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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

Mon, 05 Dec 2011 14:50:08 -0500

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/2011/Dec/05/t1323114673mmpnfrvegjgk09h.htm/, Retrieved Fri, 03 May 2024 11:25:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151226, Retrieved Fri, 03 May 2024 11:25:56 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Backward Selection] [Unemployment] [2010-11-29 17:10:28] [b98453cac15ba1066b407e146608df68]
- RMPD        [(Partial) Autocorrelation Function] [ACF - Deel1] [2011-12-05 19:50:08] [8aedcf735e397266388b06f47fe45218] [Current]

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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	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151226&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151226&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.485693	7.8165	0
2	0.412394	6.6369	0
3	0.456561	7.3476	0
4	0.19168	3.0848	0.001129
5	0.154776	2.4909	0.006685
6	0.199921	3.2174	0.000729
7	0.064913	1.0447	0.148573
8	0.179586	2.8902	0.002088
9	0.277523	4.4663	6e-06
10	0.148574	2.3911	0.008757
11	0.243952	3.926	5.5e-05
12	0.370677	5.9655	0
13	0.155339	2.4999	0.00652
14	0.221884	3.5709	0.000212
15	0.260228	4.188	1.9e-05
16	0.10108	1.6267	0.052506
17	0.18461	2.971	0.001624
18	0.142543	2.294	0.011295
19	0.069939	1.1256	0.130697
20	0.182866	2.9429	0.001773
21	0.229951	3.7007	0.000131
22	0.149078	2.3992	0.008569
23	0.249219	4.0108	4e-05
24	0.308412	4.9634	1e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.485693 & 7.8165 & 0 \tabularnewline
2 & 0.412394 & 6.6369 & 0 \tabularnewline
3 & 0.456561 & 7.3476 & 0 \tabularnewline
4 & 0.19168 & 3.0848 & 0.001129 \tabularnewline
5 & 0.154776 & 2.4909 & 0.006685 \tabularnewline
6 & 0.199921 & 3.2174 & 0.000729 \tabularnewline
7 & 0.064913 & 1.0447 & 0.148573 \tabularnewline
8 & 0.179586 & 2.8902 & 0.002088 \tabularnewline
9 & 0.277523 & 4.4663 & 6e-06 \tabularnewline
10 & 0.148574 & 2.3911 & 0.008757 \tabularnewline
11 & 0.243952 & 3.926 & 5.5e-05 \tabularnewline
12 & 0.370677 & 5.9655 & 0 \tabularnewline
13 & 0.155339 & 2.4999 & 0.00652 \tabularnewline
14 & 0.221884 & 3.5709 & 0.000212 \tabularnewline
15 & 0.260228 & 4.188 & 1.9e-05 \tabularnewline
16 & 0.10108 & 1.6267 & 0.052506 \tabularnewline
17 & 0.18461 & 2.971 & 0.001624 \tabularnewline
18 & 0.142543 & 2.294 & 0.011295 \tabularnewline
19 & 0.069939 & 1.1256 & 0.130697 \tabularnewline
20 & 0.182866 & 2.9429 & 0.001773 \tabularnewline
21 & 0.229951 & 3.7007 & 0.000131 \tabularnewline
22 & 0.149078 & 2.3992 & 0.008569 \tabularnewline
23 & 0.249219 & 4.0108 & 4e-05 \tabularnewline
24 & 0.308412 & 4.9634 & 1e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151226&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]0.485693[/C][C]7.8165[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.412394[/C][C]6.6369[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.456561[/C][C]7.3476[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.19168[/C][C]3.0848[/C][C]0.001129[/C][/ROW]
