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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 19:36:26 +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/2016/Dec/16/t1481913399jkff11exqg1ywr2.htm/, Retrieved Fri, 03 May 2024 01:25:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300475, Retrieved Fri, 03 May 2024 01:25:55 +0000

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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] [conjunctuur 1] [2016-12-16 18:36:26] [2d1dd91c3b5ba64567b1d6b2c9fe9017] [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=300475&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=300475&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300475&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	0.979847	10.5533	0
2	0.955836	10.2947	0
3	0.924495	9.9571	0
4	0.89152	9.602	0
5	0.857229	9.2326	0
6	0.820469	8.8367	0
7	0.77904	8.3905	0
8	0.737501	7.9431	0
9	0.695116	7.4866	0
10	0.651489	7.0168	0
11	0.608251	6.5511	0
12	0.565573	6.0914	0
13	0.522102	5.6232	0
14	0.480795	5.1783	0
15	0.442347	4.7642	3e-06
16	0.403078	4.3413	1.5e-05
17	0.367034	3.9531	6.7e-05
18	0.333114	3.5877	0.000245
19	0.303831	3.2724	0.000703
20	0.27826	2.9969	0.001668
21	0.255406	2.7508	0.00345
22	0.234156	2.5219	0.006514
23	0.212874	2.2927	0.011833
24	0.193605	2.0852	0.019623

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.979847 & 10.5533 & 0 \tabularnewline
2 & 0.955836 & 10.2947 & 0 \tabularnewline
3 & 0.924495 & 9.9571 & 0 \tabularnewline
4 & 0.89152 & 9.602 & 0 \tabularnewline
5 & 0.857229 & 9.2326 & 0 \tabularnewline
6 & 0.820469 & 8.8367 & 0 \tabularnewline
7 & 0.77904 & 8.3905 & 0 \tabularnewline
8 & 0.737501 & 7.9431 & 0 \tabularnewline
9 & 0.695116 & 7.4866 & 0 \tabularnewline
10 & 0.651489 & 7.0168 & 0 \tabularnewline
11 & 0.608251 & 6.5511 & 0 \tabularnewline
12 & 0.565573 & 6.0914 & 0 \tabularnewline
13 & 0.522102 & 5.6232 & 0 \tabularnewline
14 & 0.480795 & 5.1783 & 0 \tabularnewline
15 & 0.442347 & 4.7642 & 3e-06 \tabularnewline
16 & 0.403078 & 4.3413 & 1.5e-05 \tabularnewline
17 & 0.367034 & 3.9531 & 6.7e-05 \tabularnewline
18 & 0.333114 & 3.5877 & 0.000245 \tabularnewline
19 & 0.303831 & 3.2724 & 0.000703 \tabularnewline
20 & 0.27826 & 2.9969 & 0.001668 \tabularnewline
21 & 0.255406 & 2.7508 & 0.00345 \tabularnewline
22 & 0.234156 & 2.5219 & 0.006514 \tabularnewline
23 & 0.212874 & 2.2927 & 0.011833 \tabularnewline
24 & 0.193605 & 2.0852 & 0.019623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300475&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]0.979847[/C][C]10.5533[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.955836[/C][C]10.2947[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.924495[/C][C]9.9571[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.89152[/C][C]9.602[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.857229[/C][C]9.2326[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.820469[/C][C]8.8367[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.77904[/C][C]8.3905[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.737501[/C][C]7.9431[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.695116[/C][C]7.4866[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.651489[/C][C]7.0168[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.608251[/C][C]6.5511[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.565573[/C][C]6.0914[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.522102[/C][C]5.6232[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.480795[/C][C]5.1783[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.442347[/C][C]4.7642[/C][C]3e-06[/C][/ROW]
[ROW][C]16[/C][C]0.403078[/C][C]4.3413[/C][C]1.5e-05[/C][/ROW]
[ROW][C]17[/C][C]0.367034[/C][C]3.9531[/C][C]6.7e-05[/C][/ROW]
[ROW][C]18[/C][C]0.333114[/C][C]3.5877[/C][C]0.000245[/C][/ROW]
[ROW][C]19[/C][C]0.303831[/C][C]3.2724[/C][C]0.000703[/C][/ROW]
[ROW][C]20[/C][C]0.27826[/C][C]2.9969[/C][C]0.001668[/C][/ROW]
[ROW][C]21[/C][C]0.255406[/C][C]2.7508[/C][C]0.00345[/C][/ROW]
[ROW][C]22[/C][C]0.234156[/C][C]2.5219[/C][C]0.006514[/C][/ROW]
[ROW][C]23[/C][C]0.212874[/C][C]2.2927[/C][C]0.011833[/C][/ROW]
[ROW][C]24[/C][C]0.193605[/C][C]2.0852[/C][C]0.019623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300475&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300475&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	0.979847	10.5533	0
2	0.955836	10.2947	0
3	0.924495	9.9571	0
4	0.89152	9.602	0
5	0.857229	9.2326	0
6	0.820469	8.8367	0
7	0.77904	8.3905	0
8	0.737501	7.9431	0
9	0.695116	7.4866	0
10	0.651489	7.0168	0
11	0.608251	6.5511	0
12	0.565573	6.0914	0
13	0.522102	5.6232	0
14	0.480795	5.1783	0
15	0.442347	4.7642	3e-06
16	0.403078	4.3413	1.5e-05
17	0.367034	3.9531	6.7e-05
18	0.333114	3.5877	0.000245
19	0.303831	3.2724	0.000703
20	0.27826	2.9969	0.001668
21	0.255406	2.7508	0.00345
22	0.234156	2.5219	0.006514
23	0.212874	2.2927	0.011833
24	0.193605	2.0852	0.019623

