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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 03:19:49 -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/Nov/23/t1195812678pw837frrfy108tf.htm/, Retrieved Sun, 28 Apr 2024 22:48:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6128, Retrieved Sun, 28 Apr 2024 22:48:30 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q2, groep 1

Estimated Impact

205

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

-       [(Partial) Autocorrelation Function] [Q2, groep 1] [2007-11-23 10:19:49] [ce556af355e2eff84137e549c6ea8397] [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=6128&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=6128&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6128&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	8.9443	0
1	0.295523	2.6432	0.004939
2	0.075117	0.6719	0.251802
3	0.210671	1.8843	0.031578
4	0.087842	0.7857	0.217188
5	0.320171	2.8637	0.002673
6	0.502284	4.4926	1.2e-05
7	0.255259	2.2831	0.012539
8	0.058872	0.5266	0.299974
9	0.052852	0.4727	0.31885
10	-0.144946	-1.2964	0.900724
11	0.08246	0.7375	0.231475
12	0.574813	5.1413	1e-06
13	0.041317	0.3696	0.356346
14	-0.097886	-0.8755	0.808043
15	-0.018504	-0.1655	0.565516
16	-0.132805	-1.1878	0.880795
17	0.093724	0.8383	0.202181
18	0.276274	2.4711	0.007798

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.295523 & 2.6432 & 0.004939 \tabularnewline
2 & 0.075117 & 0.6719 & 0.251802 \tabularnewline
3 & 0.210671 & 1.8843 & 0.031578 \tabularnewline
4 & 0.087842 & 0.7857 & 0.217188 \tabularnewline
5 & 0.320171 & 2.8637 & 0.002673 \tabularnewline
6 & 0.502284 & 4.4926 & 1.2e-05 \tabularnewline
7 & 0.255259 & 2.2831 & 0.012539 \tabularnewline
8 & 0.058872 & 0.5266 & 0.299974 \tabularnewline
9 & 0.052852 & 0.4727 & 0.31885 \tabularnewline
10 & -0.144946 & -1.2964 & 0.900724 \tabularnewline
11 & 0.08246 & 0.7375 & 0.231475 \tabularnewline
12 & 0.574813 & 5.1413 & 1e-06 \tabularnewline
13 & 0.041317 & 0.3696 & 0.356346 \tabularnewline
14 & -0.097886 & -0.8755 & 0.808043 \tabularnewline
15 & -0.018504 & -0.1655 & 0.565516 \tabularnewline
16 & -0.132805 & -1.1878 & 0.880795 \tabularnewline
17 & 0.093724 & 0.8383 & 0.202181 \tabularnewline
18 & 0.276274 & 2.4711 & 0.007798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6128&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]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.295523[/C][C]2.6432[/C][C]0.004939[/C][/ROW]
[ROW][C]2[/C][C]0.075117[/C][C]0.6719[/C][C]0.251802[/C][/ROW]
[ROW][C]3[/C][C]0.210671[/C][C]1.8843[/C][C]0.031578[/C][/ROW]
[ROW][C]4[/C][C]0.087842[/C][C]0.7857[/C][C]0.217188[/C][/ROW]
[ROW][C]5[/C][C]0.320171[/C][C]2.8637[/C][C]0.002673[/C][/ROW]
[ROW][C]6[/C][C]0.502284[/C][C]4.4926[/C][C]1.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.255259[/C][C]2.2831[/C][C]0.012539[/C][/ROW]
[ROW][C]8[/C][C]0.058872[/C][C]0.5266[/C][C]0.299974[/C][/ROW]
[ROW][C]9[/C][C]0.052852[/C][C]0.4727[/C][C]0.31885[/C][/ROW]
[ROW][C]10[/C][C]-0.144946[/C][C]-1.2964[/C][C]0.900724[/C][/ROW]
[ROW][C]11[/C][C]0.08246[/C][C]0.7375[/C][C]0.231475[/C][/ROW]
[ROW][C]12[/C][C]0.574813[/C][C]5.1413[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.041317[/C][C]0.3696[/C][C]0.356346[/C][/ROW]
[ROW][C]14[/C][C]-0.097886[/C][C]-0.8755[/C][C]0.808043[/C][/ROW]
[ROW][C]15[/C][C]-0.018504[/C][C]-0.1655[/C][C]0.565516[/C][/ROW]
[ROW][C]16[/C][C]-0.132805[/C][C]-1.1878[/C][C]0.880795[/C][/ROW]
[ROW][C]17[/C][C]0.093724[/C][C]0.8383[/C][C]0.202181[/C][/ROW]
[ROW][C]18[/C][C]0.276274[/C][C]2.4711[/C][C]0.007798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6128&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6128&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	8.9443	0
1	0.295523	2.6432	0.004939
2	0.075117	0.6719	0.251802
3	0.210671	1.8843	0.031578
4	0.087842	0.7857	0.217188
5	0.320171	2.8637	0.002673
6	0.502284	4.4926	1.2e-05
7	0.255259	2.2831	0.012539
8	0.058872	0.5266	0.299974
9	0.052852	0.4727	0.31885
10	-0.144946	-1.2964	0.900724
11	0.08246	0.7375	0.231475
12	0.574813	5.1413	1e-06
13	0.041317	0.3696	0.356346
14	-0.097886	-0.8755	0.808043
15	-0.018504	-0.1655	0.565516
16	-0.132805	-1.1878	0.880795
17	0.093724	0.8383	0.202181
18	0.276274	2.4711	0.007798

