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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 02 Dec 2008 11:18:07 -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/02/t122824201227lcvt039dwuib6.htm/, Retrieved Sat, 25 May 2024 06:56:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28206, Retrieved Sat, 25 May 2024 06:56:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Severijns Britt

Estimated Impact

164

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD    [(Partial) Autocorrelation Function] [non stationary ti...] [2008-12-02 18:18:07] [7bf28d4d60530086dbc44ae6b648927e] [Current]

Feedback Forum

2008-12-08 18:05:28 [Jessica Alves Pires] [reply] 
Ik zou eerst de VRM gebruikt hebben om te zien welke d en D ik het best kon gebruiken (diegene bij de kleinste variantie). Erna zou ik de differentiatie met de gevonden waarden voor d en D doorvoeren adhv de ACF. Dan zou men kunnen zien of de differentiatie echt iets uithaalt of niet. Nog een bijkomende controlemiddel is de spectrale analyse.

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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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28206&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28206&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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.919431	8.8189	0
2	0.801114	7.684	0
3	0.700532	6.7193	0
4	0.636687	6.1069	0
5	0.612024	5.8703	0
6	0.581146	5.5742	0
7	0.542337	5.2019	1e-06
8	0.506147	4.8548	2e-06
9	0.508402	4.8764	2e-06
10	0.542944	5.2077	1e-06
11	0.588535	5.645	0
12	0.597586	5.7318	0
13	0.498592	4.7823	3e-06
14	0.376832	3.6144	0.000245
15	0.271228	2.6015	0.005408
16	0.19654	1.8851	0.031283
17	0.152739	1.465	0.073162
18	0.10554	1.0123	0.157025
19	0.059695	0.5726	0.284165

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.919431 & 8.8189 & 0 \tabularnewline
2 & 0.801114 & 7.684 & 0 \tabularnewline
3 & 0.700532 & 6.7193 & 0 \tabularnewline
4 & 0.636687 & 6.1069 & 0 \tabularnewline
5 & 0.612024 & 5.8703 & 0 \tabularnewline
6 & 0.581146 & 5.5742 & 0 \tabularnewline
7 & 0.542337 & 5.2019 & 1e-06 \tabularnewline
8 & 0.506147 & 4.8548 & 2e-06 \tabularnewline
9 & 0.508402 & 4.8764 & 2e-06 \tabularnewline
10 & 0.542944 & 5.2077 & 1e-06 \tabularnewline
11 & 0.588535 & 5.645 & 0 \tabularnewline
12 & 0.597586 & 5.7318 & 0 \tabularnewline
13 & 0.498592 & 4.7823 & 3e-06 \tabularnewline
14 & 0.376832 & 3.6144 & 0.000245 \tabularnewline
15 & 0.271228 & 2.6015 & 0.005408 \tabularnewline
16 & 0.19654 & 1.8851 & 0.031283 \tabularnewline
17 & 0.152739 & 1.465 & 0.073162 \tabularnewline
18 & 0.10554 & 1.0123 & 0.157025 \tabularnewline
19 & 0.059695 & 0.5726 & 0.284165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28206&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]0.919431[/C][C]8.8189[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.801114[/C][C]7.684[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.700532[/C][C]6.7193[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.636687[/C][C]6.1069[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.612024[/C][C]5.8703[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.581146[/C][C]5.5742[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.542337[/C][C]5.2019[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.506147[/C][C]4.8548[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.508402[/C][C]4.8764[/C][C]2e-06[/C][/ROW]
[ROW][C]10[/C][C]0.542944[/C][C]5.2077[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.588535[/C][C]5.645[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.597586[/C][C]5.7318[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.498592[/C][C]4.7823[/C][C]3e-06[/C][/ROW]
[ROW][C]14[/C][C]0.376832[/C][C]3.6144[/C][C]0.000245[/C][/ROW]
[ROW][C]15[/C][C]0.271228[/C][C]2.6015[/C][C]0.005408[/C][/ROW]
[ROW][C]16[/C][C]0.19654[/C][C]1.8851[/C][C]0.031283[/C][/ROW]
[ROW][C]17[/C][C]0.152739[/C][C]1.465[/C][C]0.073162[/C][/ROW]
[ROW][C]18[/C][C]0.10554[/C][C]1.0123[/C][C]0.157025[/C][/ROW]
[ROW][C]19[/C][C]0.059695[/C][C]0.5726[/C][C]0.284165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28206&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	0.919431	8.8189	0
2	0.801114	7.684	0
3	0.700532	6.7193	0
4	0.636687	6.1069	0
5	0.612024	5.8703	0
6	0.581146	5.5742	0
7	0.542337	5.2019	1e-06
8	0.506147	4.8548	2e-06
9	0.508402	4.8764	2e-06
10	0.542944	5.2077	1e-06
11	0.588535	5.645	0
12	0.597586	5.7318	0
13	0.498592	4.7823	3e-06
14	0.376832	3.6144	0.000245
15	0.271228	2.6015	0.005408
16	0.19654	1.8851	0.031283
17	0.152739	1.465	0.073162
18	0.10554	1.0123	0.157025
19	0.059695	0.5726	0.284165

