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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

Sun, 07 Dec 2008 11:10:24 -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/07/t1228673466vl3rz501n4ey4zj.htm/, Retrieved Fri, 17 May 2024 05:14:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30206, Retrieved Fri, 17 May 2024 05:14:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

186

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  [Standard Deviation-Mean Plot] [S1] [2008-12-07 17:37:06] [a0d819c22534897f04a2f0b92f1eb36a]
-    D    [Standard Deviation-Mean Plot] [S1] [2008-12-07 17:58:18] [a0d819c22534897f04a2f0b92f1eb36a]
- RM        [Variance Reduction Matrix] [s2] [2008-12-07 18:02:35] [a0d819c22534897f04a2f0b92f1eb36a]
- RMP           [(Partial) Autocorrelation Function] [S2 ACF] [2008-12-07 18:10:24] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]
-   P             [(Partial) Autocorrelation Function] [s2] [2008-12-07 18:12:59] [a0d819c22534897f04a2f0b92f1eb36a] 
-   P               [(Partial) Autocorrelation Function] [s2 ACF] [2008-12-07 18:25:03] [a0d819c22534897f04a2f0b92f1eb36a] 
-                     [(Partial) Autocorrelation Function] [s2 acf d1D1] [2008-12-07 18:26:56] [a0d819c22534897f04a2f0b92f1eb36a] 
- RM                    [Spectral Analysis] [S2 SA - d0 D0 L1] [2008-12-07 18:29:54] [a0d819c22534897f04a2f0b92f1eb36a] 
-                         [Spectral Analysis] [s2 SA d1D1 L1] [2008-12-07 18:32:14] [a0d819c22534897f04a2f0b92f1eb36a] 
-                           [Spectral Analysis] [s3] [2008-12-07 18:39:13] [a0d819c22534897f04a2f0b92f1eb36a] 
-                             [Spectral Analysis] [s3 sa] [2008-12-07 18:42:05] [a0d819c22534897f04a2f0b92f1eb36a] 
- RM                            [(Partial) Autocorrelation Function] [s4] [2008-12-07 18:48:27] [a0d819c22534897f04a2f0b92f1eb36a] 

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30206&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30206&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.811954	6.2894	0
2	0.517041	4.005	8.7e-05
3	0.271873	2.1059	0.019702
4	0.147147	1.1398	0.12945
5	0.125949	0.9756	0.166591
6	0.115588	0.8953	0.187091
7	0.105712	0.8188	0.208058
8	0.097572	0.7558	0.226366
9	0.161888	1.254	0.107357
10	0.314375	2.4351	0.008938
11	0.50636	3.9222	0.000114
12	0.607922	4.7089	8e-06
13	0.438685	3.398	0.000605
14	0.198699	1.5391	0.064517
15	0.002084	0.0161	0.493587
16	-0.094136	-0.7292	0.234366
17	-0.111026	-0.86	0.196606

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.811954 & 6.2894 & 0 \tabularnewline
2 & 0.517041 & 4.005 & 8.7e-05 \tabularnewline
3 & 0.271873 & 2.1059 & 0.019702 \tabularnewline
4 & 0.147147 & 1.1398 & 0.12945 \tabularnewline
5 & 0.125949 & 0.9756 & 0.166591 \tabularnewline
6 & 0.115588 & 0.8953 & 0.187091 \tabularnewline
7 & 0.105712 & 0.8188 & 0.208058 \tabularnewline
8 & 0.097572 & 0.7558 & 0.226366 \tabularnewline
9 & 0.161888 & 1.254 & 0.107357 \tabularnewline
10 & 0.314375 & 2.4351 & 0.008938 \tabularnewline
11 & 0.50636 & 3.9222 & 0.000114 \tabularnewline
12 & 0.607922 & 4.7089 & 8e-06 \tabularnewline
13 & 0.438685 & 3.398 & 0.000605 \tabularnewline
14 & 0.198699 & 1.5391 & 0.064517 \tabularnewline
15 & 0.002084 & 0.0161 & 0.493587 \tabularnewline
16 & -0.094136 & -0.7292 & 0.234366 \tabularnewline
17 & -0.111026 & -0.86 & 0.196606 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30206&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]0.811954[/C][C]6.2894[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.517041[/C][C]4.005[/C][C]8.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.271873[/C][C]2.1059[/C][C]0.019702[/C][/ROW]
[ROW][C]4[/C][C]0.147147[/C][C]1.1398[/C][C]0.12945[/C][/ROW]
[ROW][C]5[/C][C]0.125949[/C][C]0.9756[/C][C]0.166591[/C][/ROW]
[ROW][C]6[/C][C]0.115588[/C][C]0.8953[/C][C]0.187091[/C][/ROW]
[ROW][C]7[/C][C]0.105712[/C][C]0.8188[/C][C]0.208058[/C][/ROW]
[ROW][C]8[/C][C]0.097572[/C][C]0.7558[/C][C]0.226366[/C][/ROW]
[ROW][C]9[/C][C]0.161888[/C][C]1.254[/C][C]0.107357[/C][/ROW]
[ROW][C]10[/C][C]0.314375[/C][C]2.4351[/C][C]0.008938[/C][/ROW]
[ROW][C]11[/C][C]0.50636[/C][C]3.9222[/C][C]0.000114[/C][/ROW]
[ROW][C]12[/C][C]0.607922[/C][C]4.7089[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.438685[/C][C]3.398[/C][C]0.000605[/C][/ROW]
[ROW][C]14[/C][C]0.198699[/C][C]1.5391[/C][C]0.064517[/C][/ROW]
[ROW][C]15[/C][C]0.002084[/C][C]0.0161[/C][C]0.493587[/C][/ROW]
[ROW][C]16[/C][C]-0.094136[/C][C]-0.7292[/C][C]0.234366[/C][/ROW]
[ROW][C]17[/C][C]-0.111026[/C][C]-0.86[/C][C]0.196606[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30206&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	0.811954	6.2894	0
2	0.517041	4.005	8.7e-05
3	0.271873	2.1059	0.019702
4	0.147147	1.1398	0.12945
5	0.125949	0.9756	0.166591
6	0.115588	0.8953	0.187091
7	0.105712	0.8188	0.208058
8	0.097572	0.7558	0.226366
9	0.161888	1.254	0.107357
10	0.314375	2.4351	0.008938
11	0.50636	3.9222	0.000114
12	0.607922	4.7089	8e-06
13	0.438685	3.398	0.000605
14	0.198699	1.5391	0.064517
15	0.002084	0.0161	0.493587
16	-0.094136	-0.7292	0.234366
17	-0.111026	-0.86	0.196606

