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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

Thu, 08 Dec 2011 17:42:57 -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/08/t1323384193c26dlmht53f9lny.htm/, Retrieved Fri, 03 May 2024 14:48:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153177, Retrieved Fri, 03 May 2024 14:48:43 +0000

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Original text written by user:

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)

-       [(Partial) Autocorrelation Function] [ACF 0] [2011-12-08 22:42:57] [0956ee981dded61b2e7128dae94e5715] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153177&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]2 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=153177&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153177&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.968422	20.8604	0
2	0.94118	20.2736	0
3	0.916008	19.7314	0
4	0.886749	19.1011	0
5	0.863215	18.5942	0
6	0.843903	18.1782	0
7	0.821786	17.7018	0
8	0.801928	17.2741	0
9	0.782848	16.8631	0
10	0.761902	16.4119	0
11	0.744646	16.0402	0
12	0.722874	15.5712	0
13	0.698673	15.0499	0
14	0.679762	14.6425	0
15	0.661289	14.2446	0
16	0.640176	13.7898	0
17	0.622354	13.4059	0
18	0.598575	12.8937	0
19	0.576008	12.4076	0
20	0.558266	12.0254	0
21	0.54371	11.7119	0
22	0.528074	11.3751	0
23	0.513703	11.0655	0
24	0.500284	10.7765	0
25	0.485167	10.4508	0
26	0.473894	10.208	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.968422 & 20.8604 & 0 \tabularnewline
2 & 0.94118 & 20.2736 & 0 \tabularnewline
3 & 0.916008 & 19.7314 & 0 \tabularnewline
4 & 0.886749 & 19.1011 & 0 \tabularnewline
5 & 0.863215 & 18.5942 & 0 \tabularnewline
6 & 0.843903 & 18.1782 & 0 \tabularnewline
7 & 0.821786 & 17.7018 & 0 \tabularnewline
8 & 0.801928 & 17.2741 & 0 \tabularnewline
9 & 0.782848 & 16.8631 & 0 \tabularnewline
10 & 0.761902 & 16.4119 & 0 \tabularnewline
11 & 0.744646 & 16.0402 & 0 \tabularnewline
12 & 0.722874 & 15.5712 & 0 \tabularnewline
13 & 0.698673 & 15.0499 & 0 \tabularnewline
14 & 0.679762 & 14.6425 & 0 \tabularnewline
15 & 0.661289 & 14.2446 & 0 \tabularnewline
16 & 0.640176 & 13.7898 & 0 \tabularnewline
17 & 0.622354 & 13.4059 & 0 \tabularnewline
18 & 0.598575 & 12.8937 & 0 \tabularnewline
19 & 0.576008 & 12.4076 & 0 \tabularnewline
20 & 0.558266 & 12.0254 & 0 \tabularnewline
21 & 0.54371 & 11.7119 & 0 \tabularnewline
22 & 0.528074 & 11.3751 & 0 \tabularnewline
23 & 0.513703 & 11.0655 & 0 \tabularnewline
24 & 0.500284 & 10.7765 & 0 \tabularnewline
25 & 0.485167 & 10.4508 & 0 \tabularnewline
