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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

Thu, 06 Dec 2007 07:48:12 -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/2007/Dec/06/t1196951784bpuo43dicpmzbh1.htm/, Retrieved Fri, 03 May 2024 14:50:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2637, Retrieved Fri, 03 May 2024 14:50:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Autocorrelatie functie inflatie

Estimated Impact

176

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

-       [(Partial) Autocorrelation Function] [Workshop 4] [2007-12-06 14:48:12] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]

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Dataseries X:

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Histogram

Boxplots

0,3
2,1
2,5
2,3
2,4
3
1,7
3,5
4
3,7
3,7
3
2,7
2,5
2,2
2,9
3,1
3
2,8
2,5
1,9
1,9
1,8
2
2,6
2,5
2,5
1,6
1,4
0,8
1,1
1,3
1,2
1,3
1,1
1,3
1,2
1,6
1,7
1,5
0,9
1,5
1,4
1,6
1,7
1,4
1,8
1,7
1,4
1,2
1
1,7
2,4
2
2,1
2
1,8
2,7
2,3
1,9
2
2,3
2,8
2,4
2,3
2,7
2,7
2,9
3
2,2
2,3
2,8

Summary of compuational 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 compuational 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=2637&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]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=2637&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2637&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4261	0
1	-0.070117	-0.5908	0.72174
2	-0.065945	-0.5557	0.709906
3	-0.027171	-0.2289	0.590215
4	-0.092412	-0.7787	0.780621
5	-0.066332	-0.5589	0.711012
6	0.218352	1.8399	0.034984
7	0.002694	0.0227	0.490977
8	0.04469	0.3766	0.353809
9	0.00724	0.061	0.475765
10	-0.015425	-0.13	0.551523
11	0.051777	0.4363	0.331979
12	-0.237276	-1.9993	0.975299
13	-0.0099	-0.0834	0.533123
14	0.113828	0.9591	0.170374
15	0.013349	0.1125	0.455381
16	0.089676	0.7556	0.226187
17	-0.089431	-0.7536	0.773197

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4261 & 0 \tabularnewline
1 & -0.070117 & -0.5908 & 0.72174 \tabularnewline
2 & -0.065945 & -0.5557 & 0.709906 \tabularnewline
3 & -0.027171 & -0.2289 & 0.590215 \tabularnewline
4 & -0.092412 & -0.7787 & 0.780621 \tabularnewline
5 & -0.066332 & -0.5589 & 0.711012 \tabularnewline
6 & 0.218352 & 1.8399 & 0.034984 \tabularnewline
7 & 0.002694 & 0.0227 & 0.490977 \tabularnewline
8 & 0.04469 & 0.3766 & 0.353809 \tabularnewline
9 & 0.00724 & 0.061 & 0.475765 \tabularnewline
10 & -0.015425 & -0.13 & 0.551523 \tabularnewline
11 & 0.051777 & 0.4363 & 0.331979 \tabularnewline
12 & -0.237276 & -1.9993 & 0.975299 \tabularnewline
13 & -0.0099 & -0.0834 & 0.533123 \tabularnewline
14 & 0.113828 & 0.9591 & 0.170374 \tabularnewline
15 & 0.013349 & 0.1125 & 0.455381 \tabularnewline
16 & 0.089676 & 0.7556 & 0.226187 \tabularnewline
17 & -0.089431 & -0.7536 & 0.773197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2637&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]8.4261[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.070117[/C][C]-0.5908[/C][C]0.72174[/C][/ROW]
[ROW][C]2[/C][C]-0.065945[/C][C]-0.5557[/C][C]0.709906[/C][/ROW]
[ROW][C]3[/C][C]-0.027171[/C][C]-0.2289[/C][C]0.590215[/C][/ROW]
[ROW][C]4[/C][C]-0.092412[/C][C]-0.7787[/C][C]0.780621[/C][/ROW]
[ROW][C]5[/C][C]-0.066332[/C][C]-0.5589[/C][C]0.711012[/C][/ROW]
[ROW][C]6[/C][C]0.218352[/C][C]1.8399[/C][C]0.034984[/C][/ROW]
[ROW][C]7[/C][C]0.002694[/C][C]0.0227[/C][C]0.490977[/C][/ROW]
[ROW][C]8[/C][C]0.04469[/C][C]0.3766[/C][C]0.353809[/C][/ROW]
[ROW][C]9[/C][C]0.00724[/C][C]0.061[/C][C]0.475765[/C][/ROW]
[ROW][C]10[/C][C]-0.015425[/C][C]-0.13[/C][C]0.551523[/C][/ROW]
[ROW][C]11[/C][C]0.051777[/C][C]0.4363[/C][C]0.331979[/C][/ROW]
[ROW][C]12[/C][C]-0.237276[/C][C]-1.9993[/C][C]0.975299[/C][/ROW]
[ROW][C]13[/C][C]-0.0099[/C][C]-0.0834[/C][C]0.533123[/C][/ROW]
[ROW][C]14[/C][C]0.113828[/C][C]0.9591[/C][C]0.170374[/C][/ROW]
[ROW][C]15[/C][C]0.013349[/C][C]0.1125[/C][C]0.455381[/C][/ROW]
[ROW][C]16[/C][C]0.089676[/C][C]0.7556[/C][C]0.226187[/C][/ROW]
[ROW][C]17[/C][C]-0.089431[/C][C]-0.7536[/C][C]0.773197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2637&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2637&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	8.4261	0
1	-0.070117	-0.5908	0.72174
2	-0.065945	-0.5557	0.709906
3	-0.027171	-0.2289	0.590215
4	-0.092412	-0.7787	0.780621
5	-0.066332	-0.5589	0.711012
6	0.218352	1.8399	0.034984
7	0.002694	0.0227	0.490977
8	0.04469	0.3766	0.353809
9	0.00724	0.061	0.475765
10	-0.015425	-0.13	0.551523
11	0.051777	0.4363	0.331979
12	-0.237276	-1.9993	0.975299
13	-0.0099	-0.0834	0.533123
14	0.113828	0.9591	0.170374
15	0.013349	0.1125	0.455381
16	0.089676	0.7556	0.226187
17	-0.089431	-0.7536	0.773197