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.811954	6.2894	0
2	-0.417423	-3.2333	0.000995
3	0.055973	0.4336	0.33308
4	0.11261	0.8723	0.193269
5	0.0662	0.5128	0.304992
6	-0.099239	-0.7687	0.222542
7	0.073101	0.5662	0.286672
8	0.032475	0.2516	0.401124
9	0.258961	2.0059	0.024691
10	0.248784	1.9271	0.029355
11	0.263764	2.0431	0.022721
12	-0.015499	-0.1201	0.452422
13	-0.569253	-4.4094	2.2e-05
14	0.212459	1.6457	0.052527
15	-0.071896	-0.5569	0.289833
16	-0.107918	-0.8359	0.203256
17	-0.106242	-0.8229	0.206898

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.811954 & 6.2894 & 0 \tabularnewline
2 & -0.417423 & -3.2333 & 0.000995 \tabularnewline
3 & 0.055973 & 0.4336 & 0.33308 \tabularnewline
4 & 0.11261 & 0.8723 & 0.193269 \tabularnewline
5 & 0.0662 & 0.5128 & 0.304992 \tabularnewline
6 & -0.099239 & -0.7687 & 0.222542 \tabularnewline
7 & 0.073101 & 0.5662 & 0.286672 \tabularnewline
8 & 0.032475 & 0.2516 & 0.401124 \tabularnewline
9 & 0.258961 & 2.0059 & 0.024691 \tabularnewline
10 & 0.248784 & 1.9271 & 0.029355 \tabularnewline
11 & 0.263764 & 2.0431 & 0.022721 \tabularnewline
12 & -0.015499 & -0.1201 & 0.452422 \tabularnewline
13 & -0.569253 & -4.4094 & 2.2e-05 \tabularnewline
14 & 0.212459 & 1.6457 & 0.052527 \tabularnewline
15 & -0.071896 & -0.5569 & 0.289833 \tabularnewline
16 & -0.107918 & -0.8359 & 0.203256 \tabularnewline
17 & -0.106242 & -0.8229 & 0.206898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30206&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]0.811954[/C][C]6.2894[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.417423[/C][C]-3.2333[/C][C]0.000995[/C][/ROW]
[ROW][C]3[/C][C]0.055973[/C][C]0.4336[/C][C]0.33308[/C][/ROW]
[ROW][C]4[/C][C]0.11261[/C][C]0.8723[/C][C]0.193269[/C][/ROW]
[ROW][C]5[/C][C]0.0662[/C][C]0.5128[/C][C]0.304992[/C][/ROW]
[ROW][C]6[/C][C]-0.099239[/C][C]-0.7687[/C][C]0.222542[/C][/ROW]
[ROW][C]7[/C][C]0.073101[/C][C]0.5662[/C][C]0.286672[/C][/ROW]
[ROW][C]8[/C][C]0.032475[/C][C]0.2516[/C][C]0.401124[/C][/ROW]
[ROW][C]9[/C][C]0.258961[/C][C]2.0059[/C][C]0.024691[/C][/ROW]
[ROW][C]10[/C][C]0.248784[/C][C]1.9271[/C][C]0.029355[/C][/ROW]
[ROW][C]11[/C][C]0.263764[/C][C]2.0431[/C][C]0.022721[/C][/ROW]
[ROW][C]12[/C][C]-0.015499[/C][C]-0.1201[/C][C]0.452422[/C][/ROW]
[ROW][C]13[/C][C]-0.569253[/C][C]-4.4094[/C][C]2.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.212459[/C][C]1.6457[/C][C]0.052527[/C][/ROW]
[ROW][C]15[/C][C]-0.071896[/C][C]-0.5569[/C][C]0.289833[/C][/ROW]
[ROW][C]16[/C][C]-0.107918[/C][C]-0.8359[/C][C]0.203256[/C][/ROW]
[ROW][C]17[/C][C]-0.106242[/C][C]-0.8229[/C][C]0.206898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30206&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	0.811954	6.2894	0
2	-0.417423	-3.2333	0.000995
3	0.055973	0.4336	0.33308
4	0.11261	0.8723	0.193269
5	0.0662	0.5128	0.304992
6	-0.099239	-0.7687	0.222542
7	0.073101	0.5662	0.286672
8	0.032475	0.2516	0.401124
9	0.258961	2.0059	0.024691
10	0.248784	1.9271	0.029355
11	0.263764	2.0431	0.022721
12	-0.015499	-0.1201	0.452422
13	-0.569253	-4.4094	2.2e-05
14	0.212459	1.6457	0.052527
15	-0.071896	-0.5569	0.289833
16	-0.107918	-0.8359	0.203256
17	-0.106242	-0.8229	0.206898

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code