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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Feb 2018 09:26:15 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Feb/01/t1517473587yz5tzpbmhc1flqs.htm/, Retrieved Mon, 29 Apr 2024 05:47:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=313537, Retrieved Mon, 29 Apr 2024 05:47:44 +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] [] [2018-02-01 08:26:15] [f7fcbef48f036f8c57e773abb9891403] [Current]

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7.60998304324026e-05
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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	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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313537&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=313537&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313537&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.005416	0.0766	0.469513
2	0.373504	5.2821	0
3	0.389276	5.5052	0
4	0.089571	1.2667	0.103363
5	0.279898	3.9584	5.2e-05
6	0.147341	2.0837	0.019228
7	-0.0413	-0.5841	0.279914
8	0.07046	0.9965	0.160116
9	-0.077301	-1.0932	0.137809
10	-0.139478	-1.9725	0.024964
11	0.003836	0.0542	0.478398
12	-0.477281	-6.7498	0
13	-0.049427	-0.699	0.242682
14	-0.240767	-3.405	4e-04
15	-0.206357	-2.9183	0.001961
16	-0.175671	-2.4844	0.0069
17	-0.20427	-2.8888	0.002147
18	-0.13136	-1.8577	0.03234
19	-0.173453	-2.453	0.007512
20	-0.111361	-1.5749	0.058433
21	-0.037122	-0.525	0.300086
22	-0.176814	-2.5005	0.006602
23	0.038248	0.5409	0.294585

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.005416 & 0.0766 & 0.469513 \tabularnewline
2 & 0.373504 & 5.2821 & 0 \tabularnewline
3 & 0.389276 & 5.5052 & 0 \tabularnewline
4 & 0.089571 & 1.2667 & 0.103363 \tabularnewline
5 & 0.279898 & 3.9584 & 5.2e-05 \tabularnewline
6 & 0.147341 & 2.0837 & 0.019228 \tabularnewline
7 & -0.0413 & -0.5841 & 0.279914 \tabularnewline
8 & 0.07046 & 0.9965 & 0.160116 \tabularnewline
9 & -0.077301 & -1.0932 & 0.137809 \tabularnewline
10 & -0.139478 & -1.9725 & 0.024964 \tabularnewline
11 & 0.003836 & 0.0542 & 0.478398 \tabularnewline
12 & -0.477281 & -6.7498 & 0 \tabularnewline
13 & -0.049427 & -0.699 & 0.242682 \tabularnewline
14 & -0.240767 & -3.405 & 4e-04 \tabularnewline
15 & -0.206357 & -2.9183 & 0.001961 \tabularnewline
16 & -0.175671 & -2.4844 & 0.0069 \tabularnewline
17 & -0.20427 & -2.8888 & 0.002147 \tabularnewline
18 & -0.13136 & -1.8577 & 0.03234 \tabularnewline
19 & -0.173453 & -2.453 & 0.007512 \tabularnewline
