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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

Sat, 13 Dec 2008 07:12:34 -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/13/t1229177689y7gx756nnfcj639.htm/, Retrieved Sun, 19 May 2024 04:08:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33113, Retrieved Sun, 19 May 2024 04:08:08 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

188

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

F     [Univariate Explorative Data Analysis] [Investigation Dis...] [2007-10-21 17:06:37] [b9964c45117f7aac638ab9056d451faa]
F    D  [Univariate Explorative Data Analysis] [Reproduce Q2] [2008-10-24 13:27:07] [deb3c14ac9e4607a6d84fc9d0e0e6cc2]
- RMPD      [(Partial) Autocorrelation Function] [Paper H5 Mannen (...] [2008-12-13 14:12:34] [5e9e099b83e50415d7642e10d74756e4] [Current]
-   P         [(Partial) Autocorrelation Function] [Paper H5 Mannen c...] [2008-12-13 14:28:40] [deb3c14ac9e4607a6d84fc9d0e0e6cc2] 
- RMP         [ARIMA Backward Selection] [Paper H6 Mannen A...] [2008-12-13 16:00:00] [deb3c14ac9e4607a6d84fc9d0e0e6cc2] 
- RMP           [ARIMA Forecasting] [Paper H6 Mannen A...] [2008-12-22 19:57:49] [deb3c14ac9e4607a6d84fc9d0e0e6cc2] 
- RMP           [ARIMA Forecasting] [Paper H6 Mannen A...] [2008-12-22 20:35:43] [deb3c14ac9e4607a6d84fc9d0e0e6cc2] 
-   PD          [ARIMA Backward Selection] [Paper H6 Vrouwen ...] [2008-12-22 21:30:00] [deb3c14ac9e4607a6d84fc9d0e0e6cc2] 
- RMPD          [ARIMA Forecasting] [Paper H6 Vrouwen ...] [2008-12-22 21:38:56] [deb3c14ac9e4607a6d84fc9d0e0e6cc2] 

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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	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=33113&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=33113&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33113&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	-0.110182	-0.7791	0.219795
2	0.1228	0.8683	0.194682
3	0.143942	1.0178	0.156831
4	0.095763	0.6771	0.250718
5	0.013774	0.0974	0.461401
6	0.075097	0.531	0.298879
7	0.045047	0.3185	0.375704
8	0.113625	0.8035	0.212758
9	-0.058644	-0.4147	0.340075
10	-0.082328	-0.5821	0.281542
11	0.347953	2.4604	0.008688
12	-0.268411	-1.898	0.031741
13	-0.030089	-0.2128	0.416189
14	-0.035589	-0.2517	0.401171
15	-0.05025	-0.3553	0.361921
16	-0.159197	-1.1257	0.132835
17	-0.031402	-0.222	0.412592

