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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 17:20:35 +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/18/t14820780661k6ola3s51jigxj.htm/, Retrieved Wed, 08 May 2024 03:44:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301163, Retrieved Wed, 08 May 2024 03:44:48 +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] [partial autocorre...] [2016-12-18 16:20:35] [33f2a624cfeb2efbc43d2c77b7c0dad6] [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=301163&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=301163&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301163&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	0.787714	8.1862	0
2	0.728759	7.5735	0
3	0.656568	6.8233	0
4	0.515559	5.3578	0
5	0.431006	4.4791	9e-06
6	0.406163	4.221	2.5e-05
7	0.381824	3.968	6.5e-05
8	0.397668	4.1327	3.6e-05
9	0.489394	5.0859	1e-06
10	0.547909	5.694	0
11	0.591741	6.1495	0
12	0.591617	6.1483	0
13	0.582577	6.0543	0
14	0.532568	5.5346	0
15	0.419688	4.3615	1.5e-05
16	0.33936	3.5267	0.000309
17	0.280255	2.9125	0.002179
18	0.253646	2.636	0.004812
19	0.236854	2.4615	0.00771
20	0.227433	2.3636	0.009944
21	0.283737	2.9487	0.001956

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.787714 & 8.1862 & 0 \tabularnewline
2 & 0.728759 & 7.5735 & 0 \tabularnewline
3 & 0.656568 & 6.8233 & 0 \tabularnewline
4 & 0.515559 & 5.3578 & 0 \tabularnewline
5 & 0.431006 & 4.4791 & 9e-06 \tabularnewline
6 & 0.406163 & 4.221 & 2.5e-05 \tabularnewline
7 & 0.381824 & 3.968 & 6.5e-05 \tabularnewline
8 & 0.397668 & 4.1327 & 3.6e-05 \tabularnewline
9 & 0.489394 & 5.0859 & 1e-06 \tabularnewline
10 & 0.547909 & 5.694 & 0 \tabularnewline
11 & 0.591741 & 6.1495 & 0 \tabularnewline
12 & 0.591617 & 6.1483 & 0 \tabularnewline
13 & 0.582577 & 6.0543 & 0 \tabularnewline
14 & 0.532568 & 5.5346 & 0 \tabularnewline
15 & 0.419688 & 4.3615 & 1.5e-05 \tabularnewline
16 & 0.33936 & 3.5267 & 0.000309 \tabularnewline
17 & 0.280255 & 2.9125 & 0.002179 \tabularnewline
18 & 0.253646 & 2.636 & 0.004812 \tabularnewline
19 & 0.236854 & 2.4615 & 0.00771 \tabularnewline
20 & 0.227433 & 2.3636 & 0.009944 \tabularnewline
21 & 0.283737 & 2.9487 & 0.001956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301163&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]0.787714[/C][C]8.1862[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.728759[/C][C]7.5735[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.656568[/C][C]6.8233[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.515559[/C][C]5.3578[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.431006[/C][C]4.4791[/C][C]9e-06[/C][/ROW]
[ROW][C]6[/C][C]0.406163[/C][C]4.221[/C][C]2.5e-05[/C][/ROW]
[ROW][C]7[/C][C]0.381824[/C][C]3.968[/C][C]6.5e-05[/C][/ROW]
[ROW][C]8[/C][C]0.397668[/C][C]4.1327[/C][C]3.6e-05[/C][/ROW]
[ROW][C]9[/C][C]0.489394[/C][C]5.0859[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.547909[/C][C]5.694[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.591741[/C][C]6.1495[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.591617[/C][C]6.1483[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.582577[/C][C]6.0543[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.532568[/C][C]5.5346[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.419688[/C][C]4.3615[/C][C]1.5e-05[/C][/ROW]
[ROW][C]16[/C][C]0.33936[/C][C]3.5267[/C][C]0.000309[/C][/ROW]
[ROW][C]17[/C][C]0.280255[/C][C]2.9125[/C][C]0.002179[/C][/ROW]
[ROW][C]18[/C][C]0.253646[/C][C]2.636[/C][C]0.004812[/C][/ROW]
[ROW][C]19[/C][C]0.236854[/C][C]2.4615[/C][C]0.00771[/C][/ROW]
[ROW][C]20[/C][C]0.227433[/C][C]2.3636[/C][C]0.009944[/C][/ROW]
[ROW][C]21[/C][C]0.283737[/C][C]2.9487[/C][C]0.001956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301163&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301163&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	0.787714	8.1862	0
2	0.728759	7.5735	0
3	0.656568	6.8233	0
4	0.515559	5.3578	0
5	0.431006	4.4791	9e-06
6	0.406163	4.221	2.5e-05
7	0.381824	3.968	6.5e-05
8	0.397668	4.1327	3.6e-05
9	0.489394	5.0859	1e-06
10	0.547909	5.694	0
11	0.591741	6.1495	0
12	0.591617	6.1483	0
13	0.582577	6.0543	0
14	0.532568	5.5346	0
15	0.419688	4.3615	1.5e-05
16	0.33936	3.5267	0.000309
17	0.280255	2.9125	0.002179
18	0.253646	2.636	0.004812
19	0.236854	2.4615	0.00771
20	0.227433	2.3636	0.009944
21	0.283737	2.9487	0.001956

