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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 03:16:16 -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/t11958124744q7cyqb6hiybavo.htm/, Retrieved Mon, 29 Apr 2024 00:29:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6127, Retrieved Mon, 29 Apr 2024 00:29:38 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q2, groep 1

Estimated Impact

231

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 10:16:16] [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	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=6127&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=6127&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6127&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	8.2462	0
1	0.358411	2.9555	0.002143
2	0.390798	3.2226	0.000976
3	0.417395	3.4419	0.000496
4	0.197502	1.6286	0.054006
5	0.291382	2.4028	0.009502
6	0.23901	1.9709	0.026402
7	0.010447	0.0862	0.465799
8	0.128678	1.0611	0.146198
9	0.066916	0.5518	0.291445
10	0.009037	0.0745	0.470406
11	0.056181	0.4633	0.322323
12	-0.100611	-0.8297	0.795183
13	-0.047363	-0.3906	0.65133
14	0.047017	0.3877	0.349719
15	0.019249	0.1587	0.437177
16	-0.032566	-0.2685	0.605455
17	0.103854	0.8564	0.197391
18	0.036947	0.3047	0.380772

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.358411 & 2.9555 & 0.002143 \tabularnewline
2 & 0.390798 & 3.2226 & 0.000976 \tabularnewline
3 & 0.417395 & 3.4419 & 0.000496 \tabularnewline
4 & 0.197502 & 1.6286 & 0.054006 \tabularnewline
5 & 0.291382 & 2.4028 & 0.009502 \tabularnewline
6 & 0.23901 & 1.9709 & 0.026402 \tabularnewline
7 & 0.010447 & 0.0862 & 0.465799 \tabularnewline
8 & 0.128678 & 1.0611 & 0.146198 \tabularnewline
9 & 0.066916 & 0.5518 & 0.291445 \tabularnewline
10 & 0.009037 & 0.0745 & 0.470406 \tabularnewline
11 & 0.056181 & 0.4633 & 0.322323 \tabularnewline
12 & -0.100611 & -0.8297 & 0.795183 \tabularnewline
13 & -0.047363 & -0.3906 & 0.65133 \tabularnewline
14 & 0.047017 & 0.3877 & 0.349719 \tabularnewline
15 & 0.019249 & 0.1587 & 0.437177 \tabularnewline
16 & -0.032566 & -0.2685 & 0.605455 \tabularnewline
17 & 0.103854 & 0.8564 & 0.197391 \tabularnewline
18 & 0.036947 & 0.3047 & 0.380772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6127&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]8.2462[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.358411[/C][C]2.9555[/C][C]0.002143[/C][/ROW]
[ROW][C]2[/C][C]0.390798[/C][C]3.2226[/C][C]0.000976[/C][/ROW]
[ROW][C]3[/C][C]0.417395[/C][C]3.4419[/C][C]0.000496[/C][/ROW]
[ROW][C]4[/C][C]0.197502[/C][C]1.6286[/C][C]0.054006[/C][/ROW]
[ROW][C]5[/C][C]0.291382[/C][C]2.4028[/C][C]0.009502[/C][/ROW]
[ROW][C]6[/C][C]0.23901[/C][C]1.9709[/C][C]0.026402[/C][/ROW]
[ROW][C]7[/C][C]0.010447[/C][C]0.0862[/C][C]0.465799[/C][/ROW]
[ROW][C]8[/C][C]0.128678[/C][C]1.0611[/C][C]0.146198[/C][/ROW]
[ROW][C]9[/C][C]0.066916[/C][C]0.5518[/C][C]0.291445[/C][/ROW]
[ROW][C]10[/C][C]0.009037[/C][C]0.0745[/C][C]0.470406[/C][/ROW]
[ROW][C]11[/C][C]0.056181[/C][C]0.4633[/C][C]0.322323[/C][/ROW]
[ROW][C]12[/C][C]-0.100611[/C][C]-0.8297[/C][C]0.795183[/C][/ROW]
[ROW][C]13[/C][C]-0.047363[/C][C]-0.3906[/C][C]0.65133[/C][/ROW]
[ROW][C]14[/C][C]0.047017[/C][C]0.3877[/C][C]0.349719[/C][/ROW]
[ROW][C]15[/C][C]0.019249[/C][C]0.1587[/C][C]0.437177[/C][/ROW]
[ROW][C]16[/C][C]-0.032566[/C][C]-0.2685[/C][C]0.605455[/C][/ROW]
[ROW][C]17[/C][C]0.103854[/C][C]0.8564[/C][C]0.197391[/C][/ROW]
[ROW][C]18[/C][C]0.036947[/C][C]0.3047[/C][C]0.380772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6127&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6127&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	8.2462	0
1	0.358411	2.9555	0.002143
2	0.390798	3.2226	0.000976
3	0.417395	3.4419	0.000496
4	0.197502	1.6286	0.054006
5	0.291382	2.4028	0.009502
6	0.23901	1.9709	0.026402
7	0.010447	0.0862	0.465799
8	0.128678	1.0611	0.146198
9	0.066916	0.5518	0.291445
10	0.009037	0.0745	0.470406
11	0.056181	0.4633	0.322323
12	-0.100611	-0.8297	0.795183
13	-0.047363	-0.3906	0.65133
14	0.047017	0.3877	0.349719
15	0.019249	0.1587	0.437177
16	-0.032566	-0.2685	0.605455
17	0.103854	0.8564	0.197391
18	0.036947	0.3047	0.380772