20 & -0.111361 & -1.5749 & 0.058433 \tabularnewline
21 & -0.037122 & -0.525 & 0.300086 \tabularnewline
22 & -0.176814 & -2.5005 & 0.006602 \tabularnewline
23 & 0.038248 & 0.5409 & 0.294585 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313537&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]0.005416[/C][C]0.0766[/C][C]0.469513[/C][/ROW]
[ROW][C]2[/C][C]0.373504[/C][C]5.2821[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.389276[/C][C]5.5052[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.089571[/C][C]1.2667[/C][C]0.103363[/C][/ROW]
[ROW][C]5[/C][C]0.279898[/C][C]3.9584[/C][C]5.2e-05[/C][/ROW]
[ROW][C]6[/C][C]0.147341[/C][C]2.0837[/C][C]0.019228[/C][/ROW]
[ROW][C]7[/C][C]-0.0413[/C][C]-0.5841[/C][C]0.279914[/C][/ROW]
[ROW][C]8[/C][C]0.07046[/C][C]0.9965[/C][C]0.160116[/C][/ROW]
[ROW][C]9[/C][C]-0.077301[/C][C]-1.0932[/C][C]0.137809[/C][/ROW]
[ROW][C]10[/C][C]-0.139478[/C][C]-1.9725[/C][C]0.024964[/C][/ROW]
[ROW][C]11[/C][C]0.003836[/C][C]0.0542[/C][C]0.478398[/C][/ROW]
[ROW][C]12[/C][C]-0.477281[/C][C]-6.7498[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.049427[/C][C]-0.699[/C][C]0.242682[/C][/ROW]
[ROW][C]14[/C][C]-0.240767[/C][C]-3.405[/C][C]4e-04[/C][/ROW]
[ROW][C]15[/C][C]-0.206357[/C][C]-2.9183[/C][C]0.001961[/C][/ROW]
[ROW][C]16[/C][C]-0.175671[/C][C]-2.4844[/C][C]0.0069[/C][/ROW]
[ROW][C]17[/C][C]-0.20427[/C][C]-2.8888[/C][C]0.002147[/C][/ROW]
[ROW][C]18[/C][C]-0.13136[/C][C]-1.8577[/C][C]0.03234[/C][/ROW]
[ROW][C]19[/C][C]-0.173453[/C][C]-2.453[/C][C]0.007512[/C][/ROW]
[ROW][C]20[/C][C]-0.111361[/C][C]-1.5749[/C][C]0.058433[/C][/ROW]
[ROW][C]21[/C][C]-0.037122[/C][C]-0.525[/C][C]0.300086[/C][/ROW]
[ROW][C]22[/C][C]-0.176814[/C][C]-2.5005[/C][C]0.006602[/C][/ROW]
[ROW][C]23[/C][C]0.038248[/C][C]0.5409[/C][C]0.294585[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313537&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313537&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	0.005416	0.0766	0.469513
2	0.373504	5.2821	0
3	0.389276	5.5052	0
4	0.089571	1.2667	0.103363
5	0.279898	3.9584	5.2e-05
6	0.147341	2.0837	0.019228
7	-0.0413	-0.5841	0.279914
8	0.07046	0.9965	0.160116
9	-0.077301	-1.0932	0.137809
10	-0.139478	-1.9725	0.024964
11	0.003836	0.0542	0.478398
12	-0.477281	-6.7498	0
13	-0.049427	-0.699	0.242682
14	-0.240767	-3.405	4e-04
15	-0.206357	-2.9183	0.001961
16	-0.175671	-2.4844	0.0069
17	-0.20427	-2.8888	0.002147
18	-0.13136	-1.8577	0.03234
19	-0.173453	-2.453	0.007512
20	-0.111361	-1.5749	0.058433
21	-0.037122	-0.525	0.300086
22	-0.176814	-2.5005	0.006602
23	0.038248	0.5409	0.294585

