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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 08 Dec 2008 13:06:19 -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/2008/Dec/08/t1228766873v1ztg1tl6s049q2.htm/, Retrieved Thu, 16 May 2024 18:11:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30905, Retrieved Thu, 16 May 2024 18:11:52 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

173

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

F     [Spectral Analysis] [Diff Spectral] [2008-12-06 12:07:42] [74be16979710d4c4e7c6647856088456]
F RMP   [ARIMA Backward Selection] [Arima backward] [2008-12-06 14:19:09] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [ACF int prod] [2008-12-08 19:55:18] [11edab5c4db3615abbf782b1c6e7cacf]
-   P         [(Partial) Autocorrelation Function] [ACF en PACF inter...] [2008-12-08 20:06:19] [e1dd70d3b1099218056e8ae5041dcc2f] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30905&T=0

[TABLE]
[ROW][C]Summary of computational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30905&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30905&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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.278983	2.3836	0.009872
2	0.237739	2.0312	0.022936
3	0.133012	1.1365	0.129741
4	0.019034	0.1626	0.435632
5	0.063799	0.5451	0.293673
6	0.12177	1.0404	0.150792
7	-0.043151	-0.3687	0.356715
8	-0.126781	-1.0832	0.141139
9	0.001783	0.0152	0.493943
10	-0.140295	-1.1987	0.117264
11	-0.019779	-0.169	0.433136
12	-0.11318	-0.967	0.168366
13	-0.11323	-0.9674	0.16826
14	-0.096494	-0.8244	0.206187
15	-0.02244	-0.1917	0.424244
16	-0.075199	-0.6425	0.261281
17	0.018001	0.1538	0.439094
18	-0.06132	-0.5239	0.300963
19	-0.008466	-0.0723	0.471268

