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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 12 Mar 2016 21:34:16 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/12/t14578185071m9v7djdf67cvxx.htm/, Retrieved Sun, 05 May 2024 12:19:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293967, Retrieved Sun, 05 May 2024 12:19:47 +0000

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Estimated Impact

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

-     [(Partial) Autocorrelation Function] [] [2016-03-12 21:16:20] [600dd77654e74003cbd3c8172f556ebd]
-   PD    [(Partial) Autocorrelation Function] [] [2016-03-12 21:34:16] [bfab382a4ab6d7836f6b75894769f754] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293967&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293967&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293967&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.951925	7.3736	0
2	0.898334	6.9585	0
3	0.85209	6.6003	0
4	0.820756	6.3575	0
5	0.777928	6.0258	0
6	0.736958	5.7085	0
7	0.693573	5.3724	1e-06
8	0.640128	4.9584	3e-06
9	0.588255	4.5566	1.3e-05
10	0.533757	4.1345	5.6e-05
11	0.47646	3.6906	0.000242
12	0.418585	3.2423	0.000969
13	0.360512	2.7925	0.003503
14	0.303942	2.3543	0.010924
15	0.237526	1.8399	0.035368
16	0.17323	1.3418	0.092353
17	0.123723	0.9584	0.170866

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951925 & 7.3736 & 0 \tabularnewline
2 & 0.898334 & 6.9585 & 0 \tabularnewline
3 & 0.85209 & 6.6003 & 0 \tabularnewline
4 & 0.820756 & 6.3575 & 0 \tabularnewline
5 & 0.777928 & 6.0258 & 0 \tabularnewline
6 & 0.736958 & 5.7085 & 0 \tabularnewline
7 & 0.693573 & 5.3724 & 1e-06 \tabularnewline
8 & 0.640128 & 4.9584 & 3e-06 \tabularnewline
9 & 0.588255 & 4.5566 & 1.3e-05 \tabularnewline
10 & 0.533757 & 4.1345 & 5.6e-05 \tabularnewline
11 & 0.47646 & 3.6906 & 0.000242 \tabularnewline
12 & 0.418585 & 3.2423 & 0.000969 \tabularnewline
13 & 0.360512 & 2.7925 & 0.003503 \tabularnewline
14 & 0.303942 & 2.3543 & 0.010924 \tabularnewline
15 & 0.237526 & 1.8399 & 0.035368 \tabularnewline
16 & 0.17323 & 1.3418 & 0.092353 \tabularnewline
17 & 0.123723 & 0.9584 & 0.170866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293967&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]0.951925[/C][C]7.3736[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.898334[/C][C]6.9585[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.85209[/C][C]6.6003[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.820756[/C][C]6.3575[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.777928[/C][C]6.0258[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.736958[/C][C]5.7085[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.693573[/C][C]5.3724[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.640128[/C][C]4.9584[/C][C]3e-06[/C][/ROW]
[ROW][C]9[/C][C]0.588255[/C][C]4.5566[/C][C]1.3e-05[/C][/ROW]
[ROW][C]10[/C][C]0.533757[/C][C]4.1345[/C][C]5.6e-05[/C][/ROW]
[ROW][C]11[/C][C]0.47646[/C][C]3.6906[/C][C]0.000242[/C][/ROW]
[ROW][C]12[/C][C]0.418585[/C][C]3.2423[/C][C]0.000969[/C][/ROW]
[ROW][C]13[/C][C]0.360512[/C][C]2.7925[/C][C]0.003503[/C][/ROW]
[ROW][C]14[/C][C]0.303942[/C][C]2.3543[/C][C]0.010924[/C][/ROW]
[ROW][C]15[/C][C]0.237526[/C][C]1.8399[/C][C]0.035368[/C][/ROW]
[ROW][C]16[/C][C]0.17323[/C][C]1.3418[/C][C]0.092353[/C][/ROW]
[ROW][C]17[/C][C]0.123723[/C][C]0.9584[/C][C]0.170866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293967&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293967&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	0.951925	7.3736	0
2	0.898334	6.9585	0
3	0.85209	6.6003	0
4	0.820756	6.3575	0
5	0.777928	6.0258	0
6	0.736958	5.7085	0
7	0.693573	5.3724	1e-06
8	0.640128	4.9584	3e-06
9	0.588255	4.5566	1.3e-05
10	0.533757	4.1345	5.6e-05
11	0.47646	3.6906	0.000242
12	0.418585	3.2423	0.000969
13	0.360512	2.7925	0.003503
14	0.303942	2.3543	0.010924
15	0.237526	1.8399	0.035368
16	0.17323	1.3418	0.092353
17	0.123723	0.9584	0.170866