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.979847	10.5533	0
2	-0.106901	-1.1514	0.125977
3	-0.188933	-2.0349	0.022072
4	-0.028152	-0.3032	0.381136
5	-0.015597	-0.168	0.433446
6	-0.072219	-0.7778	0.219128
7	-0.130029	-1.4005	0.082023
8	0.008862	0.0954	0.462063
9	-0.007628	-0.0822	0.467331
10	-0.060653	-0.6533	0.257443
11	-0.009873	-0.1063	0.457749
12	0.008692	0.0936	0.462789
13	-0.04617	-0.4973	0.30997
14	0.018085	0.1948	0.422953
15	0.052814	0.5688	0.285288
16	-0.071271	-0.7676	0.222139
17	0.028355	0.3054	0.380306
18	0.032147	0.3462	0.364896
19	0.071483	0.7699	0.221463
20	0.021124	0.2275	0.410213
21	-0.004712	-0.0507	0.479807
22	0.000353	0.0038	0.498487
23	-0.063606	-0.6851	0.247336
24	0.005587	0.0602	0.476059

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.979847 & 10.5533 & 0 \tabularnewline
2 & -0.106901 & -1.1514 & 0.125977 \tabularnewline
3 & -0.188933 & -2.0349 & 0.022072 \tabularnewline
4 & -0.028152 & -0.3032 & 0.381136 \tabularnewline
5 & -0.015597 & -0.168 & 0.433446 \tabularnewline
6 & -0.072219 & -0.7778 & 0.219128 \tabularnewline
7 & -0.130029 & -1.4005 & 0.082023 \tabularnewline
8 & 0.008862 & 0.0954 & 0.462063 \tabularnewline
9 & -0.007628 & -0.0822 & 0.467331 \tabularnewline
10 & -0.060653 & -0.6533 & 0.257443 \tabularnewline
11 & -0.009873 & -0.1063 & 0.457749 \tabularnewline
12 & 0.008692 & 0.0936 & 0.462789 \tabularnewline
13 & -0.04617 & -0.4973 & 0.30997 \tabularnewline
14 & 0.018085 & 0.1948 & 0.422953 \tabularnewline
15 & 0.052814 & 0.5688 & 0.285288 \tabularnewline
16 & -0.071271 & -0.7676 & 0.222139 \tabularnewline
17 & 0.028355 & 0.3054 & 0.380306 \tabularnewline
18 & 0.032147 & 0.3462 & 0.364896 \tabularnewline
19 & 0.071483 & 0.7699 & 0.221463 \tabularnewline
20 & 0.021124 & 0.2275 & 0.410213 \tabularnewline
21 & -0.004712 & -0.0507 & 0.479807 \tabularnewline
22 & 0.000353 & 0.0038 & 0.498487 \tabularnewline
23 & -0.063606 & -0.6851 & 0.247336 \tabularnewline
24 & 0.005587 & 0.0602 & 0.476059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300475&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]0.979847[/C][C]10.5533[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.106901[/C][C]-1.1514[/C][C]0.125977[/C][/ROW]
[ROW][C]3[/C][C]-0.188933[/C][C]-2.0349[/C][C]0.022072[/C][/ROW]
[ROW][C]4[/C][C]-0.028152[/C][C]-0.3032[/C][C]0.381136[/C][/ROW]
