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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

Tue, 19 Dec 2017 17:34:21 +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/19/t1513701277k5c7guyp2eywtgw.htm/, Retrieved Wed, 15 May 2024 21:40:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310371, Retrieved Wed, 15 May 2024 21:40:49 +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] [Non-durable consu...] [2017-12-19 16:34:21] [a98cfedcb2213d624216c666f97af8d4] [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	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=310371&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=310371&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310371&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	0.89475	13.0278	0
2	0.861421	12.5425	0
3	0.889302	12.9484	0
4	0.83536	12.163	0
5	0.838139	12.2035	0
6	0.860313	12.5263	0
7	0.799131	11.6355	0
8	0.784982	11.4295	0
9	0.797622	11.6136	0
10	0.746009	10.8621	0
11	0.755052	10.9937	0
12	0.78359	11.4092	0
13	0.715113	10.4122	0
14	0.694993	10.1193	0
15	0.705343	10.2699	0
16	0.662533	9.6466	0
17	0.664301	9.6724	0
18	0.679993	9.9008	0
19	0.632685	9.212	0
20	0.633193	9.2194	0
21	0.644563	9.385	0
22	0.592446	8.6261	0
23	0.603344	8.7848	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.89475 & 13.0278 & 0 \tabularnewline
2 & 0.861421 & 12.5425 & 0 \tabularnewline
3 & 0.889302 & 12.9484 & 0 \tabularnewline
4 & 0.83536 & 12.163 & 0 \tabularnewline
5 & 0.838139 & 12.2035 & 0 \tabularnewline
6 & 0.860313 & 12.5263 & 0 \tabularnewline
7 & 0.799131 & 11.6355 & 0 \tabularnewline
8 & 0.784982 & 11.4295 & 0 \tabularnewline
9 & 0.797622 & 11.6136 & 0 \tabularnewline
10 & 0.746009 & 10.8621 & 0 \tabularnewline
11 & 0.755052 & 10.9937 & 0 \tabularnewline
12 & 0.78359 & 11.4092 & 0 \tabularnewline
13 & 0.715113 & 10.4122 & 0 \tabularnewline
14 & 0.694993 & 10.1193 & 0 \tabularnewline
15 & 0.705343 & 10.2699 & 0 \tabularnewline
16 & 0.662533 & 9.6466 & 0 \tabularnewline
17 & 0.664301 & 9.6724 & 0 \tabularnewline
18 & 0.679993 & 9.9008 & 0 \tabularnewline
19 & 0.632685 & 9.212 & 0 \tabularnewline
20 & 0.633193 & 9.2194 & 0 \tabularnewline
21 & 0.644563 & 9.385 & 0 \tabularnewline
22 & 0.592446 & 8.6261 & 0 \tabularnewline
23 & 0.603344 & 8.7848 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310371&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]0.89475[/C][C]13.0278[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.861421[/C][C]12.5425[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.889302[/C][C]12.9484[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.83536[/C][C]12.163[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.838139[/C][C]12.2035[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.860313[/C][C]12.5263[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.799131[/C][C]11.6355[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.784982[/C][C]11.4295[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.797622[/C][C]11.6136[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.746009[/C][C]10.8621[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.755052[/C][C]10.9937[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.78359[/C][C]11.4092[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.715113[/C][C]10.4122[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.694993[/C][C]10.1193[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.705343[/C][C]10.2699[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.662533[/C][C]9.6466[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.664301[/C][C]9.6724[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.679993[/C][C]9.9008[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.632685[/C][C]9.212[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.633193[/C][C]9.2194[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.644563[/C][C]9.385[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.592446[/C][C]8.6261[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.603344[/C][C]8.7848[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310371&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310371&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	0.89475	13.0278	0
2	0.861421	12.5425	0
3	0.889302	12.9484	0
4	0.83536	12.163	0
5	0.838139	12.2035	0
6	0.860313	12.5263	0
7	0.799131	11.6355	0
8	0.784982	11.4295	0
9	0.797622	11.6136	0
10	0.746009	10.8621	0
11	0.755052	10.9937	0
12	0.78359	11.4092	0
13	0.715113	10.4122	0
14	0.694993	10.1193	0
15	0.705343	10.2699	0
16	0.662533	9.6466	0
17	0.664301	9.6724	0
18	0.679993	9.9008	0
19	0.632685	9.212	0
20	0.633193	9.2194	0
21	0.644563	9.385	0
22	0.592446	8.6261	0
23	0.603344	8.7848	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.89475	13.0278	0
2	0.305097	4.4423	7e-06
3	0.446291	6.4981	0
4	-0.135252	-1.9693	0.02511
5	0.240415	3.5005	0.000283
6	0.134169	1.9535	0.026036
7	-0.1744	-2.5393	0.005912
8	-0.034156	-0.4973	0.30974
9	0.038852	0.5657	0.286102
10	-0.105403	-1.5347	0.063175
11	0.131485	1.9144	0.028455
12	0.16668	2.4269	0.008032
13	-0.203264	-2.9596	0.001716
14	-0.108789	-1.584	0.057343
15	-0.004864	-0.0708	0.471804
16	0.025456	0.3706	0.355638
17	0.002582	0.0376	0.485022
18	0.077828	1.1332	0.129206
19	0.008653	0.126	0.449931
20	0.076743	1.1174	0.132545
21	0.029395	0.428	0.334544
22	-0.111892	-1.6292	0.052381
23	0.024366	0.3548	0.361558