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.110182 & -0.7791 & 0.219795 \tabularnewline
2 & 0.1228 & 0.8683 & 0.194682 \tabularnewline
3 & 0.143942 & 1.0178 & 0.156831 \tabularnewline
4 & 0.095763 & 0.6771 & 0.250718 \tabularnewline
5 & 0.013774 & 0.0974 & 0.461401 \tabularnewline
6 & 0.075097 & 0.531 & 0.298879 \tabularnewline
7 & 0.045047 & 0.3185 & 0.375704 \tabularnewline
8 & 0.113625 & 0.8035 & 0.212758 \tabularnewline
9 & -0.058644 & -0.4147 & 0.340075 \tabularnewline
10 & -0.082328 & -0.5821 & 0.281542 \tabularnewline
11 & 0.347953 & 2.4604 & 0.008688 \tabularnewline
12 & -0.268411 & -1.898 & 0.031741 \tabularnewline
13 & -0.030089 & -0.2128 & 0.416189 \tabularnewline
14 & -0.035589 & -0.2517 & 0.401171 \tabularnewline
15 & -0.05025 & -0.3553 & 0.361921 \tabularnewline
16 & -0.159197 & -1.1257 & 0.132835 \tabularnewline
17 & -0.031402 & -0.222 & 0.412592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33113&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]-0.110182[/C][C]-0.7791[/C][C]0.219795[/C][/ROW]
[ROW][C]2[/C][C]0.1228[/C][C]0.8683[/C][C]0.194682[/C][/ROW]
[ROW][C]3[/C][C]0.143942[/C][C]1.0178[/C][C]0.156831[/C][/ROW]
[ROW][C]4[/C][C]0.095763[/C][C]0.6771[/C][C]0.250718[/C][/ROW]
[ROW][C]5[/C][C]0.013774[/C][C]0.0974[/C][C]0.461401[/C][/ROW]
[ROW][C]6[/C][C]0.075097[/C][C]0.531[/C][C]0.298879[/C][/ROW]
[ROW][C]7[/C][C]0.045047[/C][C]0.3185[/C][C]0.375704[/C][/ROW]
[ROW][C]8[/C][C]0.113625[/C][C]0.8035[/C][C]0.212758[/C][/ROW]
[ROW][C]9[/C][C]-0.058644[/C][C]-0.4147[/C][C]0.340075[/C][/ROW]
[ROW][C]10[/C][C]-0.082328[/C][C]-0.5821[/C][C]0.281542[/C][/ROW]
[ROW][C]11[/C][C]0.347953[/C][C]2.4604[/C][C]0.008688[/C][/ROW]
[ROW][C]12[/C][C]-0.268411[/C][C]-1.898[/C][C]0.031741[/C][/ROW]
[ROW][C]13[/C][C]-0.030089[/C][C]-0.2128[/C][C]0.416189[/C][/ROW]
[ROW][C]14[/C][C]-0.035589[/C][C]-0.2517[/C][C]0.401171[/C][/ROW]
[ROW][C]15[/C][C]-0.05025[/C][C]-0.3553[/C][C]0.361921[/C][/ROW]
[ROW][C]16[/C][C]-0.159197[/C][C]-1.1257[/C][C]0.132835[/C][/ROW]
[ROW][C]17[/C][C]-0.031402[/C][C]-0.222[/C][C]0.412592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33113&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33113&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	-0.110182	-0.7791	0.219795
2	0.1228	0.8683	0.194682
3	0.143942	1.0178	0.156831
4	0.095763	0.6771	0.250718
5	0.013774	0.0974	0.461401
6	0.075097	0.531	0.298879
7	0.045047	0.3185	0.375704
8	0.113625	0.8035	0.212758
9	-0.058644	-0.4147	0.340075
10	-0.082328	-0.5821	0.281542
11	0.347953	2.4604	0.008688
12	-0.268411	-1.898	0.031741
13	-0.030089	-0.2128	0.416189
14	-0.035589	-0.2517	0.401171
15	-0.05025	-0.3553	0.361921
16	-0.159197	-1.1257	0.132835
17	-0.031402	-0.222	0.412592

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.110182	-0.7791	0.219795
2	0.11202	0.7921	0.216022
3	0.172532	1.22	0.114097
4	0.122364	0.8652	0.195518
5	0.001359	0.0096	0.496186
6	0.026194	0.1852	0.426904
7	0.023168	0.1638	0.435267
8	0.103895	0.7347	0.232992
9	-0.061271	-0.4333	0.333348
10	-0.158944	-1.1239	0.133211
11	0.320825	2.2686	0.013822
12	-0.206009	-1.4567	0.075725
13	-0.142207	-1.0056	0.159736
14	-0.090241	-0.6381	0.263161
15	-0.040881	-0.2891	0.386861
16	-0.101194	-0.7156	0.238798
17	-0.044659	-0.3158	0.376738

