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Author's title

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

Fri, 05 Dec 2008 03:30:22 -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/05/t12284731228qoxbf5uq0orzsl.htm/, Retrieved Thu, 16 May 2024 14:25:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29142, Retrieved Thu, 16 May 2024 14:25:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

214

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

F     [Exercise 1.13] [Exercise 1.13 (Wo...] [2008-10-01 13:28:34] [b98453cac15ba1066b407e146608df68]
- RMPD  [Univariate Data Series] [Tijdreeks 2: Gaso...] [2008-10-20 15:56:05] [a57f5cc542637534b8bb5bcb4d37eab1]
- RMP     [(Partial) Autocorrelation Function] [Identification/es...] [2008-12-03 21:36:01] [a57f5cc542637534b8bb5bcb4d37eab1]
- RM        [Spectral Analysis] [Identification/es...] [2008-12-03 21:43:51] [a57f5cc542637534b8bb5bcb4d37eab1]
-             [Spectral Analysis] [Identification/es...] [2008-12-03 21:47:18] [a57f5cc542637534b8bb5bcb4d37eab1]
- RMP           [Standard Deviation-Mean Plot] [Identification/es...] [2008-12-05 10:17:50] [a57f5cc542637534b8bb5bcb4d37eab1]
- RMP               [(Partial) Autocorrelation Function] [Identification/es...] [2008-12-05 10:30:22] [0f30549460cf4ec26d9cf94b1fcf7789] [Current]
- RMP                 [ARIMA Backward Selection] [Identification/es...] [2008-12-05 12:40:03] [a57f5cc542637534b8bb5bcb4d37eab1] 
-   P                   [ARIMA Backward Selection] [Identification/es...] [2008-12-08 18:33:38] [a57f5cc542637534b8bb5bcb4d37eab1] 
-                         [ARIMA Backward Selection] [] [2008-12-13 20:48:17] [888addc516c3b812dd7be4bd54caa358] 

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Dataseries X:

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Histogram

Boxplots

0.33
0.33
0.32
0.33
0.34
0.36
0.34
0.33
0.35
0.31
0.28
0.26
0.26
0.26
0.29
0.30
0.30
0.28
0.29
0.29
0.32
0.33
0.29
0.31
0.33
0.36
0.39
0.30
0.27
0.28
0.29
0.30
0.30
0.30
0.31
0.30
0.31
0.29
0.32
0.33
0.35
0.35
0.36
0.40
0.40
0.47
0.43
0.38
0.38
0.40
0.45
0.47
0.45
0.50
0.54
0.55
0.59
0.51
0.50
0.50

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=29142&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=29142&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29142&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	0.801855	5.5554	1e-06
2	0.588638	4.0782	8.5e-05
3	0.463979	3.2145	0.001169
4	0.399906	2.7706	0.003967
5	0.358457	2.4835	0.008278
6	0.188331	1.3048	0.099092
7	0.045083	0.3123	0.378065
8	0.004688	0.0325	0.487111
9	0.022601	0.1566	0.438115
10	0.016362	0.1134	0.455109
11	-0.09105	-0.6308	0.265577
12	-0.213774	-1.4811	0.072561
13	-0.172085	-1.1922	0.119513
14	-0.044008	-0.3049	0.380881
15	0.067715	0.4691	0.320545
16	0.071011	0.492	0.312488
17	0.031424	0.2177	0.414287