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.89475 & 13.0278 & 0 \tabularnewline
2 & 0.305097 & 4.4423 & 7e-06 \tabularnewline
3 & 0.446291 & 6.4981 & 0 \tabularnewline
4 & -0.135252 & -1.9693 & 0.02511 \tabularnewline
5 & 0.240415 & 3.5005 & 0.000283 \tabularnewline
6 & 0.134169 & 1.9535 & 0.026036 \tabularnewline
7 & -0.1744 & -2.5393 & 0.005912 \tabularnewline
8 & -0.034156 & -0.4973 & 0.30974 \tabularnewline
9 & 0.038852 & 0.5657 & 0.286102 \tabularnewline
10 & -0.105403 & -1.5347 & 0.063175 \tabularnewline
11 & 0.131485 & 1.9144 & 0.028455 \tabularnewline
12 & 0.16668 & 2.4269 & 0.008032 \tabularnewline
13 & -0.203264 & -2.9596 & 0.001716 \tabularnewline
14 & -0.108789 & -1.584 & 0.057343 \tabularnewline
15 & -0.004864 & -0.0708 & 0.471804 \tabularnewline
16 & 0.025456 & 0.3706 & 0.355638 \tabularnewline
17 & 0.002582 & 0.0376 & 0.485022 \tabularnewline
18 & 0.077828 & 1.1332 & 0.129206 \tabularnewline
19 & 0.008653 & 0.126 & 0.449931 \tabularnewline
20 & 0.076743 & 1.1174 & 0.132545 \tabularnewline
21 & 0.029395 & 0.428 & 0.334544 \tabularnewline
22 & -0.111892 & -1.6292 & 0.052381 \tabularnewline
23 & 0.024366 & 0.3548 & 0.361558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310371&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]0.89475[/C][C]13.0278[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.305097[/C][C]4.4423[/C][C]7e-06[/C][/ROW]
[ROW][C]3[/C][C]0.446291[/C][C]6.4981[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.135252[/C][C]-1.9693[/C][C]0.02511[/C][/ROW]
[ROW][C]5[/C][C]0.240415[/C][C]3.5005[/C][C]0.000283[/C][/ROW]
[ROW][C]6[/C][C]0.134169[/C][C]1.9535[/C][C]0.026036[/C][/ROW]
[ROW][C]7[/C][C]-0.1744[/C][C]-2.5393[/C][C]0.005912[/C][/ROW]
[ROW][C]8[/C][C]-0.034156[/C][C]-0.4973[/C][C]0.30974[/C][/ROW]
[ROW][C]9[/C][C]0.038852[/C][C]0.5657[/C][C]0.286102[/C][/ROW]
[ROW][C]10[/C][C]-0.105403[/C][C]-1.5347[/C][C]0.063175[/C][/ROW]
[ROW][C]11[/C][C]0.131485[/C][C]1.9144[/C][C]0.028455[/C][/ROW]
[ROW][C]12[/C][C]0.16668[/C][C]2.4269[/C][C]0.008032[/C][/ROW]
[ROW][C]13[/C][C]-0.203264[/C][C]-2.9596[/C][C]0.001716[/C][/ROW]
[ROW][C]14[/C][C]-0.108789[/C][C]-1.584[/C][C]0.057343[/C][/ROW]
[ROW][C]15[/C][C]-0.004864[/C][C]-0.0708[/C][C]0.471804[/C][/ROW]
[ROW][C]16[/C][C]0.025456[/C][C]0.3706[/C][C]0.355638[/C][/ROW]
[ROW][C]17[/C][C]0.002582[/C][C]0.0376[/C][C]0.485022[/C][/ROW]
[ROW][C]18[/C][C]0.077828[/C][C]1.1332[/C][C]0.129206[/C][/ROW]
[ROW][C]19[/C][C]0.008653[/C][C]0.126[/C][C]0.449931[/C][/ROW]
[ROW][C]20[/C][C]0.076743[/C][C]1.1174[/C][C]0.132545[/C][/ROW]
[ROW][C]21[/C][C]0.029395[/C][C]0.428[/C][C]0.334544[/C][/ROW]
[ROW][C]22[/C][C]-0.111892[/C][C]-1.6292[/C][C]0.052381[/C][/ROW]
[ROW][C]23[/C][C]0.024366[/C][C]0.3548[/C][C]0.361558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310371&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310371&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	0.89475	13.0278	0
2	0.305097	4.4423	7e-06
3	0.446291	6.4981	0
4	-0.135252	-1.9693	0.02511
5	0.240415	3.5005	0.000283
6	0.134169	1.9535	0.026036
7	-0.1744	-2.5393	0.005912
8	-0.034156	-0.4973	0.30974
9	0.038852	0.5657	0.286102
10	-0.105403	-1.5347	0.063175
11	0.131485	1.9144	0.028455
12	0.16668	2.4269	0.008032
13	-0.203264	-2.9596	0.001716
14	-0.108789	-1.584	0.057343
15	-0.004864	-0.0708	0.471804
16	0.025456	0.3706	0.355638
17	0.002582	0.0376	0.485022
18	0.077828	1.1332	0.129206
19	0.008653	0.126	0.449931
20	0.076743	1.1174	0.132545
21	0.029395	0.428	0.334544
22	-0.111892	-1.6292	0.052381
23	0.024366	0.3548	0.361558

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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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,'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