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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Dec 2009 13:22:52 -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/2009/Dec/15/t12609086285toikmz8p6baz26.htm/, Retrieved Wed, 08 May 2024 17:15:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68122, Retrieved Wed, 08 May 2024 17:15:43 +0000

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Estimated Impact

122

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

-     [Variance Reduction Matrix] [Variance reductio...] [2008-12-11 15:42:45] [12d343c4448a5f9e527bb31caeac580b]
-  MPD  [Variance Reduction Matrix] [variance reductio...] [2009-12-14 20:17:44] [ba905ddf7cdf9ecb063c35348c4dab2e]
- RMPD      [(Partial) Autocorrelation Function] [AcF VARIANCE ] [2009-12-15 20:22:52] [244731fa3e7e6c85774b8c0902c58f85] [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	5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68122&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]5 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=68122&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68122&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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.232031	1.5737	0.061204
2	0.224018	1.5194	0.067758
3	0.261275	1.7721	0.041505
4	-0.063354	-0.4297	0.334715
5	-0.104829	-0.711	0.240342
6	0.002949	0.02	0.492064
7	-0.100184	-0.6795	0.25012
8	0.015108	0.1025	0.459416
9	-0.12543	-0.8507	0.199669
10	-0.105865	-0.718	0.23819
11	-0.064443	-0.4371	0.332053
12	-0.366024	-2.4825	0.008379
13	-0.121714	-0.8255	0.206674
14	-0.12052	-0.8174	0.208955
15	-0.13712	-0.93	0.178615
16	-0.024167	-0.1639	0.435262
17	0.069034	0.4682	0.320921

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.232031 & 1.5737 & 0.061204 \tabularnewline
2 & 0.224018 & 1.5194 & 0.067758 \tabularnewline
3 & 0.261275 & 1.7721 & 0.041505 \tabularnewline
4 & -0.063354 & -0.4297 & 0.334715 \tabularnewline
5 & -0.104829 & -0.711 & 0.240342 \tabularnewline
6 & 0.002949 & 0.02 & 0.492064 \tabularnewline
7 & -0.100184 & -0.6795 & 0.25012 \tabularnewline
8 & 0.015108 & 0.1025 & 0.459416 \tabularnewline
9 & -0.12543 & -0.8507 & 0.199669 \tabularnewline
10 & -0.105865 & -0.718 & 0.23819 \tabularnewline
11 & -0.064443 & -0.4371 & 0.332053 \tabularnewline
12 & -0.366024 & -2.4825 & 0.008379 \tabularnewline
13 & -0.121714 & -0.8255 & 0.206674 \tabularnewline
14 & -0.12052 & -0.8174 & 0.208955 \tabularnewline
15 & -0.13712 & -0.93 & 0.178615 \tabularnewline
16 & -0.024167 & -0.1639 & 0.435262 \tabularnewline
17 & 0.069034 & 0.4682 & 0.320921 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68122&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]0.232031[/C][C]1.5737[/C][C]0.061204[/C][/ROW]
[ROW][C]2[/C][C]0.224018[/C][C]1.5194[/C][C]0.067758[/C][/ROW]
[ROW][C]3[/C][C]0.261275[/C][C]1.7721[/C][C]0.041505[/C][/ROW]
[ROW][C]4[/C][C]-0.063354[/C][C]-0.4297[/C][C]0.334715[/C][/ROW]
[ROW][C]5[/C][C]-0.104829[/C][C]-0.711[/C][C]0.240342[/C][/ROW]
[ROW][C]6[/C][C]0.002949[/C][C]0.02[/C][C]0.492064[/C][/ROW]
[ROW][C]7[/C][C]-0.100184[/C][C]-0.6795[/C][C]0.25012[/C][/ROW]
[ROW][C]8[/C][C]0.015108[/C][C]0.1025[/C][C]0.459416[/C][/ROW]
[ROW][C]9[/C][C]-0.12543[/C][C]-0.8507[/C][C]0.199669[/C][/ROW]
[ROW][C]10[/C][C]-0.105865[/C][C]-0.718[/C][C]0.23819[/C][/ROW]
[ROW][C]11[/C][C]-0.064443[/C][C]-0.4371[/C][C]0.332053[/C][/ROW]
[ROW][C]12[/C][C]-0.366024[/C][C]-2.4825[/C][C]0.008379[/C][/ROW]
[ROW][C]13[/C][C]-0.121714[/C][C]-0.8255[/C][C]0.206674[/C][/ROW]
[ROW][C]14[/C][C]-0.12052[/C][C]-0.8174[/C][C]0.208955[/C][/ROW]
[ROW][C]15[/C][C]-0.13712[/C][C]-0.93[/C][C]0.178615[/C][/ROW]
[ROW][C]16[/C][C]-0.024167[/C][C]-0.1639[/C][C]0.435262[/C][/ROW]
[ROW][C]17[/C][C]0.069034[/C][C]0.4682[/C][C]0.320921[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68122&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68122&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	0.232031	1.5737	0.061204
2	0.224018	1.5194	0.067758
3	0.261275	1.7721	0.041505
4	-0.063354	-0.4297	0.334715
5	-0.104829	-0.711	0.240342
6	0.002949	0.02	0.492064
7	-0.100184	-0.6795	0.25012
8	0.015108	0.1025	0.459416
9	-0.12543	-0.8507	0.199669
10	-0.105865	-0.718	0.23819
11	-0.064443	-0.4371	0.332053
12	-0.366024	-2.4825	0.008379
13	-0.121714	-0.8255	0.206674
14	-0.12052	-0.8174	0.208955
15	-0.13712	-0.93	0.178615
16	-0.024167	-0.1639	0.435262
17	0.069034	0.4682	0.320921

