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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 03 Dec 2009 05:51:15 -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/2009/Dec/03/t1259844813xbk3891staukzsh.htm/, Retrieved Sat, 20 Apr 2024 03:54:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62703, Retrieved Sat, 20 Apr 2024 03:54:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

JSSHWWS9P3

Estimated Impact

128

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]
- RMPD    [(Partial) Autocorrelation Function] [Autocorrelation f...] [2009-12-03 12:51:15] [c8fd62404619100d8e91184019148412] [Current]

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Histogram

Boxplots

11.1
10.9
10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62703&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62703&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62703&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.863464	6.6884	0
2	0.65584	5.0801	2e-06
3	0.522582	4.0479	7.5e-05
4	0.509807	3.9489	0.000104
5	0.558091	4.323	2.9e-05
6	0.57843	4.4805	1.7e-05
7	0.526212	4.076	6.8e-05
8	0.431341	3.3412	0.00072
9	0.371217	2.8754	0.002788
10	0.377695	2.9256	0.002424
11	0.426753	3.3056	0.000801
12	0.422494	3.2726	0.000885
13	0.341558	2.6457	0.005197
14	0.237894	1.8427	0.035156
15	0.172147	1.3334	0.093713
16	0.139216	1.0784	0.142595
17	0.112003	0.8676	0.194543

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.863464 & 6.6884 & 0 \tabularnewline
2 & 0.65584 & 5.0801 & 2e-06 \tabularnewline
3 & 0.522582 & 4.0479 & 7.5e-05 \tabularnewline
4 & 0.509807 & 3.9489 & 0.000104 \tabularnewline
5 & 0.558091 & 4.323 & 2.9e-05 \tabularnewline
6 & 0.57843 & 4.4805 & 1.7e-05 \tabularnewline
7 & 0.526212 & 4.076 & 6.8e-05 \tabularnewline
8 & 0.431341 & 3.3412 & 0.00072 \tabularnewline
9 & 0.371217 & 2.8754 & 0.002788 \tabularnewline
10 & 0.377695 & 2.9256 & 0.002424 \tabularnewline
11 & 0.426753 & 3.3056 & 0.000801 \tabularnewline
12 & 0.422494 & 3.2726 & 0.000885 \tabularnewline
13 & 0.341558 & 2.6457 & 0.005197 \tabularnewline
14 & 0.237894 & 1.8427 & 0.035156 \tabularnewline
15 & 0.172147 & 1.3334 & 0.093713 \tabularnewline
16 & 0.139216 & 1.0784 & 0.142595 \tabularnewline
17 & 0.112003 & 0.8676 & 0.194543 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62703&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]0.863464[/C][C]6.6884[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.65584[/C][C]5.0801[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.522582[/C][C]4.0479[/C][C]7.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.509807[/C][C]3.9489[/C][C]0.000104[/C][/ROW]
[ROW][C]5[/C][C]0.558091[/C][C]4.323[/C][C]2.9e-05[/C][/ROW]
[ROW][C]6[/C][C]0.57843[/C][C]4.4805[/C][C]1.7e-05[/C][/ROW]
[ROW][C]7[/C][C]0.526212[/C][C]4.076[/C][C]6.8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.431341[/C][C]3.3412[/C][C]0.00072[/C][/ROW]
[ROW][C]9[/C][C]0.371217[/C][C]2.8754[/C][C]0.002788[/C][/ROW]
[ROW][C]10[/C][C]0.377695[/C][C]2.9256[/C][C]0.002424[/C][/ROW]
[ROW][C]11[/C][C]0.426753[/C][C]3.3056[/C][C]0.000801[/C][/ROW]
[ROW][C]12[/C][C]0.422494[/C][C]3.2726[/C][C]0.000885[/C][/ROW]
[ROW][C]13[/C][C]0.341558[/C][C]2.6457[/C][C]0.005197[/C][/ROW]
[ROW][C]14[/C][C]0.237894[/C][C]1.8427[/C][C]0.035156[/C][/ROW]
[ROW][C]15[/C][C]0.172147[/C][C]1.3334[/C][C]0.093713[/C][/ROW]
[ROW][C]16[/C][C]0.139216[/C][C]1.0784[/C][C]0.142595[/C][/ROW]
[ROW][C]17[/C][C]0.112003[/C][C]0.8676[/C][C]0.194543[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62703&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62703&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	0.863464	6.6884	0
2	0.65584	5.0801	2e-06
3	0.522582	4.0479	7.5e-05
4	0.509807	3.9489	0.000104
5	0.558091	4.323	2.9e-05
6	0.57843	4.4805	1.7e-05
7	0.526212	4.076	6.8e-05
8	0.431341	3.3412	0.00072
9	0.371217	2.8754	0.002788
10	0.377695	2.9256	0.002424
11	0.426753	3.3056	0.000801
12	0.422494	3.2726	0.000885
13	0.341558	2.6457	0.005197
14	0.237894	1.8427	0.035156
15	0.172147	1.3334	0.093713
16	0.139216	1.0784	0.142595
17	0.112003	0.8676	0.194543