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.358411	2.9555	0.002143
1	0.301006	2.4822	0.007767
2	0.266984	2.2016	0.015545
3	-0.082473	-0.6801	0.750622
4	0.092171	0.7601	0.224922
5	0.0475	0.3917	0.348255
6	-0.214897	-1.7721	0.95957
7	0.000596	0.0049	0.498046
8	0.032208	0.2656	0.395679
9	0.004936	0.0407	0.483825
10	-0.019045	-0.1571	0.562166
11	-0.127322	-1.0499	0.851265
12	0.018136	0.1496	0.440781
13	0.108559	0.8952	0.18692
14	0.109448	0.9025	0.184981
15	-0.098569	-0.8128	0.790421
16	0.134925	1.1126	0.134895
17	0.052958	0.4367	0.331856
18	-0.029475	-0.2431	0.595653

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.358411 & 2.9555 & 0.002143 \tabularnewline
1 & 0.301006 & 2.4822 & 0.007767 \tabularnewline
2 & 0.266984 & 2.2016 & 0.015545 \tabularnewline
3 & -0.082473 & -0.6801 & 0.750622 \tabularnewline
4 & 0.092171 & 0.7601 & 0.224922 \tabularnewline
5 & 0.0475 & 0.3917 & 0.348255 \tabularnewline
6 & -0.214897 & -1.7721 & 0.95957 \tabularnewline
7 & 0.000596 & 0.0049 & 0.498046 \tabularnewline
8 & 0.032208 & 0.2656 & 0.395679 \tabularnewline
9 & 0.004936 & 0.0407 & 0.483825 \tabularnewline
10 & -0.019045 & -0.1571 & 0.562166 \tabularnewline
11 & -0.127322 & -1.0499 & 0.851265 \tabularnewline
12 & 0.018136 & 0.1496 & 0.440781 \tabularnewline
13 & 0.108559 & 0.8952 & 0.18692 \tabularnewline
14 & 0.109448 & 0.9025 & 0.184981 \tabularnewline
15 & -0.098569 & -0.8128 & 0.790421 \tabularnewline
16 & 0.134925 & 1.1126 & 0.134895 \tabularnewline
17 & 0.052958 & 0.4367 & 0.331856 \tabularnewline
18 & -0.029475 & -0.2431 & 0.595653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6127&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]0.358411[/C][C]2.9555[/C][C]0.002143[/C][/ROW]
[ROW][C]1[/C][C]0.301006[/C][C]2.4822[/C][C]0.007767[/C][/ROW]
[ROW][C]2[/C][C]0.266984[/C][C]2.2016[/C][C]0.015545[/C][/ROW]
[ROW][C]3[/C][C]-0.082473[/C][C]-0.6801[/C][C]0.750622[/C][/ROW]
[ROW][C]4[/C][C]0.092171[/C][C]0.7601[/C][C]0.224922[/C][/ROW]
[ROW][C]5[/C][C]0.0475[/C][C]0.3917[/C][C]0.348255[/C][/ROW]
[ROW][C]6[/C][C]-0.214897[/C][C]-1.7721[/C][C]0.95957[/C][/ROW]
[ROW][C]7[/C][C]0.000596[/C][C]0.0049[/C][C]0.498046[/C][/ROW]
[ROW][C]8[/C][C]0.032208[/C][C]0.2656[/C][C]0.395679[/C][/ROW]
[ROW][C]9[/C][C]0.004936[/C][C]0.0407[/C][C]0.483825[/C][/ROW]
[ROW][C]10[/C][C]-0.019045[/C][C]-0.1571[/C][C]0.562166[/C][/ROW]
[ROW][C]11[/C][C]-0.127322[/C][C]-1.0499[/C][C]0.851265[/C][/ROW]
[ROW][C]12[/C][C]0.018136[/C][C]0.1496[/C][C]0.440781[/C][/ROW]
[ROW][C]13[/C][C]0.108559[/C][C]0.8952[/C][C]0.18692[/C][/ROW]
[ROW][C]14[/C][C]0.109448[/C][C]0.9025[/C][C]0.184981[/C][/ROW]
[ROW][C]15[/C][C]-0.098569[/C][C]-0.8128[/C][C]0.790421[/C][/ROW]
[ROW][C]16[/C][C]0.134925[/C][C]1.1126[/C][C]0.134895[/C][/ROW]
[ROW][C]17[/C][C]0.052958[/C][C]0.4367[/C][C]0.331856[/C][/ROW]
[ROW][C]18[/C][C]-0.029475[/C][C]-0.2431[/C][C]0.595653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6127&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6127&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	0.358411	2.9555	0.002143
1	0.301006	2.4822	0.007767
2	0.266984	2.2016	0.015545
3	-0.082473	-0.6801	0.750622
4	0.092171	0.7601	0.224922
5	0.0475	0.3917	0.348255
6	-0.214897	-1.7721	0.95957
7	0.000596	0.0049	0.498046
8	0.032208	0.2656	0.395679
9	0.004936	0.0407	0.483825
10	-0.019045	-0.1571	0.562166
11	-0.127322	-1.0499	0.851265
12	0.018136	0.1496	0.440781
13	0.108559	0.8952	0.18692
14	0.109448	0.9025	0.184981
15	-0.098569	-0.8128	0.790421
16	0.134925	1.1126	0.134895
17	0.052958	0.4367	0.331856
18	-0.029475	-0.2431	0.595653

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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