]
[ROW][C]11[/C][C]0.64011[/C][C]5.4315[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.727173[/C][C]6.1703[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.489141[/C][C]4.1505[/C][C]4.5e-05[/C][/ROW]
[ROW][C]14[/C][C]0.203361[/C][C]1.7256[/C][C]0.044357[/C][/ROW]
[ROW][C]15[/C][C]-0.109023[/C][C]-0.9251[/C][C]0.820997[/C][/ROW]
[ROW][C]16[/C][C]-0.3788[/C][C]-3.2142[/C][C]0.999021[/C][/ROW]
[ROW][C]17[/C][C]-0.55654[/C][C]-4.7224[/C][C]0.999994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4267&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	8.4853	0
1	0.732888	6.2188	0
2	0.372233	3.1585	0.001159
3	0.008928	0.0758	0.469911
4	-0.325973	-2.766	0.996397
5	-0.564911	-4.7934	0.999996
6	-0.634608	-5.3848	1
7	-0.443835	-3.7661	0.999832
8	-0.210363	-1.785	0.960762
9	0.097424	0.8267	0.205577
10	0.378044	3.2078	0.000999
11	0.64011	5.4315	0
12	0.727173	6.1703	0
13	0.489141	4.1505	4.5e-05
14	0.203361	1.7256	0.044357
15	-0.109023	-0.9251	0.820997
16	-0.3788	-3.2142	0.999021
17	-0.55654	-4.7224	0.999994

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.732888	6.2188	0
1	-0.356234	-3.0227	0.998266
2	-0.247393	-2.0992	0.980347
3	-0.294358	-2.4977	0.992607
4	-0.241044	-2.0453	0.977761
5	-0.114979	-0.9756	0.833743
6	0.23253	1.9731	0.026163
7	-0.121487	-1.0309	0.846969
8	0.198408	1.6835	0.0483
9	0.07639	0.6482	0.259462
10	0.420686	3.5696	0.000321
11	0.16023	1.3596	0.0891
12	-0.293021	-2.4864	0.992387
13	0.060658	0.5147	0.304169
14	0.031954	0.2711	0.39353
15	0.004654	0.0395	0.484304
16	0.024093	0.2044	0.419295
17	-0.231238	-1.9621	0.973193

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.732888 & 6.2188 & 0 \tabularnewline
1 & -0.356234 & -3.0227 & 0.998266 \tabularnewline
2 & -0.247393 & -2.0992 & 0.980347 \tabularnewline
3 & -0.294358 & -2.4977 & 0.992607 \tabularnewline
4 & -0.241044 & -2.0453 & 0.977761 \tabularnewline
5 & -0.114979 & -0.9756 & 0.833743 \tabularnewline
6 & 0.23253 & 1.9731 & 0.026163 \tabularnewline
7 & -0.121487 & -1.0309 & 0.846969 \tabularnewline
8 & 0.198408 & 1.6835 & 0.0483 \tabularnewline
9 & 0.07639 & 0.6482 & 0.259462 \tabularnewline
10 & 0.420686 & 3.5696 & 0.000321 \tabularnewline
11 & 0.16023 & 1.3596 & 0.0891 \tabularnewline
12 & -0.293021 & -2.4864 & 0.992387 \tabularnewline
13 & 0.060658 & 0.5147 & 0.304169 \tabularnewline
14 & 0.031954 & 0.2711 & 0.39353 \tabularnewline
15 & 0.004654 & 0.0395 & 0.484304 \tabularnewline
16 & 0.024093 & 0.2044 & 0.419295 \tabularnewline
17 & -0.231238 & -1.9621 & 0.973193 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4267&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]0.732888[/C][C]6.2188[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.356234[/C][C]-3.0227[/C][C]0.998266[/C][/ROW]
[ROW][C]2[/C][C]-0.247393[/C][C]-2.0992[/C][C]0.980347[/C][/ROW]
[ROW][C]3[/C][C]-0.294358[/C][C]-2.4977[/C][C]0.992607[/C][/ROW]
[ROW][C]4[/C][C]-0.241044[/C][C]-2.0453[/C][C]0.977761[/C][/ROW]
[ROW][C]5[/C][C]-0.114979[/C][C]-0.9756[/C][C]0.833743[/C][/ROW]
[ROW][C]6[/C][C]0.23253[/C][C]1.9731[/C][C]0.026163[/C][/ROW]
[ROW][C]7[/C][C]-0.121487[/C][C]-1.0309[/C][C]0.846969[/C][/ROW]
[ROW][C]8[/C][C]0.198408[/C][C]1.6835[/C][C]0.0483[/C][/ROW]
[ROW][C]9[/C][C]0.07639[/C][C]0.6482[/C][C]0.259462[/C][/ROW]
[ROW][C]10[/C][C]0.420686[/C][C]3.5696[/C][C]0.000321[/C][/ROW]
[ROW][C]11[/C][C]0.16023[/C][C]1.3596[/C][C]0.0891[/C][/ROW]
[ROW][C]12[/C][C]-0.293021[/C][C]-2.4864[/C][C]0.992387[/C][/ROW]
[ROW][C]13[/C][C]0.060658[/C][C]0.5147[/C][C]0.304169[/C][/ROW]
[ROW][C]14[/C][C]0.031954[/C][C]0.2711[/C][C]0.39353[/C][/ROW]
[ROW][C]15[/C][C]0.004654[/C][C]0.0395[/C][C]0.484304[/C][/ROW]
[ROW][C]16[/C][C]0.024093[/C][C]0.2044[/C][C]0.419295[/C][/ROW]
[ROW][C]17[/C][C]-0.231238[/C][C]-1.9621[/C][C]0.973193[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4267&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4267&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	0.732888	6.2188	0
1	-0.356234	-3.0227	0.998266
2	-0.247393	-2.0992	0.980347
3	-0.294358	-2.4977	0.992607
4	-0.241044	-2.0453	0.977761
5	-0.114979	-0.9756	0.833743
6	0.23253	1.9731	0.026163
7	-0.121487	-1.0309	0.846969
8	0.198408	1.6835	0.0483
9	0.07639	0.6482	0.259462
10	0.420686	3.5696	0.000321
11	0.16023	1.3596	0.0891
12	-0.293021	-2.4864	0.992387
13	0.060658	0.5147	0.304169
14	0.031954	0.2711	0.39353
15	0.004654	0.0395	0.484304
16	0.024093	0.2044	0.419295
17	-0.231238	-1.9621	0.973193

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 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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