[ROW][C]5[/C][C]0.154776[/C][C]2.4909[/C][C]0.006685[/C][/ROW]
[ROW][C]6[/C][C]0.199921[/C][C]3.2174[/C][C]0.000729[/C][/ROW]
[ROW][C]7[/C][C]0.064913[/C][C]1.0447[/C][C]0.148573[/C][/ROW]
[ROW][C]8[/C][C]0.179586[/C][C]2.8902[/C][C]0.002088[/C][/ROW]
[ROW][C]9[/C][C]0.277523[/C][C]4.4663[/C][C]6e-06[/C][/ROW]
[ROW][C]10[/C][C]0.148574[/C][C]2.3911[/C][C]0.008757[/C][/ROW]
[ROW][C]11[/C][C]0.243952[/C][C]3.926[/C][C]5.5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.370677[/C][C]5.9655[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.155339[/C][C]2.4999[/C][C]0.00652[/C][/ROW]
[ROW][C]14[/C][C]0.221884[/C][C]3.5709[/C][C]0.000212[/C][/ROW]
[ROW][C]15[/C][C]0.260228[/C][C]4.188[/C][C]1.9e-05[/C][/ROW]
[ROW][C]16[/C][C]0.10108[/C][C]1.6267[/C][C]0.052506[/C][/ROW]
[ROW][C]17[/C][C]0.18461[/C][C]2.971[/C][C]0.001624[/C][/ROW]
[ROW][C]18[/C][C]0.142543[/C][C]2.294[/C][C]0.011295[/C][/ROW]
[ROW][C]19[/C][C]0.069939[/C][C]1.1256[/C][C]0.130697[/C][/ROW]
[ROW][C]20[/C][C]0.182866[/C][C]2.9429[/C][C]0.001773[/C][/ROW]
[ROW][C]21[/C][C]0.229951[/C][C]3.7007[/C][C]0.000131[/C][/ROW]
[ROW][C]22[/C][C]0.149078[/C][C]2.3992[/C][C]0.008569[/C][/ROW]
[ROW][C]23[/C][C]0.249219[/C][C]4.0108[/C][C]4e-05[/C][/ROW]
[ROW][C]24[/C][C]0.308412[/C][C]4.9634[/C][C]1e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151226&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	0.485693	7.8165	0
2	0.412394	6.6369	0
3	0.456561	7.3476	0
4	0.19168	3.0848	0.001129
5	0.154776	2.4909	0.006685
6	0.199921	3.2174	0.000729
7	0.064913	1.0447	0.148573
8	0.179586	2.8902	0.002088
9	0.277523	4.4663	6e-06
10	0.148574	2.3911	0.008757
11	0.243952	3.926	5.5e-05
12	0.370677	5.9655	0
13	0.155339	2.4999	0.00652
14	0.221884	3.5709	0.000212
15	0.260228	4.188	1.9e-05
16	0.10108	1.6267	0.052506
17	0.18461	2.971	0.001624
18	0.142543	2.294	0.011295
19	0.069939	1.1256	0.130697
20	0.182866	2.9429	0.001773
21	0.229951	3.7007	0.000131
22	0.149078	2.3992	0.008569
23	0.249219	4.0108	4e-05
24	0.308412	4.9634	1e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.485693	7.8165	0
2	0.230985	3.7174	0.000123
3	0.263145	4.2349	1.6e-05
4	-0.198484	-3.1943	0.000788
5	-0.039434	-0.6346	0.263115
6	0.085845	1.3815	0.084151
7	-0.025424	-0.4092	0.341382
8	0.175457	2.8237	0.002558
9	0.175086	2.8177	0.002605
10	-0.057012	-0.9175	0.179859
11	0.043946	0.7072	0.240025
12	0.209537	3.3722	0.00043
13	-0.120133	-1.9334	0.027141
14	0.017664	0.2843	0.388214
15	0.063043	1.0146	0.155624
16	-0.013967	-0.2248	0.411163
17	0.04299	0.6919	0.244821
18	-0.058334	-0.9388	0.174354
19	0.037923	0.6103	0.271096
20	0.038732	0.6233	0.266809
21	0.128971	2.0756	0.019459
22	0.01833	0.295	0.384121
23	0.011073	0.1782	0.429351
24	0.098372	1.5831	0.057305