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.801855 & 5.5554 & 1e-06 \tabularnewline
2 & 0.588638 & 4.0782 & 8.5e-05 \tabularnewline
3 & 0.463979 & 3.2145 & 0.001169 \tabularnewline
4 & 0.399906 & 2.7706 & 0.003967 \tabularnewline
5 & 0.358457 & 2.4835 & 0.008278 \tabularnewline
6 & 0.188331 & 1.3048 & 0.099092 \tabularnewline
7 & 0.045083 & 0.3123 & 0.378065 \tabularnewline
8 & 0.004688 & 0.0325 & 0.487111 \tabularnewline
9 & 0.022601 & 0.1566 & 0.438115 \tabularnewline
10 & 0.016362 & 0.1134 & 0.455109 \tabularnewline
11 & -0.09105 & -0.6308 & 0.265577 \tabularnewline
12 & -0.213774 & -1.4811 & 0.072561 \tabularnewline
13 & -0.172085 & -1.1922 & 0.119513 \tabularnewline
14 & -0.044008 & -0.3049 & 0.380881 \tabularnewline
15 & 0.067715 & 0.4691 & 0.320545 \tabularnewline
16 & 0.071011 & 0.492 & 0.312488 \tabularnewline
17 & 0.031424 & 0.2177 & 0.414287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29142&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]0.801855[/C][C]5.5554[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.588638[/C][C]4.0782[/C][C]8.5e-05[/C][/ROW]
[ROW][C]3[/C][C]0.463979[/C][C]3.2145[/C][C]0.001169[/C][/ROW]
[ROW][C]4[/C][C]0.399906[/C][C]2.7706[/C][C]0.003967[/C][/ROW]
[ROW][C]5[/C][C]0.358457[/C][C]2.4835[/C][C]0.008278[/C][/ROW]
[ROW][C]6[/C][C]0.188331[/C][C]1.3048[/C][C]0.099092[/C][/ROW]
[ROW][C]7[/C][C]0.045083[/C][C]0.3123[/C][C]0.378065[/C][/ROW]
[ROW][C]8[/C][C]0.004688[/C][C]0.0325[/C][C]0.487111[/C][/ROW]
[ROW][C]9[/C][C]0.022601[/C][C]0.1566[/C][C]0.438115[/C][/ROW]
[ROW][C]10[/C][C]0.016362[/C][C]0.1134[/C][C]0.455109[/C][/ROW]
[ROW][C]11[/C][C]-0.09105[/C][C]-0.6308[/C][C]0.265577[/C][/ROW]
[ROW][C]12[/C][C]-0.213774[/C][C]-1.4811[/C][C]0.072561[/C][/ROW]
[ROW][C]13[/C][C]-0.172085[/C][C]-1.1922[/C][C]0.119513[/C][/ROW]
[ROW][C]14[/C][C]-0.044008[/C][C]-0.3049[/C][C]0.380881[/C][/ROW]
[ROW][C]15[/C][C]0.067715[/C][C]0.4691[/C][C]0.320545[/C][/ROW]
[ROW][C]16[/C][C]0.071011[/C][C]0.492[/C][C]0.312488[/C][/ROW]
[ROW][C]17[/C][C]0.031424[/C][C]0.2177[/C][C]0.414287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29142&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29142&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	0.801855	5.5554	1e-06
2	0.588638	4.0782	8.5e-05
3	0.463979	3.2145	0.001169
4	0.399906	2.7706	0.003967
5	0.358457	2.4835	0.008278
6	0.188331	1.3048	0.099092
7	0.045083	0.3123	0.378065
8	0.004688	0.0325	0.487111
9	0.022601	0.1566	0.438115
10	0.016362	0.1134	0.455109
11	-0.09105	-0.6308	0.265577
12	-0.213774	-1.4811	0.072561
13	-0.172085	-1.1922	0.119513
14	-0.044008	-0.3049	0.380881
15	0.067715	0.4691	0.320545
16	0.071011	0.492	0.312488
17	0.031424	0.2177	0.414287

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.801855	5.5554	1e-06
2	-0.152185	-1.0544	0.148496
3	0.120931	0.8378	0.203139
4	0.061346	0.425	0.336362
5	0.038513	0.2668	0.395372
6	-0.366847	-2.5416	0.00716
7	0.048543	0.3363	0.36905
8	0.080742	0.5594	0.289246
9	0.065419	0.4532	0.32621
10	-0.097051	-0.6724	0.252281
11	-0.147761	-1.0237	0.15555
12	-0.139154	-0.9641	0.169918
13	0.291158	2.0172	0.024643
14	0.138213	0.9576	0.17154
15	0.140564	0.9739	0.167505
16	-0.123808	-0.8578	0.197641
17	-0.016462	-0.1141	0.454835

