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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 10 Dec 2017 14:24:12 +0100

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/2017/Dec/10/t15129133014rf1y5hqrnp2pun.htm/, Retrieved Wed, 15 May 2024 02:53:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308918, Retrieved Wed, 15 May 2024 02:53:06 +0000

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2017-12-10 13:24:12] [a8eb7d5a2159f1476456749db34f2e15] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308918&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308918&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308918&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.828504	12.0632	0
2	0.768729	11.1929	0
3	0.793027	11.5466	0
4	0.767879	11.1805	0
5	0.763836	11.1216	0
6	0.775923	11.2976	0
7	0.735588	10.7103	0
8	0.718154	10.4565	0
9	0.710061	10.3386	0
10	0.670616	9.7643	0
11	0.694388	10.1104	0
12	0.765786	11.15	0
13	0.664629	9.6771	0
14	0.632932	9.2156	0
15	0.651429	9.485	0
16	0.628952	9.1577	0
17	0.623058	9.0719	0
18	0.628584	9.1523	0
19	0.584728	8.5138	0
20	0.566282	8.2452	0
21	0.542651	7.9011	0
22	0.501331	7.2995	0
23	0.521358	7.5911	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.828504 & 12.0632 & 0 \tabularnewline
2 & 0.768729 & 11.1929 & 0 \tabularnewline
3 & 0.793027 & 11.5466 & 0 \tabularnewline
4 & 0.767879 & 11.1805 & 0 \tabularnewline
5 & 0.763836 & 11.1216 & 0 \tabularnewline
6 & 0.775923 & 11.2976 & 0 \tabularnewline
7 & 0.735588 & 10.7103 & 0 \tabularnewline
8 & 0.718154 & 10.4565 & 0 \tabularnewline
9 & 0.710061 & 10.3386 & 0 \tabularnewline
10 & 0.670616 & 9.7643 & 0 \tabularnewline
11 & 0.694388 & 10.1104 & 0 \tabularnewline
12 & 0.765786 & 11.15 & 0 \tabularnewline
13 & 0.664629 & 9.6771 & 0 \tabularnewline
14 & 0.632932 & 9.2156 & 0 \tabularnewline
15 & 0.651429 & 9.485 & 0 \tabularnewline
16 & 0.628952 & 9.1577 & 0 \tabularnewline
17 & 0.623058 & 9.0719 & 0 \tabularnewline
18 & 0.628584 & 9.1523 & 0 \tabularnewline
19 & 0.584728 & 8.5138 & 0 \tabularnewline
20 & 0.566282 & 8.2452 & 0 \tabularnewline
21 & 0.542651 & 7.9011 & 0 \tabularnewline
22 & 0.501331 & 7.2995 & 0 \tabularnewline
23 & 0.521358 & 7.5911 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308918&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]0.828504[/C][C]12.0632[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.768729[/C][C]11.1929[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.793027[/C][C]11.5466[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.767879[/C][C]11.1805[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.763836[/C][C]11.1216[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.775923[/C][C]11.2976[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.735588[/C][C]10.7103[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.718154[/C][C]10.4565[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.710061[/C][C]10.3386[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.670616[/C][C]9.7643[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.694388[/C][C]10.1104[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.765786[/C][C]11.15[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.664629[/C][C]9.6771[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.632932[/C][C]9.2156[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.651429[/C][C]9.485[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.628952[/C][C]9.1577[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.623058[/C][C]9.0719[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.628584[/C][C]9.1523[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.584728[/C][C]8.5138[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.566282[/C][C]8.2452[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.542651[/C][C]7.9011[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.501331[/C][C]7.2995[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.521358[/C][C]7.5911[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308918&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308918&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	0.828504	12.0632	0
2	0.768729	11.1929	0
3	0.793027	11.5466	0
4	0.767879	11.1805	0
5	0.763836	11.1216	0
6	0.775923	11.2976	0
7	0.735588	10.7103	0
8	0.718154	10.4565	0
9	0.710061	10.3386	0
10	0.670616	9.7643	0
11	0.694388	10.1104	0
12	0.765786	11.15	0
13	0.664629	9.6771	0
14	0.632932	9.2156	0
15	0.651429	9.485	0
16	0.628952	9.1577	0
17	0.623058	9.0719	0
18	0.628584	9.1523	0
19	0.584728	8.5138	0
20	0.566282	8.2452	0
21	0.542651	7.9011	0
22	0.501331	7.2995	0
23	0.521358	7.5911	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.828504	12.0632	0
2	0.262483	3.8218	8.7e-05
3	0.362488	5.2779	0
4	0.106196	1.5462	0.061769
5	0.174188	2.5362	0.005963
6	0.153997	2.2422	0.012991
7	-0.030563	-0.445	0.328383
8	0.019062	0.2775	0.390815
9	-0.020635	-0.3004	0.382065
10	-0.094871	-1.3813	0.084313
11	0.13061	1.9017	0.029282
12	0.332793	4.8455	1e-06
13	-0.274257	-3.9932	4.5e-05
14	-0.038978	-0.5675	0.285477
15	-0.031495	-0.4586	0.323503
16	0.003125	0.0455	0.481877
17	-0.016623	-0.242	0.404492
18	-0.005179	-0.0754	0.469983
19	-0.06206	-0.9036	0.183615
20	-0.034075	-0.4961	0.310154
21	-0.091683	-1.3349	0.091667
22	-0.057786	-0.8414	0.200541
23	0.035434	0.5159	0.30322