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.863464	6.6884	0
2	-0.352674	-2.7318	0.00413
3	0.274219	2.1241	0.018897
4	0.259546	2.0104	0.024443
5	0.111102	0.8606	0.196444
6	-0.002533	-0.0196	0.492204
7	-0.063537	-0.4922	0.312203
8	-0.030852	-0.239	0.405968
9	0.090823	0.7035	0.242229
10	0.066131	0.5123	0.305178
11	0.07743	0.5998	0.275459
12	-0.176837	-1.3698	0.087931
13	-0.076346	-0.5914	0.278245
14	-0.014916	-0.1155	0.454202
15	-0.041256	-0.3196	0.375203
16	-0.165179	-1.2795	0.102829
17	-0.097089	-0.752	0.227481

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.863464 & 6.6884 & 0 \tabularnewline
2 & -0.352674 & -2.7318 & 0.00413 \tabularnewline
3 & 0.274219 & 2.1241 & 0.018897 \tabularnewline
4 & 0.259546 & 2.0104 & 0.024443 \tabularnewline
5 & 0.111102 & 0.8606 & 0.196444 \tabularnewline
6 & -0.002533 & -0.0196 & 0.492204 \tabularnewline
7 & -0.063537 & -0.4922 & 0.312203 \tabularnewline
8 & -0.030852 & -0.239 & 0.405968 \tabularnewline
9 & 0.090823 & 0.7035 & 0.242229 \tabularnewline
10 & 0.066131 & 0.5123 & 0.305178 \tabularnewline
11 & 0.07743 & 0.5998 & 0.275459 \tabularnewline
12 & -0.176837 & -1.3698 & 0.087931 \tabularnewline
13 & -0.076346 & -0.5914 & 0.278245 \tabularnewline
14 & -0.014916 & -0.1155 & 0.454202 \tabularnewline
15 & -0.041256 & -0.3196 & 0.375203 \tabularnewline
16 & -0.165179 & -1.2795 & 0.102829 \tabularnewline
17 & -0.097089 & -0.752 & 0.227481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62703&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]0.863464[/C][C]6.6884[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.352674[/C][C]-2.7318[/C][C]0.00413[/C][/ROW]
[ROW][C]3[/C][C]0.274219[/C][C]2.1241[/C][C]0.018897[/C][/ROW]
[ROW][C]4[/C][C]0.259546[/C][C]2.0104[/C][C]0.024443[/C][/ROW]
[ROW][C]5[/C][C]0.111102[/C][C]0.8606[/C][C]0.196444[/C][/ROW]
[ROW][C]6[/C][C]-0.002533[/C][C]-0.0196[/C][C]0.492204[/C][/ROW]
[ROW][C]7[/C][C]-0.063537[/C][C]-0.4922[/C][C]0.312203[/C][/ROW]
[ROW][C]8[/C][C]-0.030852[/C][C]-0.239[/C][C]0.405968[/C][/ROW]
[ROW][C]9[/C][C]0.090823[/C][C]0.7035[/C][C]0.242229[/C][/ROW]
[ROW][C]10[/C][C]0.066131[/C][C]0.5123[/C][C]0.305178[/C][/ROW]
[ROW][C]11[/C][C]0.07743[/C][C]0.5998[/C][C]0.275459[/C][/ROW]
[ROW][C]12[/C][C]-0.176837[/C][C]-1.3698[/C][C]0.087931[/C][/ROW]
[ROW][C]13[/C][C]-0.076346[/C][C]-0.5914[/C][C]0.278245[/C][/ROW]
[ROW][C]14[/C][C]-0.014916[/C][C]-0.1155[/C][C]0.454202[/C][/ROW]
[ROW][C]15[/C][C]-0.041256[/C][C]-0.3196[/C][C]0.375203[/C][/ROW]
[ROW][C]16[/C][C]-0.165179[/C][C]-1.2795[/C][C]0.102829[/C][/ROW]
[ROW][C]17[/C][C]-0.097089[/C][C]-0.752[/C][C]0.227481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62703&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62703&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	0.863464	6.6884	0
2	-0.352674	-2.7318	0.00413
3	0.274219	2.1241	0.018897
4	0.259546	2.0104	0.024443
5	0.111102	0.8606	0.196444
6	-0.002533	-0.0196	0.492204
7	-0.063537	-0.4922	0.312203
8	-0.030852	-0.239	0.405968
9	0.090823	0.7035	0.242229
10	0.066131	0.5123	0.305178
11	0.07743	0.5998	0.275459
12	-0.176837	-1.3698	0.087931
13	-0.076346	-0.5914	0.278245
14	-0.014916	-0.1155	0.454202
15	-0.041256	-0.3196	0.375203
16	-0.165179	-1.2795	0.102829
17	-0.097089	-0.752	0.227481

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 ;

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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code