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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

Sun, 06 Jan 2008 13:49:57 -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/Jan/06/t1199652574kn0nxw94p5oisgj.htm/, Retrieved Sun, 05 May 2024 01:34:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7895, Retrieved Sun, 05 May 2024 01:34:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

inducing time seris Q2b EA

Estimated Impact

174

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

-     [Central Tendency] [WS2 - Robustness ...] [2007-10-20 13:06:37] [5343e105a400b9e32bf6f011133bbaf4]
- RM D    [(Partial) Autocorrelation Function] [CVWS7EAQ2b] [2008-01-06 20:49:57] [b523c8d839cc24a05ea912c062a47207] [Current]

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Dataseries X:

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Histogram

Boxplots

13,5
16,2
17,6
15,8
17,6
15,2
15,9
12,0
13,3
14,8
16,1
16,9
17,6
13,9
10,0
7,6
7,1
8,1
8,1
7,7
4,0
1,4
0,3
-1,0
-1,9
-1,5
-0,2
3,4
3,0
4,1
3,4
3,2
6,1
5,8
6,2
5,8
5,9
6,7
5,9
3,8
1,7
1,4
1,8
3,0
3,6
4,8
4,3
4,2
2,9
4,9
7,2
8,7
9,1
8,9
9,0
11,6
9,6
9,1
9,2
10,8
11,0
8,5
6,5
7,2
7,8
8,7
7,8
7,5
7,7
7,5
8,3
7,9
10,4
11,5
14,0
11,9
11,9
10,3
11,3
9,9
8,9
9,2
8,8
6,7
7,1
6,6
7,2
5,0
5,3
6,3

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7895&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7895&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.434	0
1	0.16302	1.5379	0.063807
2	0.116082	1.0951	0.13821
3	-0.23353	-2.2031	0.984916
4	-0.040667	-0.3837	0.648924
5	-0.013871	-0.1309	0.551909
6	0.003261	0.0308	0.487765
7	0.034793	0.3282	0.371752
8	0.200266	1.8893	0.031053
9	0.022317	0.2105	0.416866
10	0.020219	0.1908	0.424578
11	-0.250139	-2.3598	0.989765
12	-0.342359	-3.2298	0.999132
13	-0.163636	-1.5437	0.9369
14	-0.065705	-0.6199	0.731534
15	0.087512	0.8256	0.205624
16	0.03077	0.2903	0.386139
17	0.112201	1.0585	0.146345
18	0.086039	0.8117	0.209567