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.070117	-0.5908	0.72174
1	-0.071212	-0.6	0.724805
2	-0.037491	-0.3159	0.623498
3	-0.103207	-0.8696	0.806286
4	-0.088266	-0.7437	0.770256
5	0.195273	1.6454	0.052154
6	0.018284	0.1541	0.438999
7	0.063969	0.539	0.295781
8	0.019789	0.1667	0.434021
9	0.030164	0.2542	0.40005
10	0.095137	0.8016	0.212718
11	-0.278758	-2.3489	0.989191
12	-0.034935	-0.2944	0.615333
13	0.071271	0.6005	0.27503
14	0.010721	0.0903	0.464136
15	0.075743	0.6382	0.262692
16	-0.168117	-1.4166	0.91951
17	0.049283	0.4153	0.339599

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.070117 & -0.5908 & 0.72174 \tabularnewline
1 & -0.071212 & -0.6 & 0.724805 \tabularnewline
2 & -0.037491 & -0.3159 & 0.623498 \tabularnewline
3 & -0.103207 & -0.8696 & 0.806286 \tabularnewline
4 & -0.088266 & -0.7437 & 0.770256 \tabularnewline
5 & 0.195273 & 1.6454 & 0.052154 \tabularnewline
6 & 0.018284 & 0.1541 & 0.438999 \tabularnewline
7 & 0.063969 & 0.539 & 0.295781 \tabularnewline
8 & 0.019789 & 0.1667 & 0.434021 \tabularnewline
9 & 0.030164 & 0.2542 & 0.40005 \tabularnewline
10 & 0.095137 & 0.8016 & 0.212718 \tabularnewline
11 & -0.278758 & -2.3489 & 0.989191 \tabularnewline
12 & -0.034935 & -0.2944 & 0.615333 \tabularnewline
13 & 0.071271 & 0.6005 & 0.27503 \tabularnewline
14 & 0.010721 & 0.0903 & 0.464136 \tabularnewline
15 & 0.075743 & 0.6382 & 0.262692 \tabularnewline
16 & -0.168117 & -1.4166 & 0.91951 \tabularnewline
17 & 0.049283 & 0.4153 & 0.339599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2637&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]-0.070117[/C][C]-0.5908[/C][C]0.72174[/C][/ROW]
[ROW][C]1[/C][C]-0.071212[/C][C]-0.6[/C][C]0.724805[/C][/ROW]
[ROW][C]2[/C][C]-0.037491[/C][C]-0.3159[/C][C]0.623498[/C][/ROW]
[ROW][C]3[/C][C]-0.103207[/C][C]-0.8696[/C][C]0.806286[/C][/ROW]
[ROW][C]4[/C][C]-0.088266[/C][C]-0.7437[/C][C]0.770256[/C][/ROW]
[ROW][C]5[/C][C]0.195273[/C][C]1.6454[/C][C]0.052154[/C][/ROW]
[ROW][C]6[/C][C]0.018284[/C][C]0.1541[/C][C]0.438999[/C][/ROW]
[ROW][C]7[/C][C]0.063969[/C][C]0.539[/C][C]0.295781[/C][/ROW]
[ROW][C]8[/C][C]0.019789[/C][C]0.1667[/C][C]0.434021[/C][/ROW]
[ROW][C]9[/C][C]0.030164[/C][C]0.2542[/C][C]0.40005[/C][/ROW]
[ROW][C]10[/C][C]0.095137[/C][C]0.8016[/C][C]0.212718[/C][/ROW]
[ROW][C]11[/C][C]-0.278758[/C][C]-2.3489[/C][C]0.989191[/C][/ROW]
[ROW][C]12[/C][C]-0.034935[/C][C]-0.2944[/C][C]0.615333[/C][/ROW]
[ROW][C]13[/C][C]0.071271[/C][C]0.6005[/C][C]0.27503[/C][/ROW]
[ROW][C]14[/C][C]0.010721[/C][C]0.0903[/C][C]0.464136[/C][/ROW]
[ROW][C]15[/C][C]0.075743[/C][C]0.6382[/C][C]0.262692[/C][/ROW]
[ROW][C]16[/C][C]-0.168117[/C][C]-1.4166[/C][C]0.91951[/C][/ROW]
[ROW][C]17[/C][C]0.049283[/C][C]0.4153[/C][C]0.339599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2637&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2637&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	-0.070117	-0.5908	0.72174
1	-0.071212	-0.6	0.724805
2	-0.037491	-0.3159	0.623498
3	-0.103207	-0.8696	0.806286
4	-0.088266	-0.7437	0.770256
5	0.195273	1.6454	0.052154
6	0.018284	0.1541	0.438999
7	0.063969	0.539	0.295781
8	0.019789	0.1667	0.434021
9	0.030164	0.2542	0.40005
10	0.095137	0.8016	0.212718
11	-0.278758	-2.3489	0.989191
12	-0.034935	-0.2944	0.615333
13	0.071271	0.6005	0.27503
14	0.010721	0.0903	0.464136
15	0.075743	0.6382	0.262692
16	-0.168117	-1.4166	0.91951
17	0.049283	0.4153	0.339599

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.2 ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code