26 & 0.473894 & 10.208 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153177&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]0.968422[/C][C]20.8604[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.94118[/C][C]20.2736[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.916008[/C][C]19.7314[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.886749[/C][C]19.1011[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.863215[/C][C]18.5942[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.843903[/C][C]18.1782[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.821786[/C][C]17.7018[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.801928[/C][C]17.2741[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.782848[/C][C]16.8631[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.761902[/C][C]16.4119[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.744646[/C][C]16.0402[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.722874[/C][C]15.5712[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.698673[/C][C]15.0499[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.679762[/C][C]14.6425[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.661289[/C][C]14.2446[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.640176[/C][C]13.7898[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.622354[/C][C]13.4059[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.598575[/C][C]12.8937[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.576008[/C][C]12.4076[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.558266[/C][C]12.0254[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.54371[/C][C]11.7119[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.528074[/C][C]11.3751[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.513703[/C][C]11.0655[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.500284[/C][C]10.7765[/C][C]0[/C][/ROW]
[ROW][C]25[/C][C]0.485167[/C][C]10.4508[/C][C]0[/C][/ROW]
[ROW][C]26[/C][C]0.473894[/C][C]10.208[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153177&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153177&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	0.968422	20.8604	0
2	0.94118	20.2736	0
3	0.916008	19.7314	0
4	0.886749	19.1011	0
5	0.863215	18.5942	0
6	0.843903	18.1782	0
7	0.821786	17.7018	0
8	0.801928	17.2741	0
9	0.782848	16.8631	0
10	0.761902	16.4119	0
11	0.744646	16.0402	0
12	0.722874	15.5712	0
13	0.698673	15.0499	0
14	0.679762	14.6425	0
15	0.661289	14.2446	0
16	0.640176	13.7898	0
17	0.622354	13.4059	0
18	0.598575	12.8937	0
19	0.576008	12.4076	0
20	0.558266	12.0254	0
21	0.54371	11.7119	0
22	0.528074	11.3751	0
23	0.513703	11.0655	0
24	0.500284	10.7765	0
25	0.485167	10.4508	0
26	0.473894	10.208	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.968422	20.8604	0
2	0.053725	1.1573	0.12388
3	0.024015	0.5173	0.302599
4	-0.074289	-1.6002	0.055115
5	0.069994	1.5077	0.066153
6	0.063473	1.3672	0.086105
7	-0.037603	-0.81	0.209177
8	0.013887	0.2991	0.382488
9	0.003016	0.065	0.474111
10	-0.02131	-0.459	0.323216
11	0.042229	0.9096	0.181744
12	-0.079288	-1.7079	0.04416
13	-0.048482	-1.0443	0.148437
14	0.055528	1.1961	0.116133
15	0.017743	0.3822	0.351244
16	-0.04757	-1.0247	0.153021
17	0.008991	0.1937	0.423256
18	-0.09481	-2.0423	0.020844
19	0.015668	0.3375	0.367947
20	0.047717	1.0278	0.152278
21	0.066643	1.4355	0.075905
22	-0.03052	-0.6574	0.25562
23	-0.008913	-0.192	0.423914
24	0.031876	0.6866	0.246329
25	-0.020789	-0.4478	0.327248
26	0.04039	0.87	0.192366