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.787714	8.1862	0
2	0.28528	2.9647	0.001864
3	0.061848	0.6427	0.260878
4	-0.212346	-2.2068	0.014723
5	-0.05574	-0.5793	0.281808
6	0.17278	1.7956	0.037679
7	0.162651	1.6903	0.046925
8	0.135553	1.4087	0.080897
9	0.269244	2.7981	0.003045
10	0.17406	1.8089	0.036625
11	0.05518	0.5734	0.283767
12	-0.140154	-1.4565	0.074075
13	-0.039521	-0.4107	0.341047
14	0.002734	0.0284	0.488692
15	-0.171063	-1.7777	0.03913
16	-0.105692	-1.0984	0.137239
17	0.053637	0.5574	0.289198
18	0.171339	1.7806	0.038894
19	-0.018175	-0.1889	0.425272
20	-0.232414	-2.4153	0.0087
21	0.037547	0.3902	0.34858

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.787714 & 8.1862 & 0 \tabularnewline
2 & 0.28528 & 2.9647 & 0.001864 \tabularnewline
3 & 0.061848 & 0.6427 & 0.260878 \tabularnewline
4 & -0.212346 & -2.2068 & 0.014723 \tabularnewline
5 & -0.05574 & -0.5793 & 0.281808 \tabularnewline
6 & 0.17278 & 1.7956 & 0.037679 \tabularnewline
7 & 0.162651 & 1.6903 & 0.046925 \tabularnewline
8 & 0.135553 & 1.4087 & 0.080897 \tabularnewline
9 & 0.269244 & 2.7981 & 0.003045 \tabularnewline
10 & 0.17406 & 1.8089 & 0.036625 \tabularnewline
11 & 0.05518 & 0.5734 & 0.283767 \tabularnewline
12 & -0.140154 & -1.4565 & 0.074075 \tabularnewline
13 & -0.039521 & -0.4107 & 0.341047 \tabularnewline
14 & 0.002734 & 0.0284 & 0.488692 \tabularnewline
15 & -0.171063 & -1.7777 & 0.03913 \tabularnewline
16 & -0.105692 & -1.0984 & 0.137239 \tabularnewline
17 & 0.053637 & 0.5574 & 0.289198 \tabularnewline
18 & 0.171339 & 1.7806 & 0.038894 \tabularnewline
19 & -0.018175 & -0.1889 & 0.425272 \tabularnewline
20 & -0.232414 & -2.4153 & 0.0087 \tabularnewline
21 & 0.037547 & 0.3902 & 0.34858 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301163&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]0.787714[/C][C]8.1862[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.28528[/C][C]2.9647[/C][C]0.001864[/C][/ROW]
[ROW][C]3[/C][C]0.061848[/C][C]0.6427[/C][C]0.260878[/C][/ROW]
[ROW][C]4[/C][C]-0.212346[/C][C]-2.2068[/C][C]0.014723[/C][/ROW]
[ROW][C]5[/C][C]-0.05574[/C][C]-0.5793[/C][C]0.281808[/C][/ROW]
[ROW][C]6[/C][C]0.17278[/C][C]1.7956[/C][C]0.037679[/C][/ROW]
[ROW][C]7[/C][C]0.162651[/C][C]1.6903[/C][C]0.046925[/C][/ROW]
[ROW][C]8[/C][C]0.135553[/C][C]1.4087[/C][C]0.080897[/C][/ROW]
[ROW][C]9[/C][C]0.269244[/C][C]2.7981[/C][C]0.003045[/C][/ROW]
[ROW][C]10[/C][C]0.17406[/C][C]1.8089[/C][C]0.036625[/C][/ROW]
[ROW][C]11[/C][C]0.05518[/C][C]0.5734[/C][C]0.283767[/C][/ROW]
[ROW][C]12[/C][C]-0.140154[/C][C]-1.4565[/C][C]0.074075[/C][/ROW]
[ROW][C]13[/C][C]-0.039521[/C][C]-0.4107[/C][C]0.341047[/C][/ROW]
[ROW][C]14[/C][C]0.002734[/C][C]0.0284[/C][C]0.488692[/C][/ROW]
[ROW][C]15[/C][C]-0.171063[/C][C]-1.7777[/C][C]0.03913[/C][/ROW]
[ROW][C]16[/C][C]-0.105692[/C][C]-1.0984[/C][C]0.137239[/C][/ROW]
[ROW][C]17[/C][C]0.053637[/C][C]0.5574[/C][C]0.289198[/C][/ROW]
[ROW][C]18[/C][C]0.171339[/C][C]1.7806[/C][C]0.038894[/C][/ROW]
[ROW][C]19[/C][C]-0.018175[/C][C]-0.1889[/C][C]0.425272[/C][/ROW]
[ROW][C]20[/C][C]-0.232414[/C][C]-2.4153[/C][C]0.0087[/C][/ROW]
[ROW][C]21[/C][C]0.037547[/C][C]0.3902[/C][C]0.34858[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301163&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301163&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	0.787714	8.1862	0
2	0.28528	2.9647	0.001864
3	0.061848	0.6427	0.260878
4	-0.212346	-2.2068	0.014723
5	-0.05574	-0.5793	0.281808
6	0.17278	1.7956	0.037679
7	0.162651	1.6903	0.046925
8	0.135553	1.4087	0.080897
9	0.269244	2.7981	0.003045
10	0.17406	1.8089	0.036625
11	0.05518	0.5734	0.283767
12	-0.140154	-1.4565	0.074075
13	-0.039521	-0.4107	0.341047
14	0.002734	0.0284	0.488692
15	-0.171063	-1.7777	0.03913
16	-0.105692	-1.0984	0.137239
17	0.053637	0.5574	0.289198
18	0.171339	1.7806	0.038894
19	-0.018175	-0.1889	0.425272
20	-0.232414	-2.4153	0.0087
21	0.037547	0.3902	0.34858

Figure 1

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Figure 2

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Figure 3

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Parameters (Session):

par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.0 ; 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,'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