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.295523	2.6432	0.004939
1	-0.013386	-0.1197	0.547499
2	0.210554	1.8833	0.03165
3	-0.037068	-0.3315	0.62945
4	0.349002	3.1216	0.001252
5	0.35023	3.1325	0.001211
6	0.107099	0.9579	0.170495
7	-0.106942	-0.9565	0.829154
8	-0.094083	-0.8415	0.798712
9	-0.399945	-3.5772	0.999703
10	-0.117276	-1.0489	0.85132
11	0.513716	4.5948	8e-06
12	-0.230209	-2.0591	0.978629
13	-0.040807	-0.365	0.641958
14	-0.008432	-0.0754	0.529963
15	0.124733	1.1156	0.133956
16	-0.052562	-0.4701	0.68023
17	0.02522	0.2256	0.411053
18	-0.050628	-0.4528	0.674052

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.295523 & 2.6432 & 0.004939 \tabularnewline
1 & -0.013386 & -0.1197 & 0.547499 \tabularnewline
2 & 0.210554 & 1.8833 & 0.03165 \tabularnewline
3 & -0.037068 & -0.3315 & 0.62945 \tabularnewline
4 & 0.349002 & 3.1216 & 0.001252 \tabularnewline
5 & 0.35023 & 3.1325 & 0.001211 \tabularnewline
6 & 0.107099 & 0.9579 & 0.170495 \tabularnewline
7 & -0.106942 & -0.9565 & 0.829154 \tabularnewline
8 & -0.094083 & -0.8415 & 0.798712 \tabularnewline
9 & -0.399945 & -3.5772 & 0.999703 \tabularnewline
10 & -0.117276 & -1.0489 & 0.85132 \tabularnewline
11 & 0.513716 & 4.5948 & 8e-06 \tabularnewline
12 & -0.230209 & -2.0591 & 0.978629 \tabularnewline
13 & -0.040807 & -0.365 & 0.641958 \tabularnewline
14 & -0.008432 & -0.0754 & 0.529963 \tabularnewline
15 & 0.124733 & 1.1156 & 0.133956 \tabularnewline
16 & -0.052562 & -0.4701 & 0.68023 \tabularnewline
17 & 0.02522 & 0.2256 & 0.411053 \tabularnewline
18 & -0.050628 & -0.4528 & 0.674052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6128&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]0.295523[/C][C]2.6432[/C][C]0.004939[/C][/ROW]
[ROW][C]1[/C][C]-0.013386[/C][C]-0.1197[/C][C]0.547499[/C][/ROW]
[ROW][C]2[/C][C]0.210554[/C][C]1.8833[/C][C]0.03165[/C][/ROW]
[ROW][C]3[/C][C]-0.037068[/C][C]-0.3315[/C][C]0.62945[/C][/ROW]
[ROW][C]4[/C][C]0.349002[/C][C]3.1216[/C][C]0.001252[/C][/ROW]
[ROW][C]5[/C][C]0.35023[/C][C]3.1325[/C][C]0.001211[/C][/ROW]
[ROW][C]6[/C][C]0.107099[/C][C]0.9579[/C][C]0.170495[/C][/ROW]
[ROW][C]7[/C][C]-0.106942[/C][C]-0.9565[/C][C]0.829154[/C][/ROW]
[ROW][C]8[/C][C]-0.094083[/C][C]-0.8415[/C][C]0.798712[/C][/ROW]
[ROW][C]9[/C][C]-0.399945[/C][C]-3.5772[/C][C]0.999703[/C][/ROW]
[ROW][C]10[/C][C]-0.117276[/C][C]-1.0489[/C][C]0.85132[/C][/ROW]
[ROW][C]11[/C][C]0.513716[/C][C]4.5948[/C][C]8e-06[/C][/ROW]
[ROW][C]12[/C][C]-0.230209[/C][C]-2.0591[/C][C]0.978629[/C][/ROW]
[ROW][C]13[/C][C]-0.040807[/C][C]-0.365[/C][C]0.641958[/C][/ROW]
[ROW][C]14[/C][C]-0.008432[/C][C]-0.0754[/C][C]0.529963[/C][/ROW]
[ROW][C]15[/C][C]0.124733[/C][C]1.1156[/C][C]0.133956[/C][/ROW]
[ROW][C]16[/C][C]-0.052562[/C][C]-0.4701[/C][C]0.68023[/C][/ROW]
[ROW][C]17[/C][C]0.02522[/C][C]0.2256[/C][C]0.411053[/C][/ROW]
[ROW][C]18[/C][C]-0.050628[/C][C]-0.4528[/C][C]0.674052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6128&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6128&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	0.295523	2.6432	0.004939
1	-0.013386	-0.1197	0.547499
2	0.210554	1.8833	0.03165
3	-0.037068	-0.3315	0.62945
4	0.349002	3.1216	0.001252
5	0.35023	3.1325	0.001211
6	0.107099	0.9579	0.170495
7	-0.106942	-0.9565	0.829154
8	-0.094083	-0.8415	0.798712
9	-0.399945	-3.5772	0.999703
10	-0.117276	-1.0489	0.85132
11	0.513716	4.5948	8e-06
12	-0.230209	-2.0591	0.978629
13	-0.040807	-0.365	0.641958
14	-0.008432	-0.0754	0.529963
15	0.124733	1.1156	0.133956
16	-0.052562	-0.4701	0.68023
17	0.02522	0.2256	0.411053
18	-0.050628	-0.4528	0.674052

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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