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.951925	7.3736	0
2	-0.083411	-0.6461	0.260339
3	0.053831	0.417	0.339093
4	0.126005	0.976	0.166483
5	-0.155837	-1.2071	0.116063
6	0.03582	0.2775	0.391191
7	-0.049511	-0.3835	0.35135
8	-0.170912	-1.3239	0.095283
9	0.033174	0.257	0.399043
10	-0.105909	-0.8204	0.207627
11	-0.092656	-0.7177	0.237861
12	0.004362	0.0338	0.486581
13	-0.095636	-0.7408	0.230855
14	-0.01362	-0.1055	0.458166
15	-0.137535	-1.0653	0.145494
16	-0.040626	-0.3147	0.377046
17	0.13836	1.0717	0.144067

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.951925 & 7.3736 & 0 \tabularnewline
2 & -0.083411 & -0.6461 & 0.260339 \tabularnewline
3 & 0.053831 & 0.417 & 0.339093 \tabularnewline
4 & 0.126005 & 0.976 & 0.166483 \tabularnewline
5 & -0.155837 & -1.2071 & 0.116063 \tabularnewline
6 & 0.03582 & 0.2775 & 0.391191 \tabularnewline
7 & -0.049511 & -0.3835 & 0.35135 \tabularnewline
8 & -0.170912 & -1.3239 & 0.095283 \tabularnewline
9 & 0.033174 & 0.257 & 0.399043 \tabularnewline
10 & -0.105909 & -0.8204 & 0.207627 \tabularnewline
11 & -0.092656 & -0.7177 & 0.237861 \tabularnewline
12 & 0.004362 & 0.0338 & 0.486581 \tabularnewline
13 & -0.095636 & -0.7408 & 0.230855 \tabularnewline
14 & -0.01362 & -0.1055 & 0.458166 \tabularnewline
15 & -0.137535 & -1.0653 & 0.145494 \tabularnewline
16 & -0.040626 & -0.3147 & 0.377046 \tabularnewline
17 & 0.13836 & 1.0717 & 0.144067 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293967&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]0.951925[/C][C]7.3736[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.083411[/C][C]-0.6461[/C][C]0.260339[/C][/ROW]
[ROW][C]3[/C][C]0.053831[/C][C]0.417[/C][C]0.339093[/C][/ROW]
[ROW][C]4[/C][C]0.126005[/C][C]0.976[/C][C]0.166483[/C][/ROW]
[ROW][C]5[/C][C]-0.155837[/C][C]-1.2071[/C][C]0.116063[/C][/ROW]
[ROW][C]6[/C][C]0.03582[/C][C]0.2775[/C][C]0.391191[/C][/ROW]
[ROW][C]7[/C][C]-0.049511[/C][C]-0.3835[/C][C]0.35135[/C][/ROW]
[ROW][C]8[/C][C]-0.170912[/C][C]-1.3239[/C][C]0.095283[/C][/ROW]
[ROW][C]9[/C][C]0.033174[/C][C]0.257[/C][C]0.399043[/C][/ROW]
[ROW][C]10[/C][C]-0.105909[/C][C]-0.8204[/C][C]0.207627[/C][/ROW]
[ROW][C]11[/C][C]-0.092656[/C][C]-0.7177[/C][C]0.237861[/C][/ROW]
[ROW][C]12[/C][C]0.004362[/C][C]0.0338[/C][C]0.486581[/C][/ROW]
[ROW][C]13[/C][C]-0.095636[/C][C]-0.7408[/C][C]0.230855[/C][/ROW]
[ROW][C]14[/C][C]-0.01362[/C][C]-0.1055[/C][C]0.458166[/C][/ROW]
[ROW][C]15[/C][C]-0.137535[/C][C]-1.0653[/C][C]0.145494[/C][/ROW]
[ROW][C]16[/C][C]-0.040626[/C][C]-0.3147[/C][C]0.377046[/C][/ROW]
[ROW][C]17[/C][C]0.13836[/C][C]1.0717[/C][C]0.144067[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293967&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293967&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	0.951925	7.3736	0
2	-0.083411	-0.6461	0.260339
3	0.053831	0.417	0.339093
4	0.126005	0.976	0.166483
5	-0.155837	-1.2071	0.116063
6	0.03582	0.2775	0.391191
7	-0.049511	-0.3835	0.35135
8	-0.170912	-1.3239	0.095283
9	0.033174	0.257	0.399043
10	-0.105909	-0.8204	0.207627
11	-0.092656	-0.7177	0.237861
12	0.004362	0.0338	0.486581
13	-0.095636	-0.7408	0.230855
14	-0.01362	-0.1055	0.458166
15	-0.137535	-1.0653	0.145494
16	-0.040626	-0.3147	0.377046
17	0.13836	1.0717	0.144067

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)
x <- na.omit(x)
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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code