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.485693 & 7.8165 & 0 \tabularnewline
2 & 0.230985 & 3.7174 & 0.000123 \tabularnewline
3 & 0.263145 & 4.2349 & 1.6e-05 \tabularnewline
4 & -0.198484 & -3.1943 & 0.000788 \tabularnewline
5 & -0.039434 & -0.6346 & 0.263115 \tabularnewline
6 & 0.085845 & 1.3815 & 0.084151 \tabularnewline
7 & -0.025424 & -0.4092 & 0.341382 \tabularnewline
8 & 0.175457 & 2.8237 & 0.002558 \tabularnewline
9 & 0.175086 & 2.8177 & 0.002605 \tabularnewline
10 & -0.057012 & -0.9175 & 0.179859 \tabularnewline
11 & 0.043946 & 0.7072 & 0.240025 \tabularnewline
12 & 0.209537 & 3.3722 & 0.00043 \tabularnewline
13 & -0.120133 & -1.9334 & 0.027141 \tabularnewline
14 & 0.017664 & 0.2843 & 0.388214 \tabularnewline
15 & 0.063043 & 1.0146 & 0.155624 \tabularnewline
16 & -0.013967 & -0.2248 & 0.411163 \tabularnewline
17 & 0.04299 & 0.6919 & 0.244821 \tabularnewline
18 & -0.058334 & -0.9388 & 0.174354 \tabularnewline
19 & 0.037923 & 0.6103 & 0.271096 \tabularnewline
20 & 0.038732 & 0.6233 & 0.266809 \tabularnewline
21 & 0.128971 & 2.0756 & 0.019459 \tabularnewline
22 & 0.01833 & 0.295 & 0.384121 \tabularnewline
23 & 0.011073 & 0.1782 & 0.429351 \tabularnewline
24 & 0.098372 & 1.5831 & 0.057305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151226&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]0.485693[/C][C]7.8165[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.230985[/C][C]3.7174[/C][C]0.000123[/C][/ROW]
[ROW][C]3[/C][C]0.263145[/C][C]4.2349[/C][C]1.6e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.198484[/C][C]-3.1943[/C][C]0.000788[/C][/ROW]
[ROW][C]5[/C][C]-0.039434[/C][C]-0.6346[/C][C]0.263115[/C][/ROW]
[ROW][C]6[/C][C]0.085845[/C][C]1.3815[/C][C]0.084151[/C][/ROW]
[ROW][C]7[/C][C]-0.025424[/C][C]-0.4092[/C][C]0.341382[/C][/ROW]
[ROW][C]8[/C][C]0.175457[/C][C]2.8237[/C][C]0.002558[/C][/ROW]
[ROW][C]9[/C][C]0.175086[/C][C]2.8177[/C][C]0.002605[/C][/ROW]
[ROW][C]10[/C][C]-0.057012[/C][C]-0.9175[/C][C]0.179859[/C][/ROW]
[ROW][C]11[/C][C]0.043946[/C][C]0.7072[/C][C]0.240025[/C][/ROW]
[ROW][C]12[/C][C]0.209537[/C][C]3.3722[/C][C]0.00043[/C][/ROW]
[ROW][C]13[/C][C]-0.120133[/C][C]-1.9334[/C][C]0.027141[/C][/ROW]
[ROW][C]14[/C][C]0.017664[/C][C]0.2843[/C][C]0.388214[/C][/ROW]
[ROW][C]15[/C][C]0.063043[/C][C]1.0146[/C][C]0.155624[/C][/ROW]
[ROW][C]16[/C][C]-0.013967[/C][C]-0.2248[/C][C]0.411163[/C][/ROW]
[ROW][C]17[/C][C]0.04299[/C][C]0.6919[/C][C]0.244821[/C][/ROW]
[ROW][C]18[/C][C]-0.058334[/C][C]-0.9388[/C][C]0.174354[/C][/ROW]
[ROW][C]19[/C][C]0.037923[/C][C]0.6103[/C][C]0.271096[/C][/ROW]
[ROW][C]20[/C][C]0.038732[/C][C]0.6233[/C][C]0.266809[/C][/ROW]
[ROW][C]21[/C][C]0.128971[/C][C]2.0756[/C][C]0.019459[/C][/ROW]
[ROW][C]22[/C][C]0.01833[/C][C]0.295[/C][C]0.384121[/C][/ROW]
[ROW][C]23[/C][C]0.011073[/C][C]0.1782[/C][C]0.429351[/C][/ROW]
[ROW][C]24[/C][C]0.098372[/C][C]1.5831[/C][C]0.057305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151226&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	0.485693	7.8165	0
2	0.230985	3.7174	0.000123
3	0.263145	4.2349	1.6e-05
4	-0.198484	-3.1943	0.000788
5	-0.039434	-0.6346	0.263115
6	0.085845	1.3815	0.084151
7	-0.025424	-0.4092	0.341382
8	0.175457	2.8237	0.002558
9	0.175086	2.8177	0.002605
10	-0.057012	-0.9175	0.179859
11	0.043946	0.7072	0.240025
12	0.209537	3.3722	0.00043
13	-0.120133	-1.9334	0.027141
14	0.017664	0.2843	0.388214
15	0.063043	1.0146	0.155624
16	-0.013967	-0.2248	0.411163
17	0.04299	0.6919	0.244821
18	-0.058334	-0.9388	0.174354
19	0.037923	0.6103	0.271096
20	0.038732	0.6233	0.266809
21	0.128971	2.0756	0.019459
22	0.01833	0.295	0.384121
23	0.011073	0.1782	0.429351
24	0.098372	1.5831	0.057305

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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