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.434 & 0 \tabularnewline
1 & 0.16302 & 1.5379 & 0.063807 \tabularnewline
2 & 0.116082 & 1.0951 & 0.13821 \tabularnewline
3 & -0.23353 & -2.2031 & 0.984916 \tabularnewline
4 & -0.040667 & -0.3837 & 0.648924 \tabularnewline
5 & -0.013871 & -0.1309 & 0.551909 \tabularnewline
6 & 0.003261 & 0.0308 & 0.487765 \tabularnewline
7 & 0.034793 & 0.3282 & 0.371752 \tabularnewline
8 & 0.200266 & 1.8893 & 0.031053 \tabularnewline
9 & 0.022317 & 0.2105 & 0.416866 \tabularnewline
10 & 0.020219 & 0.1908 & 0.424578 \tabularnewline
11 & -0.250139 & -2.3598 & 0.989765 \tabularnewline
12 & -0.342359 & -3.2298 & 0.999132 \tabularnewline
13 & -0.163636 & -1.5437 & 0.9369 \tabularnewline
14 & -0.065705 & -0.6199 & 0.731534 \tabularnewline
15 & 0.087512 & 0.8256 & 0.205624 \tabularnewline
16 & 0.03077 & 0.2903 & 0.386139 \tabularnewline
17 & 0.112201 & 1.0585 & 0.146345 \tabularnewline
18 & 0.086039 & 0.8117 & 0.209567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7895&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]9.434[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.16302[/C][C]1.5379[/C][C]0.063807[/C][/ROW]
[ROW][C]2[/C][C]0.116082[/C][C]1.0951[/C][C]0.13821[/C][/ROW]
[ROW][C]3[/C][C]-0.23353[/C][C]-2.2031[/C][C]0.984916[/C][/ROW]
[ROW][C]4[/C][C]-0.040667[/C][C]-0.3837[/C][C]0.648924[/C][/ROW]
[ROW][C]5[/C][C]-0.013871[/C][C]-0.1309[/C][C]0.551909[/C][/ROW]
[ROW][C]6[/C][C]0.003261[/C][C]0.0308[/C][C]0.487765[/C][/ROW]
[ROW][C]7[/C][C]0.034793[/C][C]0.3282[/C][C]0.371752[/C][/ROW]
[ROW][C]8[/C][C]0.200266[/C][C]1.8893[/C][C]0.031053[/C][/ROW]
[ROW][C]9[/C][C]0.022317[/C][C]0.2105[/C][C]0.416866[/C][/ROW]
[ROW][C]10[/C][C]0.020219[/C][C]0.1908[/C][C]0.424578[/C][/ROW]
[ROW][C]11[/C][C]-0.250139[/C][C]-2.3598[/C][C]0.989765[/C][/ROW]
[ROW][C]12[/C][C]-0.342359[/C][C]-3.2298[/C][C]0.999132[/C][/ROW]
[ROW][C]13[/C][C]-0.163636[/C][C]-1.5437[/C][C]0.9369[/C][/ROW]
[ROW][C]14[/C][C]-0.065705[/C][C]-0.6199[/C][C]0.731534[/C][/ROW]
[ROW][C]15[/C][C]0.087512[/C][C]0.8256[/C][C]0.205624[/C][/ROW]
[ROW][C]16[/C][C]0.03077[/C][C]0.2903[/C][C]0.386139[/C][/ROW]
[ROW][C]17[/C][C]0.112201[/C][C]1.0585[/C][C]0.146345[/C][/ROW]
[ROW][C]18[/C][C]0.086039[/C][C]0.8117[/C][C]0.209567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7895&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	9.434	0
1	0.16302	1.5379	0.063807
2	0.116082	1.0951	0.13821
3	-0.23353	-2.2031	0.984916
4	-0.040667	-0.3837	0.648924
5	-0.013871	-0.1309	0.551909
6	0.003261	0.0308	0.487765
7	0.034793	0.3282	0.371752
8	0.200266	1.8893	0.031053
9	0.022317	0.2105	0.416866
10	0.020219	0.1908	0.424578
11	-0.250139	-2.3598	0.989765
12	-0.342359	-3.2298	0.999132
13	-0.163636	-1.5437	0.9369
14	-0.065705	-0.6199	0.731534
15	0.087512	0.8256	0.205624
16	0.03077	0.2903	0.386139
17	0.112201	1.0585	0.146345
18	0.086039	0.8117	0.209567

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.16302	1.5379	0.063807
1	0.09195	0.8675	0.194013
2	-0.275285	-2.597	0.994499
3	0.032831	0.3097	0.378747
4	0.056989	0.5376	0.296086
5	-0.076092	-0.7179	0.762635
6	0.040315	0.3803	0.352304
7	0.237148	2.2373	0.013884
8	-0.093131	-0.8786	0.809007
9	-0.02545	-0.2401	0.594594
10	-0.145172	-1.3696	0.912864
11	-0.354387	-3.3433	0.999394
12	-0.020772	-0.196	0.577457
13	-0.024841	-0.2343	0.592372
14	-0.078056	-0.7364	0.768283
15	0.002072	0.0195	0.492226
16	0.16928	1.597	0.056907
17	0.055827	0.5267	0.299865
18	0.036809	0.3473	0.364609