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.828504 & 12.0632 & 0 \tabularnewline
2 & 0.262483 & 3.8218 & 8.7e-05 \tabularnewline
3 & 0.362488 & 5.2779 & 0 \tabularnewline
4 & 0.106196 & 1.5462 & 0.061769 \tabularnewline
5 & 0.174188 & 2.5362 & 0.005963 \tabularnewline
6 & 0.153997 & 2.2422 & 0.012991 \tabularnewline
7 & -0.030563 & -0.445 & 0.328383 \tabularnewline
8 & 0.019062 & 0.2775 & 0.390815 \tabularnewline
9 & -0.020635 & -0.3004 & 0.382065 \tabularnewline
10 & -0.094871 & -1.3813 & 0.084313 \tabularnewline
11 & 0.13061 & 1.9017 & 0.029282 \tabularnewline
12 & 0.332793 & 4.8455 & 1e-06 \tabularnewline
13 & -0.274257 & -3.9932 & 4.5e-05 \tabularnewline
14 & -0.038978 & -0.5675 & 0.285477 \tabularnewline
15 & -0.031495 & -0.4586 & 0.323503 \tabularnewline
16 & 0.003125 & 0.0455 & 0.481877 \tabularnewline
17 & -0.016623 & -0.242 & 0.404492 \tabularnewline
18 & -0.005179 & -0.0754 & 0.469983 \tabularnewline
19 & -0.06206 & -0.9036 & 0.183615 \tabularnewline
20 & -0.034075 & -0.4961 & 0.310154 \tabularnewline
21 & -0.091683 & -1.3349 & 0.091667 \tabularnewline
22 & -0.057786 & -0.8414 & 0.200541 \tabularnewline
23 & 0.035434 & 0.5159 & 0.30322 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308918&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]0.828504[/C][C]12.0632[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.262483[/C][C]3.8218[/C][C]8.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.362488[/C][C]5.2779[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.106196[/C][C]1.5462[/C][C]0.061769[/C][/ROW]
[ROW][C]5[/C][C]0.174188[/C][C]2.5362[/C][C]0.005963[/C][/ROW]
[ROW][C]6[/C][C]0.153997[/C][C]2.2422[/C][C]0.012991[/C][/ROW]
[ROW][C]7[/C][C]-0.030563[/C][C]-0.445[/C][C]0.328383[/C][/ROW]
[ROW][C]8[/C][C]0.019062[/C][C]0.2775[/C][C]0.390815[/C][/ROW]
[ROW][C]9[/C][C]-0.020635[/C][C]-0.3004[/C][C]0.382065[/C][/ROW]
[ROW][C]10[/C][C]-0.094871[/C][C]-1.3813[/C][C]0.084313[/C][/ROW]
[ROW][C]11[/C][C]0.13061[/C][C]1.9017[/C][C]0.029282[/C][/ROW]
[ROW][C]12[/C][C]0.332793[/C][C]4.8455[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.274257[/C][C]-3.9932[/C][C]4.5e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.038978[/C][C]-0.5675[/C][C]0.285477[/C][/ROW]
[ROW][C]15[/C][C]-0.031495[/C][C]-0.4586[/C][C]0.323503[/C][/ROW]
[ROW][C]16[/C][C]0.003125[/C][C]0.0455[/C][C]0.481877[/C][/ROW]
[ROW][C]17[/C][C]-0.016623[/C][C]-0.242[/C][C]0.404492[/C][/ROW]
[ROW][C]18[/C][C]-0.005179[/C][C]-0.0754[/C][C]0.469983[/C][/ROW]
[ROW][C]19[/C][C]-0.06206[/C][C]-0.9036[/C][C]0.183615[/C][/ROW]
[ROW][C]20[/C][C]-0.034075[/C][C]-0.4961[/C][C]0.310154[/C][/ROW]
[ROW][C]21[/C][C]-0.091683[/C][C]-1.3349[/C][C]0.091667[/C][/ROW]
[ROW][C]22[/C][C]-0.057786[/C][C]-0.8414[/C][C]0.200541[/C][/ROW]
[ROW][C]23[/C][C]0.035434[/C][C]0.5159[/C][C]0.30322[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308918&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308918&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	0.828504	12.0632	0
2	0.262483	3.8218	8.7e-05
3	0.362488	5.2779	0
4	0.106196	1.5462	0.061769
5	0.174188	2.5362	0.005963
6	0.153997	2.2422	0.012991
7	-0.030563	-0.445	0.328383
8	0.019062	0.2775	0.390815
9	-0.020635	-0.3004	0.382065
10	-0.094871	-1.3813	0.084313
11	0.13061	1.9017	0.029282
12	0.332793	4.8455	1e-06
13	-0.274257	-3.9932	4.5e-05
14	-0.038978	-0.5675	0.285477
15	-0.031495	-0.4586	0.323503
16	0.003125	0.0455	0.481877
17	-0.016623	-0.242	0.404492
18	-0.005179	-0.0754	0.469983
19	-0.06206	-0.9036	0.183615
20	-0.034075	-0.4961	0.310154
21	-0.091683	-1.3349	0.091667
22	-0.057786	-0.8414	0.200541
23	0.035434	0.5159	0.30322

Figure 1

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Postscript link

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Figure 2

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Figure 3

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Parameters (Session):

par1 = Default ; par2 = -0.3 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.3 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '0'
par2 <- '-0.3'
par1 <- 'Default'
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,'ACF(k)',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,'PACF(k)',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