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.278983 & 2.3836 & 0.009872 \tabularnewline
2 & 0.237739 & 2.0312 & 0.022936 \tabularnewline
3 & 0.133012 & 1.1365 & 0.129741 \tabularnewline
4 & 0.019034 & 0.1626 & 0.435632 \tabularnewline
5 & 0.063799 & 0.5451 & 0.293673 \tabularnewline
6 & 0.12177 & 1.0404 & 0.150792 \tabularnewline
7 & -0.043151 & -0.3687 & 0.356715 \tabularnewline
8 & -0.126781 & -1.0832 & 0.141139 \tabularnewline
9 & 0.001783 & 0.0152 & 0.493943 \tabularnewline
10 & -0.140295 & -1.1987 & 0.117264 \tabularnewline
11 & -0.019779 & -0.169 & 0.433136 \tabularnewline
12 & -0.11318 & -0.967 & 0.168366 \tabularnewline
13 & -0.11323 & -0.9674 & 0.16826 \tabularnewline
14 & -0.096494 & -0.8244 & 0.206187 \tabularnewline
15 & -0.02244 & -0.1917 & 0.424244 \tabularnewline
16 & -0.075199 & -0.6425 & 0.261281 \tabularnewline
17 & 0.018001 & 0.1538 & 0.439094 \tabularnewline
18 & -0.06132 & -0.5239 & 0.300963 \tabularnewline
19 & -0.008466 & -0.0723 & 0.471268 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30905&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]1[/C][C]0.278983[/C][C]2.3836[/C][C]0.009872[/C][/ROW]
[ROW][C]2[/C][C]0.237739[/C][C]2.0312[/C][C]0.022936[/C][/ROW]
[ROW][C]3[/C][C]0.133012[/C][C]1.1365[/C][C]0.129741[/C][/ROW]
[ROW][C]4[/C][C]0.019034[/C][C]0.1626[/C][C]0.435632[/C][/ROW]
[ROW][C]5[/C][C]0.063799[/C][C]0.5451[/C][C]0.293673[/C][/ROW]
[ROW][C]6[/C][C]0.12177[/C][C]1.0404[/C][C]0.150792[/C][/ROW]
[ROW][C]7[/C][C]-0.043151[/C][C]-0.3687[/C][C]0.356715[/C][/ROW]
[ROW][C]8[/C][C]-0.126781[/C][C]-1.0832[/C][C]0.141139[/C][/ROW]
[ROW][C]9[/C][C]0.001783[/C][C]0.0152[/C][C]0.493943[/C][/ROW]
[ROW][C]10[/C][C]-0.140295[/C][C]-1.1987[/C][C]0.117264[/C][/ROW]
[ROW][C]11[/C][C]-0.019779[/C][C]-0.169[/C][C]0.433136[/C][/ROW]
[ROW][C]12[/C][C]-0.11318[/C][C]-0.967[/C][C]0.168366[/C][/ROW]
[ROW][C]13[/C][C]-0.11323[/C][C]-0.9674[/C][C]0.16826[/C][/ROW]
[ROW][C]14[/C][C]-0.096494[/C][C]-0.8244[/C][C]0.206187[/C][/ROW]
[ROW][C]15[/C][C]-0.02244[/C][C]-0.1917[/C][C]0.424244[/C][/ROW]
[ROW][C]16[/C][C]-0.075199[/C][C]-0.6425[/C][C]0.261281[/C][/ROW]
[ROW][C]17[/C][C]0.018001[/C][C]0.1538[/C][C]0.439094[/C][/ROW]
[ROW][C]18[/C][C]-0.06132[/C][C]-0.5239[/C][C]0.300963[/C][/ROW]
[ROW][C]19[/C][C]-0.008466[/C][C]-0.0723[/C][C]0.471268[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30905&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30905&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
1	0.278983	2.3836	0.009872
2	0.237739	2.0312	0.022936
3	0.133012	1.1365	0.129741
4	0.019034	0.1626	0.435632
5	0.063799	0.5451	0.293673
6	0.12177	1.0404	0.150792
7	-0.043151	-0.3687	0.356715
8	-0.126781	-1.0832	0.141139
9	0.001783	0.0152	0.493943
10	-0.140295	-1.1987	0.117264
11	-0.019779	-0.169	0.433136
12	-0.11318	-0.967	0.168366
13	-0.11323	-0.9674	0.16826
14	-0.096494	-0.8244	0.206187
15	-0.02244	-0.1917	0.424244
16	-0.075199	-0.6425	0.261281
17	0.018001	0.1538	0.439094
18	-0.06132	-0.5239	0.300963
19	-0.008466	-0.0723	0.471268

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.278983	2.3836	0.009872
2	0.173404	1.4816	0.07138
3	0.03333	0.2848	0.388314
4	-0.066671	-0.5696	0.285337
5	0.048431	0.4138	0.340119
6	0.116548	0.9958	0.161321
7	-0.122802	-1.0492	0.148769
8	-0.16784	-1.434	0.077917
9	0.100317	0.8571	0.197095
10	-0.089998	-0.7689	0.222203
11	0.015741	0.1345	0.446693
12	-0.118799	-1.015	0.156724
13	-0.014585	-0.1246	0.450586
14	-0.004261	-0.0364	0.485529
15	0.022706	0.194	0.423359
16	-0.059362	-0.5072	0.306775
17	0.058624	0.5009	0.30898
18	-0.072515	-0.6196	0.268735
19	0.053534	0.4574	0.324374