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.110182 & -0.7791 & 0.219795 \tabularnewline
2 & 0.11202 & 0.7921 & 0.216022 \tabularnewline
3 & 0.172532 & 1.22 & 0.114097 \tabularnewline
4 & 0.122364 & 0.8652 & 0.195518 \tabularnewline
5 & 0.001359 & 0.0096 & 0.496186 \tabularnewline
6 & 0.026194 & 0.1852 & 0.426904 \tabularnewline
7 & 0.023168 & 0.1638 & 0.435267 \tabularnewline
8 & 0.103895 & 0.7347 & 0.232992 \tabularnewline
9 & -0.061271 & -0.4333 & 0.333348 \tabularnewline
10 & -0.158944 & -1.1239 & 0.133211 \tabularnewline
11 & 0.320825 & 2.2686 & 0.013822 \tabularnewline
12 & -0.206009 & -1.4567 & 0.075725 \tabularnewline
13 & -0.142207 & -1.0056 & 0.159736 \tabularnewline
14 & -0.090241 & -0.6381 & 0.263161 \tabularnewline
15 & -0.040881 & -0.2891 & 0.386861 \tabularnewline
16 & -0.101194 & -0.7156 & 0.238798 \tabularnewline
17 & -0.044659 & -0.3158 & 0.376738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33113&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]-0.110182[/C][C]-0.7791[/C][C]0.219795[/C][/ROW]
[ROW][C]2[/C][C]0.11202[/C][C]0.7921[/C][C]0.216022[/C][/ROW]
[ROW][C]3[/C][C]0.172532[/C][C]1.22[/C][C]0.114097[/C][/ROW]
[ROW][C]4[/C][C]0.122364[/C][C]0.8652[/C][C]0.195518[/C][/ROW]
[ROW][C]5[/C][C]0.001359[/C][C]0.0096[/C][C]0.496186[/C][/ROW]
[ROW][C]6[/C][C]0.026194[/C][C]0.1852[/C][C]0.426904[/C][/ROW]
[ROW][C]7[/C][C]0.023168[/C][C]0.1638[/C][C]0.435267[/C][/ROW]
[ROW][C]8[/C][C]0.103895[/C][C]0.7347[/C][C]0.232992[/C][/ROW]
[ROW][C]9[/C][C]-0.061271[/C][C]-0.4333[/C][C]0.333348[/C][/ROW]
[ROW][C]10[/C][C]-0.158944[/C][C]-1.1239[/C][C]0.133211[/C][/ROW]
[ROW][C]11[/C][C]0.320825[/C][C]2.2686[/C][C]0.013822[/C][/ROW]
[ROW][C]12[/C][C]-0.206009[/C][C]-1.4567[/C][C]0.075725[/C][/ROW]
[ROW][C]13[/C][C]-0.142207[/C][C]-1.0056[/C][C]0.159736[/C][/ROW]
[ROW][C]14[/C][C]-0.090241[/C][C]-0.6381[/C][C]0.263161[/C][/ROW]
[ROW][C]15[/C][C]-0.040881[/C][C]-0.2891[/C][C]0.386861[/C][/ROW]
[ROW][C]16[/C][C]-0.101194[/C][C]-0.7156[/C][C]0.238798[/C][/ROW]
[ROW][C]17[/C][C]-0.044659[/C][C]-0.3158[/C][C]0.376738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33113&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33113&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	-0.110182	-0.7791	0.219795
2	0.11202	0.7921	0.216022
3	0.172532	1.22	0.114097
4	0.122364	0.8652	0.195518
5	0.001359	0.0096	0.496186
6	0.026194	0.1852	0.426904
7	0.023168	0.1638	0.435267
8	0.103895	0.7347	0.232992
9	-0.061271	-0.4333	0.333348
10	-0.158944	-1.1239	0.133211
11	0.320825	2.2686	0.013822
12	-0.206009	-1.4567	0.075725
13	-0.142207	-1.0056	0.159736
14	-0.090241	-0.6381	0.263161
15	-0.040881	-0.2891	0.386861
16	-0.101194	-0.7156	0.238798
17	-0.044659	-0.3158	0.376738

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

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

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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code