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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:16:20 -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/24/t1195913296qv0y3k0iegrl8wo.htm/, Retrieved Fri, 03 May 2024 14:56:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6309, Retrieved Fri, 03 May 2024 14:56:10 +0000

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Estimated Impact

231

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

-       [(Partial) Autocorrelation Function] [WS7Q2.2.2] [2007-11-24 14:16:20] [77c9c0d97755c69877fabe95ec1f485a] [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=6309&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=6309&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6309&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	9.6437	0
1	0.96882	9.343	0
2	0.937528	9.0412	0
3	0.906055	8.7377	0
4	0.874573	8.4341	0
5	0.842398	8.1238	0
6	0.81003	7.8116	0
7	0.777291	7.4959	0
8	0.74462	7.1809	0
9	0.711743	6.8638	0
10	0.679103	6.549	0
11	0.646313	6.2328	0
12	0.612711	5.9088	0
13	0.578434	5.5782	0
14	0.545321	5.2589	0
15	0.512031	4.9378	2e-06
16	0.478862	4.618	6e-06
17	0.445632	4.2975	2.1e-05
18	0.412515	3.9781	6.9e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6437 & 0 \tabularnewline
1 & 0.96882 & 9.343 & 0 \tabularnewline
2 & 0.937528 & 9.0412 & 0 \tabularnewline
3 & 0.906055 & 8.7377 & 0 \tabularnewline
4 & 0.874573 & 8.4341 & 0 \tabularnewline
5 & 0.842398 & 8.1238 & 0 \tabularnewline
6 & 0.81003 & 7.8116 & 0 \tabularnewline
7 & 0.777291 & 7.4959 & 0 \tabularnewline
8 & 0.74462 & 7.1809 & 0 \tabularnewline
9 & 0.711743 & 6.8638 & 0 \tabularnewline
10 & 0.679103 & 6.549 & 0 \tabularnewline
11 & 0.646313 & 6.2328 & 0 \tabularnewline
12 & 0.612711 & 5.9088 & 0 \tabularnewline
13 & 0.578434 & 5.5782 & 0 \tabularnewline
14 & 0.545321 & 5.2589 & 0 \tabularnewline
15 & 0.512031 & 4.9378 & 2e-06 \tabularnewline
16 & 0.478862 & 4.618 & 6e-06 \tabularnewline
17 & 0.445632 & 4.2975 & 2.1e-05 \tabularnewline
18 & 0.412515 & 3.9781 & 6.9e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6309&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]9.6437[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.96882[/C][C]9.343[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.937528[/C][C]9.0412[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.906055[/C][C]8.7377[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.874573[/C][C]8.4341[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.842398[/C][C]8.1238[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.81003[/C][C]7.8116[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.777291[/C][C]7.4959[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.74462[/C][C]7.1809[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.711743[/C][C]6.8638[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.679103[/C][C]6.549[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.646313[/C][C]6.2328[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.612711[/C][C]5.9088[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.578434[/C][C]5.5782[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.545321[/C][C]5.2589[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.512031[/C][C]4.9378[/C][C]2e-06[/C][/ROW]
[ROW][C]16[/C][C]0.478862[/C][C]4.618[/C][C]6e-06[/C][/ROW]
[ROW][C]17[/C][C]0.445632[/C][C]4.2975[/C][C]2.1e-05[/C][/ROW]
[ROW][C]18[/C][C]0.412515[/C][C]3.9781[/C][C]6.9e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6309&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6309&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	9.6437	0
1	0.96882	9.343	0
2	0.937528	9.0412	0
3	0.906055	8.7377	0
4	0.874573	8.4341	0
5	0.842398	8.1238	0
6	0.81003	7.8116	0
7	0.777291	7.4959	0
8	0.74462	7.1809	0
9	0.711743	6.8638	0
10	0.679103	6.549	0
11	0.646313	6.2328	0
12	0.612711	5.9088	0
13	0.578434	5.5782	0
14	0.545321	5.2589	0
15	0.512031	4.9378	2e-06
16	0.478862	4.618	6e-06
17	0.445632	4.2975	2.1e-05
18	0.412515	3.9781	6.9e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.96882	9.343	0
1	-0.017646	-0.1702	0.567377
2	-0.019116	-0.1844	0.57293
3	-0.016642	-0.1605	0.563579
4	-0.028078	-0.2708	0.606416
5	-0.020591	-0.1986	0.578484
6	-0.023856	-0.2301	0.590723
7	-0.017309	-0.1669	0.566103
8	-0.021937	-0.2116	0.58354
9	-0.015274	-0.1473	0.558392
10	-0.021754	-0.2098	0.582854
11	-0.033198	-0.3201	0.625213
12	-0.031778	-0.3065	0.620027
13	-0.002675	-0.0258	0.510264
14	-0.024282	-0.2342	0.592316
15	-0.019877	-0.1917	0.575799
16	-0.023058	-0.2224	0.587741
17	-0.021376	-0.2061	0.581437
18	-0.030691	-0.296	0.616046