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.232031	1.5737	0.061204
2	0.179863	1.2199	0.114362
3	0.193229	1.3105	0.098259
4	-0.20523	-1.3919	0.085317
5	-0.166231	-1.1274	0.132703
6	0.053712	0.3643	0.358655
7	0.015039	0.102	0.459601
8	0.093588	0.6347	0.26437
9	-0.205906	-1.3965	0.08463
10	-0.090412	-0.6132	0.271381
11	-0.007656	-0.0519	0.479408
12	-0.302332	-2.0505	0.023019
13	0.04978	0.3376	0.36859
14	-0.035162	-0.2385	0.406285
15	0.066468	0.4508	0.327124
16	-0.083056	-0.5633	0.28798
17	0.019525	0.1324	0.447613

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.232031 & 1.5737 & 0.061204 \tabularnewline
2 & 0.179863 & 1.2199 & 0.114362 \tabularnewline
3 & 0.193229 & 1.3105 & 0.098259 \tabularnewline
4 & -0.20523 & -1.3919 & 0.085317 \tabularnewline
5 & -0.166231 & -1.1274 & 0.132703 \tabularnewline
6 & 0.053712 & 0.3643 & 0.358655 \tabularnewline
7 & 0.015039 & 0.102 & 0.459601 \tabularnewline
8 & 0.093588 & 0.6347 & 0.26437 \tabularnewline
9 & -0.205906 & -1.3965 & 0.08463 \tabularnewline
10 & -0.090412 & -0.6132 & 0.271381 \tabularnewline
11 & -0.007656 & -0.0519 & 0.479408 \tabularnewline
12 & -0.302332 & -2.0505 & 0.023019 \tabularnewline
13 & 0.04978 & 0.3376 & 0.36859 \tabularnewline
14 & -0.035162 & -0.2385 & 0.406285 \tabularnewline
15 & 0.066468 & 0.4508 & 0.327124 \tabularnewline
16 & -0.083056 & -0.5633 & 0.28798 \tabularnewline
17 & 0.019525 & 0.1324 & 0.447613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68122&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]0.232031[/C][C]1.5737[/C][C]0.061204[/C][/ROW]
[ROW][C]2[/C][C]0.179863[/C][C]1.2199[/C][C]0.114362[/C][/ROW]
[ROW][C]3[/C][C]0.193229[/C][C]1.3105[/C][C]0.098259[/C][/ROW]
[ROW][C]4[/C][C]-0.20523[/C][C]-1.3919[/C][C]0.085317[/C][/ROW]
[ROW][C]5[/C][C]-0.166231[/C][C]-1.1274[/C][C]0.132703[/C][/ROW]
[ROW][C]6[/C][C]0.053712[/C][C]0.3643[/C][C]0.358655[/C][/ROW]
[ROW][C]7[/C][C]0.015039[/C][C]0.102[/C][C]0.459601[/C][/ROW]
[ROW][C]8[/C][C]0.093588[/C][C]0.6347[/C][C]0.26437[/C][/ROW]
[ROW][C]9[/C][C]-0.205906[/C][C]-1.3965[/C][C]0.08463[/C][/ROW]
[ROW][C]10[/C][C]-0.090412[/C][C]-0.6132[/C][C]0.271381[/C][/ROW]
[ROW][C]11[/C][C]-0.007656[/C][C]-0.0519[/C][C]0.479408[/C][/ROW]
[ROW][C]12[/C][C]-0.302332[/C][C]-2.0505[/C][C]0.023019[/C][/ROW]
[ROW][C]13[/C][C]0.04978[/C][C]0.3376[/C][C]0.36859[/C][/ROW]
[ROW][C]14[/C][C]-0.035162[/C][C]-0.2385[/C][C]0.406285[/C][/ROW]
[ROW][C]15[/C][C]0.066468[/C][C]0.4508[/C][C]0.327124[/C][/ROW]
[ROW][C]16[/C][C]-0.083056[/C][C]-0.5633[/C][C]0.28798[/C][/ROW]
[ROW][C]17[/C][C]0.019525[/C][C]0.1324[/C][C]0.447613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68122&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68122&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	0.232031	1.5737	0.061204
2	0.179863	1.2199	0.114362
3	0.193229	1.3105	0.098259
4	-0.20523	-1.3919	0.085317
5	-0.166231	-1.1274	0.132703
6	0.053712	0.3643	0.358655
7	0.015039	0.102	0.459601
8	0.093588	0.6347	0.26437
9	-0.205906	-1.3965	0.08463
10	-0.090412	-0.6132	0.271381
11	-0.007656	-0.0519	0.479408
12	-0.302332	-2.0505	0.023019
13	0.04978	0.3376	0.36859
14	-0.035162	-0.2385	0.406285
15	0.066468	0.4508	0.327124
16	-0.083056	-0.5633	0.28798
17	0.019525	0.1324	0.447613

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.7 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -1.7 ; par3 = 0 ; par4 = 1 ; 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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code