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.919431	8.8189	0
2	-0.286073	-2.7439	0.003649
3	0.114616	1.0994	0.137241
4	0.126599	1.2143	0.113872
5	0.148808	1.4273	0.078437
6	-0.129596	-1.243	0.108506
7	0.042438	0.4071	0.342456
8	0.053013	0.5085	0.306165
9	0.265388	2.5455	0.006288
10	0.08669	0.8315	0.203921
11	0.118213	1.1339	0.129899
12	-0.163565	-1.5689	0.060057
13	-0.581288	-5.5755	0
14	0.064589	0.6195	0.268554
15	-0.090936	-0.8722	0.192678
16	-0.072845	-0.6987	0.243248
17	-0.048768	-0.4678	0.32053
18	0.038504	0.3693	0.356368
19	0.035407	0.3396	0.367462

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.919431 & 8.8189 & 0 \tabularnewline
2 & -0.286073 & -2.7439 & 0.003649 \tabularnewline
3 & 0.114616 & 1.0994 & 0.137241 \tabularnewline
4 & 0.126599 & 1.2143 & 0.113872 \tabularnewline
5 & 0.148808 & 1.4273 & 0.078437 \tabularnewline
6 & -0.129596 & -1.243 & 0.108506 \tabularnewline
7 & 0.042438 & 0.4071 & 0.342456 \tabularnewline
8 & 0.053013 & 0.5085 & 0.306165 \tabularnewline
9 & 0.265388 & 2.5455 & 0.006288 \tabularnewline
10 & 0.08669 & 0.8315 & 0.203921 \tabularnewline
11 & 0.118213 & 1.1339 & 0.129899 \tabularnewline
12 & -0.163565 & -1.5689 & 0.060057 \tabularnewline
13 & -0.581288 & -5.5755 & 0 \tabularnewline
14 & 0.064589 & 0.6195 & 0.268554 \tabularnewline
15 & -0.090936 & -0.8722 & 0.192678 \tabularnewline
16 & -0.072845 & -0.6987 & 0.243248 \tabularnewline
17 & -0.048768 & -0.4678 & 0.32053 \tabularnewline
18 & 0.038504 & 0.3693 & 0.356368 \tabularnewline
19 & 0.035407 & 0.3396 & 0.367462 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28206&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]0.919431[/C][C]8.8189[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.286073[/C][C]-2.7439[/C][C]0.003649[/C][/ROW]
[ROW][C]3[/C][C]0.114616[/C][C]1.0994[/C][C]0.137241[/C][/ROW]
[ROW][C]4[/C][C]0.126599[/C][C]1.2143[/C][C]0.113872[/C][/ROW]
[ROW][C]5[/C][C]0.148808[/C][C]1.4273[/C][C]0.078437[/C][/ROW]
[ROW][C]6[/C][C]-0.129596[/C][C]-1.243[/C][C]0.108506[/C][/ROW]
[ROW][C]7[/C][C]0.042438[/C][C]0.4071[/C][C]0.342456[/C][/ROW]
[ROW][C]8[/C][C]0.053013[/C][C]0.5085[/C][C]0.306165[/C][/ROW]
[ROW][C]9[/C][C]0.265388[/C][C]2.5455[/C][C]0.006288[/C][/ROW]
[ROW][C]10[/C][C]0.08669[/C][C]0.8315[/C][C]0.203921[/C][/ROW]
[ROW][C]11[/C][C]0.118213[/C][C]1.1339[/C][C]0.129899[/C][/ROW]
[ROW][C]12[/C][C]-0.163565[/C][C]-1.5689[/C][C]0.060057[/C][/ROW]
[ROW][C]13[/C][C]-0.581288[/C][C]-5.5755[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.064589[/C][C]0.6195[/C][C]0.268554[/C][/ROW]
[ROW][C]15[/C][C]-0.090936[/C][C]-0.8722[/C][C]0.192678[/C][/ROW]
[ROW][C]16[/C][C]-0.072845[/C][C]-0.6987[/C][C]0.243248[/C][/ROW]
[ROW][C]17[/C][C]-0.048768[/C][C]-0.4678[/C][C]0.32053[/C][/ROW]
[ROW][C]18[/C][C]0.038504[/C][C]0.3693[/C][C]0.356368[/C][/ROW]
[ROW][C]19[/C][C]0.035407[/C][C]0.3396[/C][C]0.367462[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28206&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	0.919431	8.8189	0
2	-0.286073	-2.7439	0.003649
3	0.114616	1.0994	0.137241
4	0.126599	1.2143	0.113872
5	0.148808	1.4273	0.078437
6	-0.129596	-1.243	0.108506
7	0.042438	0.4071	0.342456
8	0.053013	0.5085	0.306165
9	0.265388	2.5455	0.006288
10	0.08669	0.8315	0.203921
11	0.118213	1.1339	0.129899
12	-0.163565	-1.5689	0.060057
13	-0.581288	-5.5755	0
14	0.064589	0.6195	0.268554
15	-0.090936	-0.8722	0.192678
16	-0.072845	-0.6987	0.243248
17	-0.048768	-0.4678	0.32053
18	0.038504	0.3693	0.356368
19	0.035407	0.3396	0.367462

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 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code