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.96882 & 9.343 & 0 \tabularnewline
1 & -0.017646 & -0.1702 & 0.567377 \tabularnewline
2 & -0.019116 & -0.1844 & 0.57293 \tabularnewline
3 & -0.016642 & -0.1605 & 0.563579 \tabularnewline
4 & -0.028078 & -0.2708 & 0.606416 \tabularnewline
5 & -0.020591 & -0.1986 & 0.578484 \tabularnewline
6 & -0.023856 & -0.2301 & 0.590723 \tabularnewline
7 & -0.017309 & -0.1669 & 0.566103 \tabularnewline
8 & -0.021937 & -0.2116 & 0.58354 \tabularnewline
9 & -0.015274 & -0.1473 & 0.558392 \tabularnewline
10 & -0.021754 & -0.2098 & 0.582854 \tabularnewline
11 & -0.033198 & -0.3201 & 0.625213 \tabularnewline
12 & -0.031778 & -0.3065 & 0.620027 \tabularnewline
13 & -0.002675 & -0.0258 & 0.510264 \tabularnewline
14 & -0.024282 & -0.2342 & 0.592316 \tabularnewline
15 & -0.019877 & -0.1917 & 0.575799 \tabularnewline
16 & -0.023058 & -0.2224 & 0.587741 \tabularnewline
17 & -0.021376 & -0.2061 & 0.581437 \tabularnewline
18 & -0.030691 & -0.296 & 0.616046 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6309&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]0.96882[/C][C]9.343[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.017646[/C][C]-0.1702[/C][C]0.567377[/C][/ROW]
[ROW][C]2[/C][C]-0.019116[/C][C]-0.1844[/C][C]0.57293[/C][/ROW]
[ROW][C]3[/C][C]-0.016642[/C][C]-0.1605[/C][C]0.563579[/C][/ROW]
[ROW][C]4[/C][C]-0.028078[/C][C]-0.2708[/C][C]0.606416[/C][/ROW]
[ROW][C]5[/C][C]-0.020591[/C][C]-0.1986[/C][C]0.578484[/C][/ROW]
[ROW][C]6[/C][C]-0.023856[/C][C]-0.2301[/C][C]0.590723[/C][/ROW]
[ROW][C]7[/C][C]-0.017309[/C][C]-0.1669[/C][C]0.566103[/C][/ROW]
[ROW][C]8[/C][C]-0.021937[/C][C]-0.2116[/C][C]0.58354[/C][/ROW]
[ROW][C]9[/C][C]-0.015274[/C][C]-0.1473[/C][C]0.558392[/C][/ROW]
[ROW][C]10[/C][C]-0.021754[/C][C]-0.2098[/C][C]0.582854[/C][/ROW]
[ROW][C]11[/C][C]-0.033198[/C][C]-0.3201[/C][C]0.625213[/C][/ROW]
[ROW][C]12[/C][C]-0.031778[/C][C]-0.3065[/C][C]0.620027[/C][/ROW]
[ROW][C]13[/C][C]-0.002675[/C][C]-0.0258[/C][C]0.510264[/C][/ROW]
[ROW][C]14[/C][C]-0.024282[/C][C]-0.2342[/C][C]0.592316[/C][/ROW]
[ROW][C]15[/C][C]-0.019877[/C][C]-0.1917[/C][C]0.575799[/C][/ROW]
[ROW][C]16[/C][C]-0.023058[/C][C]-0.2224[/C][C]0.587741[/C][/ROW]
[ROW][C]17[/C][C]-0.021376[/C][C]-0.2061[/C][C]0.581437[/C][/ROW]
[ROW][C]18[/C][C]-0.030691[/C][C]-0.296[/C][C]0.616046[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6309&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6309&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	0.96882	9.343	0
1	-0.017646	-0.1702	0.567377
2	-0.019116	-0.1844	0.57293
3	-0.016642	-0.1605	0.563579
4	-0.028078	-0.2708	0.606416
5	-0.020591	-0.1986	0.578484
6	-0.023856	-0.2301	0.590723
7	-0.017309	-0.1669	0.566103
8	-0.021937	-0.2116	0.58354
9	-0.015274	-0.1473	0.558392
10	-0.021754	-0.2098	0.582854
11	-0.033198	-0.3201	0.625213
12	-0.031778	-0.3065	0.620027
13	-0.002675	-0.0258	0.510264
14	-0.024282	-0.2342	0.592316
15	-0.019877	-0.1917	0.575799
16	-0.023058	-0.2224	0.587741
17	-0.021376	-0.2061	0.581437
18	-0.030691	-0.296	0.616046

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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