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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 19 Dec 2009 01:46:23 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/19/t1261212476mbsbui8yrmw213c.htm/, Retrieved Fri, 03 May 2024 19:23:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69461, Retrieved Fri, 03 May 2024 19:23:54 +0000

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Estimated Impact

146

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-       [(Partial) Autocorrelation Function] [PACF Appelen Jona...] [2009-12-19 08:46:23] [5c2088b06970f9a7d6fea063ee8d5871] [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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69461&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69461&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69461&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.826773	7.0154	0
2	0.602034	5.1084	1e-06
3	0.42876	3.6382	0.000257
4	0.302189	2.5642	0.006215
5	0.239037	2.0283	0.023115
6	0.200028	1.6973	0.04698
7	0.174622	1.4817	0.071389
8	0.162243	1.3767	0.086439
9	0.198404	1.6835	0.048304
10	0.237255	2.0132	0.023918
11	0.323655	2.7463	0.003804
12	0.409986	3.4788	0.000429
13	0.320171	2.7167	0.004125
14	0.176229	1.4953	0.069597
15	0.048747	0.4136	0.340187
16	-0.032867	-0.2789	0.390564
17	-0.075006	-0.6365	0.26325
18	-0.112717	-0.9564	0.171025

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.826773 & 7.0154 & 0 \tabularnewline
2 & 0.602034 & 5.1084 & 1e-06 \tabularnewline
3 & 0.42876 & 3.6382 & 0.000257 \tabularnewline
4 & 0.302189 & 2.5642 & 0.006215 \tabularnewline
5 & 0.239037 & 2.0283 & 0.023115 \tabularnewline
6 & 0.200028 & 1.6973 & 0.04698 \tabularnewline
7 & 0.174622 & 1.4817 & 0.071389 \tabularnewline
8 & 0.162243 & 1.3767 & 0.086439 \tabularnewline
9 & 0.198404 & 1.6835 & 0.048304 \tabularnewline
10 & 0.237255 & 2.0132 & 0.023918 \tabularnewline
11 & 0.323655 & 2.7463 & 0.003804 \tabularnewline
12 & 0.409986 & 3.4788 & 0.000429 \tabularnewline
13 & 0.320171 & 2.7167 & 0.004125 \tabularnewline
14 & 0.176229 & 1.4953 & 0.069597 \tabularnewline
15 & 0.048747 & 0.4136 & 0.340187 \tabularnewline
16 & -0.032867 & -0.2789 & 0.390564 \tabularnewline
17 & -0.075006 & -0.6365 & 0.26325 \tabularnewline
18 & -0.112717 & -0.9564 & 0.171025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69461&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]0.826773[/C][C]7.0154[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.602034[/C][C]5.1084[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.42876[/C][C]3.6382[/C][C]0.000257[/C][/ROW]
[ROW][C]4[/C][C]0.302189[/C][C]2.5642[/C][C]0.006215[/C][/ROW]
[ROW][C]5[/C][C]0.239037[/C][C]2.0283[/C][C]0.023115[/C][/ROW]
[ROW][C]6[/C][C]0.200028[/C][C]1.6973[/C][C]0.04698[/C][/ROW]
[ROW][C]7[/C][C]0.174622[/C][C]1.4817[/C][C]0.071389[/C][/ROW]
[ROW][C]8[/C][C]0.162243[/C][C]1.3767[/C][C]0.086439[/C][/ROW]
[ROW][C]9[/C][C]0.198404[/C][C]1.6835[/C][C]0.048304[/C][/ROW]
[ROW][C]10[/C][C]0.237255[/C][C]2.0132[/C][C]0.023918[/C][/ROW]
[ROW][C]11[/C][C]0.323655[/C][C]2.7463[/C][C]0.003804[/C][/ROW]
[ROW][C]12[/C][C]0.409986[/C][C]3.4788[/C][C]0.000429[/C][/ROW]
[ROW][C]13[/C][C]0.320171[/C][C]2.7167[/C][C]0.004125[/C][/ROW]
[ROW][C]14[/C][C]0.176229[/C][C]1.4953[/C][C]0.069597[/C][/ROW]
[ROW][C]15[/C][C]0.048747[/C][C]0.4136[/C][C]0.340187[/C][/ROW]
[ROW][C]16[/C][C]-0.032867[/C][C]-0.2789[/C][C]0.390564[/C][/ROW]
[ROW][C]17[/C][C]-0.075006[/C][C]-0.6365[/C][C]0.26325[/C][/ROW]
[ROW][C]18[/C][C]-0.112717[/C][C]-0.9564[/C][C]0.171025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69461&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69461&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	0.826773	7.0154	0
2	0.602034	5.1084	1e-06
3	0.42876	3.6382	0.000257
4	0.302189	2.5642	0.006215
5	0.239037	2.0283	0.023115
6	0.200028	1.6973	0.04698
7	0.174622	1.4817	0.071389
8	0.162243	1.3767	0.086439
9	0.198404	1.6835	0.048304
10	0.237255	2.0132	0.023918
11	0.323655	2.7463	0.003804
12	0.409986	3.4788	0.000429
13	0.320171	2.7167	0.004125
14	0.176229	1.4953	0.069597
15	0.048747	0.4136	0.340187
16	-0.032867	-0.2789	0.390564
17	-0.075006	-0.6365	0.26325
18	-0.112717	-0.9564	0.171025