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.801855 & 5.5554 & 1e-06 \tabularnewline
2 & -0.152185 & -1.0544 & 0.148496 \tabularnewline
3 & 0.120931 & 0.8378 & 0.203139 \tabularnewline
4 & 0.061346 & 0.425 & 0.336362 \tabularnewline
5 & 0.038513 & 0.2668 & 0.395372 \tabularnewline
6 & -0.366847 & -2.5416 & 0.00716 \tabularnewline
7 & 0.048543 & 0.3363 & 0.36905 \tabularnewline
8 & 0.080742 & 0.5594 & 0.289246 \tabularnewline
9 & 0.065419 & 0.4532 & 0.32621 \tabularnewline
10 & -0.097051 & -0.6724 & 0.252281 \tabularnewline
11 & -0.147761 & -1.0237 & 0.15555 \tabularnewline
12 & -0.139154 & -0.9641 & 0.169918 \tabularnewline
13 & 0.291158 & 2.0172 & 0.024643 \tabularnewline
14 & 0.138213 & 0.9576 & 0.17154 \tabularnewline
15 & 0.140564 & 0.9739 & 0.167505 \tabularnewline
16 & -0.123808 & -0.8578 & 0.197641 \tabularnewline
17 & -0.016462 & -0.1141 & 0.454835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29142&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]0.801855[/C][C]5.5554[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.152185[/C][C]-1.0544[/C][C]0.148496[/C][/ROW]
[ROW][C]3[/C][C]0.120931[/C][C]0.8378[/C][C]0.203139[/C][/ROW]
[ROW][C]4[/C][C]0.061346[/C][C]0.425[/C][C]0.336362[/C][/ROW]
[ROW][C]5[/C][C]0.038513[/C][C]0.2668[/C][C]0.395372[/C][/ROW]
[ROW][C]6[/C][C]-0.366847[/C][C]-2.5416[/C][C]0.00716[/C][/ROW]
[ROW][C]7[/C][C]0.048543[/C][C]0.3363[/C][C]0.36905[/C][/ROW]
[ROW][C]8[/C][C]0.080742[/C][C]0.5594[/C][C]0.289246[/C][/ROW]
[ROW][C]9[/C][C]0.065419[/C][C]0.4532[/C][C]0.32621[/C][/ROW]
[ROW][C]10[/C][C]-0.097051[/C][C]-0.6724[/C][C]0.252281[/C][/ROW]
[ROW][C]11[/C][C]-0.147761[/C][C]-1.0237[/C][C]0.15555[/C][/ROW]
[ROW][C]12[/C][C]-0.139154[/C][C]-0.9641[/C][C]0.169918[/C][/ROW]
[ROW][C]13[/C][C]0.291158[/C][C]2.0172[/C][C]0.024643[/C][/ROW]
[ROW][C]14[/C][C]0.138213[/C][C]0.9576[/C][C]0.17154[/C][/ROW]
[ROW][C]15[/C][C]0.140564[/C][C]0.9739[/C][C]0.167505[/C][/ROW]
[ROW][C]16[/C][C]-0.123808[/C][C]-0.8578[/C][C]0.197641[/C][/ROW]
[ROW][C]17[/C][C]-0.016462[/C][C]-0.1141[/C][C]0.454835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29142&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29142&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	0.801855	5.5554	1e-06
2	-0.152185	-1.0544	0.148496
3	0.120931	0.8378	0.203139
4	0.061346	0.425	0.336362
5	0.038513	0.2668	0.395372
6	-0.366847	-2.5416	0.00716
7	0.048543	0.3363	0.36905
8	0.080742	0.5594	0.289246
9	0.065419	0.4532	0.32621
10	-0.097051	-0.6724	0.252281
11	-0.147761	-1.0237	0.15555
12	-0.139154	-0.9641	0.169918
13	0.291158	2.0172	0.024643
14	0.138213	0.9576	0.17154
15	0.140564	0.9739	0.167505
16	-0.123808	-0.8578	0.197641
17	-0.016462	-0.1141	0.454835

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -0.9 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -0.9 ; 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code