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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 18 Dec 2010 15:02:15 +0000

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/2010/Dec/18/t12926858092madxe2q3kiq91q.htm/, Retrieved Tue, 30 Apr 2024 03:49:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112040, Retrieved Tue, 30 Apr 2024 03:49:06 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

145

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D      [(Partial) Autocorrelation Function] [Paper - Stationar...] [2010-12-18 15:02:15] [ffc0b3af89e3f152a248771909785efd] [Current]
-    D        [(Partial) Autocorrelation Function] [Paper 'stationari...] [2010-12-28 18:18:39] [40c8b935cbad1b0be3c22a481f9723f7] 
-             [(Partial) Autocorrelation Function] [paper (5)] [2010-12-29 19:08:52] [34b8ec63a78ce61b49b6bd4fc5a61e1c] 

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Dataseries X:

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Histogram

Boxplots

9,3
14,2
17,3
23
16,3
18,4
14,2
9,1
5,9
7,2
6,8
8
14,3
14,6
17,5
17,2
17,2
14,1
10,4
6,8
4,1
6,5
6,1
6,3
9,3
16,4
16,1
18
17,6
14
10,5
6,9
2,8
0,7
3,6
6,7
12,5
14,4
16,5
18,7
19,4
15,8
11,3
9,7
2,9
0,1
2,5
6,7
10,3
11,2
17,4
20,5
17
14,2
10,6
6,1

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	'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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112040&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112040&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.791599	5.9238	0
2	0.445237	3.3318	0.000766
3	0.012497	0.0935	0.462912
4	-0.396901	-2.9701	0.002189
5	-0.700339	-5.2409	1e-06
6	-0.778308	-5.8243	0
7	-0.650719	-4.8695	5e-06
8	-0.368055	-2.7543	0.003959
9	0.02595	0.1942	0.423364
10	0.376102	2.8145	0.003365
11	0.626643	4.6894	9e-06
12	0.685091	5.1268	2e-06
13	0.595833	4.4588	2e-05
14	0.339599	2.5413	0.00692
15	0.026535	0.1986	0.421658
16	-0.286782	-2.1461	0.018107
17	-0.527741	-3.9492	0.000111

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.791599 & 5.9238 & 0 \tabularnewline
2 & 0.445237 & 3.3318 & 0.000766 \tabularnewline
3 & 0.012497 & 0.0935 & 0.462912 \tabularnewline
4 & -0.396901 & -2.9701 & 0.002189 \tabularnewline
5 & -0.700339 & -5.2409 & 1e-06 \tabularnewline
6 & -0.778308 & -5.8243 & 0 \tabularnewline
7 & -0.650719 & -4.8695 & 5e-06 \tabularnewline
8 & -0.368055 & -2.7543 & 0.003959 \tabularnewline
9 & 0.02595 & 0.1942 & 0.423364 \tabularnewline
10 & 0.376102 & 2.8145 & 0.003365 \tabularnewline
11 & 0.626643 & 4.6894 & 9e-06 \tabularnewline
12 & 0.685091 & 5.1268 & 2e-06 \tabularnewline
13 & 0.595833 & 4.4588 & 2e-05 \tabularnewline
14 & 0.339599 & 2.5413 & 0.00692 \tabularnewline
15 & 0.026535 & 0.1986 & 0.421658 \tabularnewline
16 & -0.286782 & -2.1461 & 0.018107 \tabularnewline
17 & -0.527741 & -3.9492 & 0.000111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112040&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]0.791599[/C][C]5.9238[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.445237[/C][C]3.3318[/C][C]0.000766[/C][/ROW]
[ROW][C]3[/C][C]0.012497[/C][C]0.0935[/C][C]0.462912[/C][/ROW]
[ROW][C]4[/C][C]-0.396901[/C][C]-2.9701[/C][C]0.002189[/C][/ROW]
[ROW][C]5[/C][C]-0.700339[/C][C]-5.2409[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.778308[/C][C]-5.8243[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.650719[/C][C]-4.8695[/C][C]5e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.368055[/C][C]-2.7543[/C][C]0.003959[/C][/ROW]
[ROW][C]9[/C][C]0.02595[/C][C]0.1942[/C][C]0.423364[/C][/ROW]
[ROW][C]10[/C][C]0.376102[/C][C]2.8145[/C][C]0.003365[/C][/ROW]
[ROW][C]11[/C][C]0.626643[/C][C]4.6894[/C][C]9e-06[/C][/ROW]
[ROW][C]12[/C][C]0.685091[/C][C]5.1268[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.595833[/C][C]4.4588[/C][C]2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.339599[/C][C]2.5413[/C][C]0.00692[/C][/ROW]
[ROW][C]15[/C][C]0.026535[/C][C]0.1986[/C][C]0.421658[/C][/ROW]
[ROW][C]16[/C][C]-0.286782[/C][C]-2.1461[/C][C]0.018107[/C][/ROW]
[ROW][C]17[/C][C]-0.527741[/C][C]-3.9492[/C][C]0.000111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112040&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	0.791599	5.9238	0
2	0.445237	3.3318	0.000766
3	0.012497	0.0935	0.462912
4	-0.396901	-2.9701	0.002189
5	-0.700339	-5.2409	1e-06
6	-0.778308	-5.8243	0
7	-0.650719	-4.8695	5e-06
8	-0.368055	-2.7543	0.003959
9	0.02595	0.1942	0.423364
10	0.376102	2.8145	0.003365
11	0.626643	4.6894	9e-06
12	0.685091	5.1268	2e-06
13	0.595833	4.4588	2e-05
14	0.339599	2.5413	0.00692
15	0.026535	0.1986	0.421658
16	-0.286782	-2.1461	0.018107
17	-0.527741	-3.9492	0.000111