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.968422 & 20.8604 & 0 \tabularnewline
2 & 0.053725 & 1.1573 & 0.12388 \tabularnewline
3 & 0.024015 & 0.5173 & 0.302599 \tabularnewline
4 & -0.074289 & -1.6002 & 0.055115 \tabularnewline
5 & 0.069994 & 1.5077 & 0.066153 \tabularnewline
6 & 0.063473 & 1.3672 & 0.086105 \tabularnewline
7 & -0.037603 & -0.81 & 0.209177 \tabularnewline
8 & 0.013887 & 0.2991 & 0.382488 \tabularnewline
9 & 0.003016 & 0.065 & 0.474111 \tabularnewline
10 & -0.02131 & -0.459 & 0.323216 \tabularnewline
11 & 0.042229 & 0.9096 & 0.181744 \tabularnewline
12 & -0.079288 & -1.7079 & 0.04416 \tabularnewline
13 & -0.048482 & -1.0443 & 0.148437 \tabularnewline
14 & 0.055528 & 1.1961 & 0.116133 \tabularnewline
15 & 0.017743 & 0.3822 & 0.351244 \tabularnewline
16 & -0.04757 & -1.0247 & 0.153021 \tabularnewline
17 & 0.008991 & 0.1937 & 0.423256 \tabularnewline
18 & -0.09481 & -2.0423 & 0.020844 \tabularnewline
19 & 0.015668 & 0.3375 & 0.367947 \tabularnewline
20 & 0.047717 & 1.0278 & 0.152278 \tabularnewline
21 & 0.066643 & 1.4355 & 0.075905 \tabularnewline
22 & -0.03052 & -0.6574 & 0.25562 \tabularnewline
23 & -0.008913 & -0.192 & 0.423914 \tabularnewline
24 & 0.031876 & 0.6866 & 0.246329 \tabularnewline
25 & -0.020789 & -0.4478 & 0.327248 \tabularnewline
26 & 0.04039 & 0.87 & 0.192366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153177&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]0.968422[/C][C]20.8604[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.053725[/C][C]1.1573[/C][C]0.12388[/C][/ROW]
[ROW][C]3[/C][C]0.024015[/C][C]0.5173[/C][C]0.302599[/C][/ROW]
[ROW][C]4[/C][C]-0.074289[/C][C]-1.6002[/C][C]0.055115[/C][/ROW]
[ROW][C]5[/C][C]0.069994[/C][C]1.5077[/C][C]0.066153[/C][/ROW]
[ROW][C]6[/C][C]0.063473[/C][C]1.3672[/C][C]0.086105[/C][/ROW]
[ROW][C]7[/C][C]-0.037603[/C][C]-0.81[/C][C]0.209177[/C][/ROW]
[ROW][C]8[/C][C]0.013887[/C][C]0.2991[/C][C]0.382488[/C][/ROW]
[ROW][C]9[/C][C]0.003016[/C][C]0.065[/C][C]0.474111[/C][/ROW]
[ROW][C]10[/C][C]-0.02131[/C][C]-0.459[/C][C]0.323216[/C][/ROW]
[ROW][C]11[/C][C]0.042229[/C][C]0.9096[/C][C]0.181744[/C][/ROW]
[ROW][C]12[/C][C]-0.079288[/C][C]-1.7079[/C][C]0.04416[/C][/ROW]
[ROW][C]13[/C][C]-0.048482[/C][C]-1.0443[/C][C]0.148437[/C][/ROW]
[ROW][C]14[/C][C]0.055528[/C][C]1.1961[/C][C]0.116133[/C][/ROW]
[ROW][C]15[/C][C]0.017743[/C][C]0.3822[/C][C]0.351244[/C][/ROW]
[ROW][C]16[/C][C]-0.04757[/C][C]-1.0247[/C][C]0.153021[/C][/ROW]
[ROW][C]17[/C][C]0.008991[/C][C]0.1937[/C][C]0.423256[/C][/ROW]
[ROW][C]18[/C][C]-0.09481[/C][C]-2.0423[/C][C]0.020844[/C][/ROW]
[ROW][C]19[/C][C]0.015668[/C][C]0.3375[/C][C]0.367947[/C][/ROW]
[ROW][C]20[/C][C]0.047717[/C][C]1.0278[/C][C]0.152278[/C][/ROW]
[ROW][C]21[/C][C]0.066643[/C][C]1.4355[/C][C]0.075905[/C][/ROW]
[ROW][C]22[/C][C]-0.03052[/C][C]-0.6574[/C][C]0.25562[/C][/ROW]
[ROW][C]23[/C][C]-0.008913[/C][C]-0.192[/C][C]0.423914[/C][/ROW]
[ROW][C]24[/C][C]0.031876[/C][C]0.6866[/C][C]0.246329[/C][/ROW]
[ROW][C]25[/C][C]-0.020789[/C][C]-0.4478[/C][C]0.327248[/C][/ROW]
[ROW][C]26[/C][C]0.04039[/C][C]0.87[/C][C]0.192366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153177&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153177&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	0.968422	20.8604	0
2	0.053725	1.1573	0.12388
3	0.024015	0.5173	0.302599
4	-0.074289	-1.6002	0.055115
5	0.069994	1.5077	0.066153
6	0.063473	1.3672	0.086105
7	-0.037603	-0.81	0.209177
8	0.013887	0.2991	0.382488
9	0.003016	0.065	0.474111
10	-0.02131	-0.459	0.323216
11	0.042229	0.9096	0.181744
12	-0.079288	-1.7079	0.04416
13	-0.048482	-1.0443	0.148437
14	0.055528	1.1961	0.116133
15	0.017743	0.3822	0.351244
16	-0.04757	-1.0247	0.153021
17	0.008991	0.1937	0.423256
18	-0.09481	-2.0423	0.020844
19	0.015668	0.3375	0.367947
20	0.047717	1.0278	0.152278
21	0.066643	1.4355	0.075905
22	-0.03052	-0.6574	0.25562
23	-0.008913	-0.192	0.423914
24	0.031876	0.6866	0.246329
25	-0.020789	-0.4478	0.327248
26	0.04039	0.87	0.192366

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

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