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.826773	7.0154	0
2	-0.257611	-2.1859	0.016038
3	0.053398	0.4531	0.325922
4	-0.017474	-0.1483	0.441272
5	0.095805	0.8129	0.209468
6	-0.019922	-0.169	0.433118
7	0.032661	0.2771	0.391234
8	0.026402	0.224	0.411685
9	0.173652	1.4735	0.072489
10	0.001594	0.0135	0.494624
11	0.270534	2.2956	0.012308
12	0.052521	0.4457	0.328592
13	-0.430629	-3.654	0.000244
14	0.006559	0.0557	0.477886
15	-0.042894	-0.364	0.358474
16	0.015626	0.1326	0.447443
17	-0.072082	-0.6116	0.271353
18	-0.098843	-0.8387	0.202204

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.826773 & 7.0154 & 0 \tabularnewline
2 & -0.257611 & -2.1859 & 0.016038 \tabularnewline
3 & 0.053398 & 0.4531 & 0.325922 \tabularnewline
4 & -0.017474 & -0.1483 & 0.441272 \tabularnewline
5 & 0.095805 & 0.8129 & 0.209468 \tabularnewline
6 & -0.019922 & -0.169 & 0.433118 \tabularnewline
7 & 0.032661 & 0.2771 & 0.391234 \tabularnewline
8 & 0.026402 & 0.224 & 0.411685 \tabularnewline
9 & 0.173652 & 1.4735 & 0.072489 \tabularnewline
10 & 0.001594 & 0.0135 & 0.494624 \tabularnewline
11 & 0.270534 & 2.2956 & 0.012308 \tabularnewline
12 & 0.052521 & 0.4457 & 0.328592 \tabularnewline
13 & -0.430629 & -3.654 & 0.000244 \tabularnewline
14 & 0.006559 & 0.0557 & 0.477886 \tabularnewline
15 & -0.042894 & -0.364 & 0.358474 \tabularnewline
16 & 0.015626 & 0.1326 & 0.447443 \tabularnewline
17 & -0.072082 & -0.6116 & 0.271353 \tabularnewline
18 & -0.098843 & -0.8387 & 0.202204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69461&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]0.826773[/C][C]7.0154[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.257611[/C][C]-2.1859[/C][C]0.016038[/C][/ROW]
[ROW][C]3[/C][C]0.053398[/C][C]0.4531[/C][C]0.325922[/C][/ROW]
[ROW][C]4[/C][C]-0.017474[/C][C]-0.1483[/C][C]0.441272[/C][/ROW]
[ROW][C]5[/C][C]0.095805[/C][C]0.8129[/C][C]0.209468[/C][/ROW]
[ROW][C]6[/C][C]-0.019922[/C][C]-0.169[/C][C]0.433118[/C][/ROW]
[ROW][C]7[/C][C]0.032661[/C][C]0.2771[/C][C]0.391234[/C][/ROW]
[ROW][C]8[/C][C]0.026402[/C][C]0.224[/C][C]0.411685[/C][/ROW]
[ROW][C]9[/C][C]0.173652[/C][C]1.4735[/C][C]0.072489[/C][/ROW]
[ROW][C]10[/C][C]0.001594[/C][C]0.0135[/C][C]0.494624[/C][/ROW]
[ROW][C]11[/C][C]0.270534[/C][C]2.2956[/C][C]0.012308[/C][/ROW]
[ROW][C]12[/C][C]0.052521[/C][C]0.4457[/C][C]0.328592[/C][/ROW]
[ROW][C]13[/C][C]-0.430629[/C][C]-3.654[/C][C]0.000244[/C][/ROW]
[ROW][C]14[/C][C]0.006559[/C][C]0.0557[/C][C]0.477886[/C][/ROW]
[ROW][C]15[/C][C]-0.042894[/C][C]-0.364[/C][C]0.358474[/C][/ROW]
[ROW][C]16[/C][C]0.015626[/C][C]0.1326[/C][C]0.447443[/C][/ROW]
[ROW][C]17[/C][C]-0.072082[/C][C]-0.6116[/C][C]0.271353[/C][/ROW]
[ROW][C]18[/C][C]-0.098843[/C][C]-0.8387[/C][C]0.202204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69461&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69461&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	0.826773	7.0154	0
2	-0.257611	-2.1859	0.016038
3	0.053398	0.4531	0.325922
4	-0.017474	-0.1483	0.441272
5	0.095805	0.8129	0.209468
6	-0.019922	-0.169	0.433118
7	0.032661	0.2771	0.391234
8	0.026402	0.224	0.411685
9	0.173652	1.4735	0.072489
10	0.001594	0.0135	0.494624
11	0.270534	2.2956	0.012308
12	0.052521	0.4457	0.328592
13	-0.430629	-3.654	0.000244
14	0.006559	0.0557	0.477886
15	-0.042894	-0.364	0.358474
16	0.015626	0.1326	0.447443
17	-0.072082	-0.6116	0.271353
18	-0.098843	-0.8387	0.202204

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 ; 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 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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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Dataset

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Input Parameters & R Code