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.16302 & 1.5379 & 0.063807 \tabularnewline
1 & 0.09195 & 0.8675 & 0.194013 \tabularnewline
2 & -0.275285 & -2.597 & 0.994499 \tabularnewline
3 & 0.032831 & 0.3097 & 0.378747 \tabularnewline
4 & 0.056989 & 0.5376 & 0.296086 \tabularnewline
5 & -0.076092 & -0.7179 & 0.762635 \tabularnewline
6 & 0.040315 & 0.3803 & 0.352304 \tabularnewline
7 & 0.237148 & 2.2373 & 0.013884 \tabularnewline
8 & -0.093131 & -0.8786 & 0.809007 \tabularnewline
9 & -0.02545 & -0.2401 & 0.594594 \tabularnewline
10 & -0.145172 & -1.3696 & 0.912864 \tabularnewline
11 & -0.354387 & -3.3433 & 0.999394 \tabularnewline
12 & -0.020772 & -0.196 & 0.577457 \tabularnewline
13 & -0.024841 & -0.2343 & 0.592372 \tabularnewline
14 & -0.078056 & -0.7364 & 0.768283 \tabularnewline
15 & 0.002072 & 0.0195 & 0.492226 \tabularnewline
16 & 0.16928 & 1.597 & 0.056907 \tabularnewline
17 & 0.055827 & 0.5267 & 0.299865 \tabularnewline
18 & 0.036809 & 0.3473 & 0.364609 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7895&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]0.16302[/C][C]1.5379[/C][C]0.063807[/C][/ROW]
[ROW][C]1[/C][C]0.09195[/C][C]0.8675[/C][C]0.194013[/C][/ROW]
[ROW][C]2[/C][C]-0.275285[/C][C]-2.597[/C][C]0.994499[/C][/ROW]
[ROW][C]3[/C][C]0.032831[/C][C]0.3097[/C][C]0.378747[/C][/ROW]
[ROW][C]4[/C][C]0.056989[/C][C]0.5376[/C][C]0.296086[/C][/ROW]
[ROW][C]5[/C][C]-0.076092[/C][C]-0.7179[/C][C]0.762635[/C][/ROW]
[ROW][C]6[/C][C]0.040315[/C][C]0.3803[/C][C]0.352304[/C][/ROW]
[ROW][C]7[/C][C]0.237148[/C][C]2.2373[/C][C]0.013884[/C][/ROW]
[ROW][C]8[/C][C]-0.093131[/C][C]-0.8786[/C][C]0.809007[/C][/ROW]
[ROW][C]9[/C][C]-0.02545[/C][C]-0.2401[/C][C]0.594594[/C][/ROW]
[ROW][C]10[/C][C]-0.145172[/C][C]-1.3696[/C][C]0.912864[/C][/ROW]
[ROW][C]11[/C][C]-0.354387[/C][C]-3.3433[/C][C]0.999394[/C][/ROW]
[ROW][C]12[/C][C]-0.020772[/C][C]-0.196[/C][C]0.577457[/C][/ROW]
[ROW][C]13[/C][C]-0.024841[/C][C]-0.2343[/C][C]0.592372[/C][/ROW]
[ROW][C]14[/C][C]-0.078056[/C][C]-0.7364[/C][C]0.768283[/C][/ROW]
[ROW][C]15[/C][C]0.002072[/C][C]0.0195[/C][C]0.492226[/C][/ROW]
[ROW][C]16[/C][C]0.16928[/C][C]1.597[/C][C]0.056907[/C][/ROW]
[ROW][C]17[/C][C]0.055827[/C][C]0.5267[/C][C]0.299865[/C][/ROW]
[ROW][C]18[/C][C]0.036809[/C][C]0.3473[/C][C]0.364609[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7895&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7895&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	0.16302	1.5379	0.063807
1	0.09195	0.8675	0.194013
2	-0.275285	-2.597	0.994499
3	0.032831	0.3097	0.378747
4	0.056989	0.5376	0.296086
5	-0.076092	-0.7179	0.762635
6	0.040315	0.3803	0.352304
7	0.237148	2.2373	0.013884
8	-0.093131	-0.8786	0.809007
9	-0.02545	-0.2401	0.594594
10	-0.145172	-1.3696	0.912864
11	-0.354387	-3.3433	0.999394
12	-0.020772	-0.196	0.577457
13	-0.024841	-0.2343	0.592372
14	-0.078056	-0.7364	0.768283
15	0.002072	0.0195	0.492226
16	0.16928	1.597	0.056907
17	0.055827	0.5267	0.299865
18	0.036809	0.3473	0.364609

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code