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.278983 & 2.3836 & 0.009872 \tabularnewline
2 & 0.173404 & 1.4816 & 0.07138 \tabularnewline
3 & 0.03333 & 0.2848 & 0.388314 \tabularnewline
4 & -0.066671 & -0.5696 & 0.285337 \tabularnewline
5 & 0.048431 & 0.4138 & 0.340119 \tabularnewline
6 & 0.116548 & 0.9958 & 0.161321 \tabularnewline
7 & -0.122802 & -1.0492 & 0.148769 \tabularnewline
8 & -0.16784 & -1.434 & 0.077917 \tabularnewline
9 & 0.100317 & 0.8571 & 0.197095 \tabularnewline
10 & -0.089998 & -0.7689 & 0.222203 \tabularnewline
11 & 0.015741 & 0.1345 & 0.446693 \tabularnewline
12 & -0.118799 & -1.015 & 0.156724 \tabularnewline
13 & -0.014585 & -0.1246 & 0.450586 \tabularnewline
14 & -0.004261 & -0.0364 & 0.485529 \tabularnewline
15 & 0.022706 & 0.194 & 0.423359 \tabularnewline
16 & -0.059362 & -0.5072 & 0.306775 \tabularnewline
17 & 0.058624 & 0.5009 & 0.30898 \tabularnewline
18 & -0.072515 & -0.6196 & 0.268735 \tabularnewline
19 & 0.053534 & 0.4574 & 0.324374 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30905&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]1[/C][C]0.278983[/C][C]2.3836[/C][C]0.009872[/C][/ROW]
[ROW][C]2[/C][C]0.173404[/C][C]1.4816[/C][C]0.07138[/C][/ROW]
[ROW][C]3[/C][C]0.03333[/C][C]0.2848[/C][C]0.388314[/C][/ROW]
[ROW][C]4[/C][C]-0.066671[/C][C]-0.5696[/C][C]0.285337[/C][/ROW]
[ROW][C]5[/C][C]0.048431[/C][C]0.4138[/C][C]0.340119[/C][/ROW]
[ROW][C]6[/C][C]0.116548[/C][C]0.9958[/C][C]0.161321[/C][/ROW]
[ROW][C]7[/C][C]-0.122802[/C][C]-1.0492[/C][C]0.148769[/C][/ROW]
[ROW][C]8[/C][C]-0.16784[/C][C]-1.434[/C][C]0.077917[/C][/ROW]
[ROW][C]9[/C][C]0.100317[/C][C]0.8571[/C][C]0.197095[/C][/ROW]
[ROW][C]10[/C][C]-0.089998[/C][C]-0.7689[/C][C]0.222203[/C][/ROW]
[ROW][C]11[/C][C]0.015741[/C][C]0.1345[/C][C]0.446693[/C][/ROW]
[ROW][C]12[/C][C]-0.118799[/C][C]-1.015[/C][C]0.156724[/C][/ROW]
[ROW][C]13[/C][C]-0.014585[/C][C]-0.1246[/C][C]0.450586[/C][/ROW]
[ROW][C]14[/C][C]-0.004261[/C][C]-0.0364[/C][C]0.485529[/C][/ROW]
[ROW][C]15[/C][C]0.022706[/C][C]0.194[/C][C]0.423359[/C][/ROW]
[ROW][C]16[/C][C]-0.059362[/C][C]-0.5072[/C][C]0.306775[/C][/ROW]
[ROW][C]17[/C][C]0.058624[/C][C]0.5009[/C][C]0.30898[/C][/ROW]
[ROW][C]18[/C][C]-0.072515[/C][C]-0.6196[/C][C]0.268735[/C][/ROW]
[ROW][C]19[/C][C]0.053534[/C][C]0.4574[/C][C]0.324374[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30905&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30905&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
1	0.278983	2.3836	0.009872
2	0.173404	1.4816	0.07138
3	0.03333	0.2848	0.388314
4	-0.066671	-0.5696	0.285337
5	0.048431	0.4138	0.340119
6	0.116548	0.9958	0.161321
7	-0.122802	-1.0492	0.148769
8	-0.16784	-1.434	0.077917
9	0.100317	0.8571	0.197095
10	-0.089998	-0.7689	0.222203
11	0.015741	0.1345	0.446693
12	-0.118799	-1.015	0.156724
13	-0.014585	-0.1246	0.450586
14	-0.004261	-0.0364	0.485529
15	0.022706	0.194	0.423359
16	-0.059362	-0.5072	0.306775
17	0.058624	0.5009	0.30898
18	-0.072515	-0.6196	0.268735
19	0.053534	0.4574	0.324374

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.6 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1.6 ; 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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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