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.005416	0.0766	0.469513
2	0.373486	5.2819	0
3	0.448569	6.3437	0
4	0.017615	0.2491	0.401763
5	-0.022784	-0.3222	0.373812
6	-0.032389	-0.4581	0.323705
7	-0.237601	-3.3602	0.000466
8	-0.206205	-2.9162	0.001974
9	-0.125451	-1.7742	0.03878
10	-0.11041	-1.5614	0.060002
11	0.102844	1.4544	0.073696
12	-0.390741	-5.5259	0
13	-0.08291	-1.1725	0.12119
14	0.092643	1.3102	0.095821
15	0.292688	4.1392	2.6e-05
16	0.002936	0.0415	0.483464
17	-0.04072	-0.5759	0.282674
18	0.058418	0.8262	0.204849
19	-0.172909	-2.4453	0.007669
20	-0.243023	-3.4369	0.000358
21	0.017408	0.2462	0.402896
22	-0.107588	-1.5215	0.064853
23	0.090647	1.2819	0.100673

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.005416 & 0.0766 & 0.469513 \tabularnewline
2 & 0.373486 & 5.2819 & 0 \tabularnewline
3 & 0.448569 & 6.3437 & 0 \tabularnewline
4 & 0.017615 & 0.2491 & 0.401763 \tabularnewline
5 & -0.022784 & -0.3222 & 0.373812 \tabularnewline
6 & -0.032389 & -0.4581 & 0.323705 \tabularnewline
7 & -0.237601 & -3.3602 & 0.000466 \tabularnewline
8 & -0.206205 & -2.9162 & 0.001974 \tabularnewline
9 & -0.125451 & -1.7742 & 0.03878 \tabularnewline
10 & -0.11041 & -1.5614 & 0.060002 \tabularnewline
11 & 0.102844 & 1.4544 & 0.073696 \tabularnewline
12 & -0.390741 & -5.5259 & 0 \tabularnewline
13 & -0.08291 & -1.1725 & 0.12119 \tabularnewline
14 & 0.092643 & 1.3102 & 0.095821 \tabularnewline
15 & 0.292688 & 4.1392 & 2.6e-05 \tabularnewline
16 & 0.002936 & 0.0415 & 0.483464 \tabularnewline
17 & -0.04072 & -0.5759 & 0.282674 \tabularnewline
18 & 0.058418 & 0.8262 & 0.204849 \tabularnewline
19 & -0.172909 & -2.4453 & 0.007669 \tabularnewline
20 & -0.243023 & -3.4369 & 0.000358 \tabularnewline
21 & 0.017408 & 0.2462 & 0.402896 \tabularnewline
22 & -0.107588 & -1.5215 & 0.064853 \tabularnewline
23 & 0.090647 & 1.2819 & 0.100673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313537&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]0.005416[/C][C]0.0766[/C][C]0.469513[/C][/ROW]
[ROW][C]2[/C][C]0.373486[/C][C]5.2819[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.448569[/C][C]6.3437[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.017615[/C][C]0.2491[/C][C]0.401763[/C][/ROW]
[ROW][C]5[/C][C]-0.022784[/C][C]-0.3222[/C][C]0.373812[/C][/ROW]
[ROW][C]6[/C][C]-0.032389[/C][C]-0.4581[/C][C]0.323705[/C][/ROW]
[ROW][C]7[/C][C]-0.237601[/C][C]-3.3602[/C][C]0.000466[/C][/ROW]
[ROW][C]8[/C][C]-0.206205[/C][C]-2.9162[/C][C]0.001974[/C][/ROW]
[ROW][C]9[/C][C]-0.125451[/C][C]-1.7742[/C][C]0.03878[/C][/ROW]
[ROW][C]10[/C][C]-0.11041[/C][C]-1.5614[/C][C]0.060002[/C][/ROW]
[ROW][C]11[/C][C]0.102844[/C][C]1.4544[/C][C]0.073696[/C][/ROW]
[ROW][C]12[/C][C]-0.390741[/C][C]-5.5259[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.08291[/C][C]-1.1725[/C][C]0.12119[/C][/ROW]
[ROW][C]14[/C][C]0.092643[/C][C]1.3102[/C][C]0.095821[/C][/ROW]
[ROW][C]15[/C][C]0.292688[/C][C]4.1392[/C][C]2.6e-05[/C][/ROW]
[ROW][C]16[/C][C]0.002936[/C][C]0.0415[/C][C]0.483464[/C][/ROW]
[ROW][C]17[/C][C]-0.04072[/C][C]-0.5759[/C][C]0.282674[/C][/ROW]
[ROW][C]18[/C][C]0.058418[/C][C]0.8262[/C][C]0.204849[/C][/ROW]
[ROW][C]19[/C][C]-0.172909[/C][C]-2.4453[/C][C]0.007669[/C][/ROW]
[ROW][C]20[/C][C]-0.243023[/C][C]-3.4369[/C][C]0.000358[/C][/ROW]
[ROW][C]21[/C][C]0.017408[/C][C]0.2462[/C][C]0.402896[/C][/ROW]
[ROW][C]22[/C][C]-0.107588[/C][C]-1.5215[/C][C]0.064853[/C][/ROW]
[ROW][C]23[/C][C]0.090647[/C][C]1.2819[/C][C]0.100673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313537&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313537&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	0.005416	0.0766	0.469513
2	0.373486	5.2819	0
3	0.448569	6.3437	0
4	0.017615	0.2491	0.401763
5	-0.022784	-0.3222	0.373812
6	-0.032389	-0.4581	0.323705
7	-0.237601	-3.3602	0.000466
8	-0.206205	-2.9162	0.001974
9	-0.125451	-1.7742	0.03878
10	-0.11041	-1.5614	0.060002
11	0.102844	1.4544	0.073696
12	-0.390741	-5.5259	0
13	-0.08291	-1.1725	0.12119
14	0.092643	1.3102	0.095821
15	0.292688	4.1392	2.6e-05
16	0.002936	0.0415	0.483464
17	-0.04072	-0.5759	0.282674
18	0.058418	0.8262	0.204849
19	-0.172909	-2.4453	0.007669
20	-0.243023	-3.4369	0.000358
21	0.017408	0.2462	0.402896
22	-0.107588	-1.5215	0.064853
23	0.090647	1.2819	0.100673

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 = 200 ; par2 = 5 ; par3 = 0 ; par4 = P1 P5 Q1 Q3 P95 P99 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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