[ROW][C]5[/C][C]-0.015597[/C][C]-0.168[/C][C]0.433446[/C][/ROW]
[ROW][C]6[/C][C]-0.072219[/C][C]-0.7778[/C][C]0.219128[/C][/ROW]
[ROW][C]7[/C][C]-0.130029[/C][C]-1.4005[/C][C]0.082023[/C][/ROW]
[ROW][C]8[/C][C]0.008862[/C][C]0.0954[/C][C]0.462063[/C][/ROW]
[ROW][C]9[/C][C]-0.007628[/C][C]-0.0822[/C][C]0.467331[/C][/ROW]
[ROW][C]10[/C][C]-0.060653[/C][C]-0.6533[/C][C]0.257443[/C][/ROW]
[ROW][C]11[/C][C]-0.009873[/C][C]-0.1063[/C][C]0.457749[/C][/ROW]
[ROW][C]12[/C][C]0.008692[/C][C]0.0936[/C][C]0.462789[/C][/ROW]
[ROW][C]13[/C][C]-0.04617[/C][C]-0.4973[/C][C]0.30997[/C][/ROW]
[ROW][C]14[/C][C]0.018085[/C][C]0.1948[/C][C]0.422953[/C][/ROW]
[ROW][C]15[/C][C]0.052814[/C][C]0.5688[/C][C]0.285288[/C][/ROW]
[ROW][C]16[/C][C]-0.071271[/C][C]-0.7676[/C][C]0.222139[/C][/ROW]
[ROW][C]17[/C][C]0.028355[/C][C]0.3054[/C][C]0.380306[/C][/ROW]
[ROW][C]18[/C][C]0.032147[/C][C]0.3462[/C][C]0.364896[/C][/ROW]
[ROW][C]19[/C][C]0.071483[/C][C]0.7699[/C][C]0.221463[/C][/ROW]
[ROW][C]20[/C][C]0.021124[/C][C]0.2275[/C][C]0.410213[/C][/ROW]
[ROW][C]21[/C][C]-0.004712[/C][C]-0.0507[/C][C]0.479807[/C][/ROW]
[ROW][C]22[/C][C]0.000353[/C][C]0.0038[/C][C]0.498487[/C][/ROW]
[ROW][C]23[/C][C]-0.063606[/C][C]-0.6851[/C][C]0.247336[/C][/ROW]
[ROW][C]24[/C][C]0.005587[/C][C]0.0602[/C][C]0.476059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300475&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300475&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	0.979847	10.5533	0
2	-0.106901	-1.1514	0.125977
3	-0.188933	-2.0349	0.022072
4	-0.028152	-0.3032	0.381136
5	-0.015597	-0.168	0.433446
6	-0.072219	-0.7778	0.219128
7	-0.130029	-1.4005	0.082023
8	0.008862	0.0954	0.462063
9	-0.007628	-0.0822	0.467331
10	-0.060653	-0.6533	0.257443
11	-0.009873	-0.1063	0.457749
12	0.008692	0.0936	0.462789
13	-0.04617	-0.4973	0.30997
14	0.018085	0.1948	0.422953
15	0.052814	0.5688	0.285288
16	-0.071271	-0.7676	0.222139
17	0.028355	0.3054	0.380306
18	0.032147	0.3462	0.364896
19	0.071483	0.7699	0.221463
20	0.021124	0.2275	0.410213
21	-0.004712	-0.0507	0.479807
22	0.000353	0.0038	0.498487
23	-0.063606	-0.6851	0.247336
24	0.005587	0.0602	0.476059

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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,'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