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.791599	5.9238	0
2	-0.485825	-3.6356	0.000302
3	-0.443835	-3.3214	0.000791
4	-0.321693	-2.4073	0.009695
5	-0.300351	-2.2476	0.014279
6	0.014968	0.112	0.455609
7	0.002934	0.022	0.491282
8	-0.030856	-0.2309	0.409116
9	0.177142	1.3256	0.095175
10	-0.051465	-0.3851	0.3508
11	0.10623	0.795	0.214999
12	-0.035223	-0.2636	0.396535
13	0.156293	1.1696	0.12356
14	0.023984	0.1795	0.429105
15	0.075116	0.5621	0.288141
16	-0.004331	-0.0324	0.487132
17	-0.128114	-0.9587	0.170911

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.791599 & 5.9238 & 0 \tabularnewline
2 & -0.485825 & -3.6356 & 0.000302 \tabularnewline
3 & -0.443835 & -3.3214 & 0.000791 \tabularnewline
4 & -0.321693 & -2.4073 & 0.009695 \tabularnewline
5 & -0.300351 & -2.2476 & 0.014279 \tabularnewline
6 & 0.014968 & 0.112 & 0.455609 \tabularnewline
7 & 0.002934 & 0.022 & 0.491282 \tabularnewline
8 & -0.030856 & -0.2309 & 0.409116 \tabularnewline
9 & 0.177142 & 1.3256 & 0.095175 \tabularnewline
10 & -0.051465 & -0.3851 & 0.3508 \tabularnewline
11 & 0.10623 & 0.795 & 0.214999 \tabularnewline
12 & -0.035223 & -0.2636 & 0.396535 \tabularnewline
13 & 0.156293 & 1.1696 & 0.12356 \tabularnewline
14 & 0.023984 & 0.1795 & 0.429105 \tabularnewline
15 & 0.075116 & 0.5621 & 0.288141 \tabularnewline
16 & -0.004331 & -0.0324 & 0.487132 \tabularnewline
17 & -0.128114 & -0.9587 & 0.170911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112040&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]0.791599[/C][C]5.9238[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.485825[/C][C]-3.6356[/C][C]0.000302[/C][/ROW]
[ROW][C]3[/C][C]-0.443835[/C][C]-3.3214[/C][C]0.000791[/C][/ROW]
[ROW][C]4[/C][C]-0.321693[/C][C]-2.4073[/C][C]0.009695[/C][/ROW]
[ROW][C]5[/C][C]-0.300351[/C][C]-2.2476[/C][C]0.014279[/C][/ROW]
[ROW][C]6[/C][C]0.014968[/C][C]0.112[/C][C]0.455609[/C][/ROW]
[ROW][C]7[/C][C]0.002934[/C][C]0.022[/C][C]0.491282[/C][/ROW]
[ROW][C]8[/C][C]-0.030856[/C][C]-0.2309[/C][C]0.409116[/C][/ROW]
[ROW][C]9[/C][C]0.177142[/C][C]1.3256[/C][C]0.095175[/C][/ROW]
[ROW][C]10[/C][C]-0.051465[/C][C]-0.3851[/C][C]0.3508[/C][/ROW]
[ROW][C]11[/C][C]0.10623[/C][C]0.795[/C][C]0.214999[/C][/ROW]
[ROW][C]12[/C][C]-0.035223[/C][C]-0.2636[/C][C]0.396535[/C][/ROW]
[ROW][C]13[/C][C]0.156293[/C][C]1.1696[/C][C]0.12356[/C][/ROW]
[ROW][C]14[/C][C]0.023984[/C][C]0.1795[/C][C]0.429105[/C][/ROW]
[ROW][C]15[/C][C]0.075116[/C][C]0.5621[/C][C]0.288141[/C][/ROW]
[ROW][C]16[/C][C]-0.004331[/C][C]-0.0324[/C][C]0.487132[/C][/ROW]
[ROW][C]17[/C][C]-0.128114[/C][C]-0.9587[/C][C]0.170911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112040&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112040&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	0.791599	5.9238	0
2	-0.485825	-3.6356	0.000302
3	-0.443835	-3.3214	0.000791
4	-0.321693	-2.4073	0.009695
5	-0.300351	-2.2476	0.014279
6	0.014968	0.112	0.455609
7	0.002934	0.022	0.491282
8	-0.030856	-0.2309	0.409116
9	0.177142	1.3256	0.095175
10	-0.051465	-0.3851	0.3508
11	0.10623	0.795	0.214999
12	-0.035223	-0.2636	0.396535
13	0.156293	1.1696	0.12356
14	0.023984	0.1795	0.429105
15	0.075116	0.5621	0.288141
16	-0.004331	-0.0324	0.487132
17	-0.128114	-0.9587	0.170911

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code