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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 16:00:14 +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/14/t1481727641zyv40yft3kne6k4.htm/, Retrieved Sat, 04 May 2024 02:12:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299540, Retrieved Sat, 04 May 2024 02:12:32 +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] [Autocorrelatie me...] [2016-12-14 15:00:14] [7b02c9ca65294818d9c418453f92ae83] [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=299540&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=299540&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299540&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	-0.556787	-6.2251	0
2	0.080227	0.897	0.18573
3	-0.002225	-0.0249	0.490098
4	-0.0055	-0.0615	0.475534
5	-0.085485	-0.9558	0.17052
6	0.142393	1.592	0.056956
7	-0.045188	-0.5052	0.307146
8	-0.078085	-0.873	0.192165
9	0.03968	0.4436	0.329035
10	0.044654	0.4992	0.309243
11	5.1e-05	6e-04	0.499771
12	-0.11109	-1.242	0.108276
13	0.086942	0.972	0.166454
14	0.023667	0.2646	0.395876
15	0.0015	0.0168	0.493323
16	-0.104227	-1.1653	0.123059
17	0.176851	1.9773	0.025107
18	-0.160588	-1.7954	0.037501
19	0.020938	0.2341	0.407646
20	0.093401	1.0443	0.149191
21	-0.07678	-0.8584	0.19615

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.556787 & -6.2251 & 0 \tabularnewline
2 & 0.080227 & 0.897 & 0.18573 \tabularnewline
3 & -0.002225 & -0.0249 & 0.490098 \tabularnewline
4 & -0.0055 & -0.0615 & 0.475534 \tabularnewline
5 & -0.085485 & -0.9558 & 0.17052 \tabularnewline
6 & 0.142393 & 1.592 & 0.056956 \tabularnewline
7 & -0.045188 & -0.5052 & 0.307146 \tabularnewline
8 & -0.078085 & -0.873 & 0.192165 \tabularnewline
9 & 0.03968 & 0.4436 & 0.329035 \tabularnewline
10 & 0.044654 & 0.4992 & 0.309243 \tabularnewline
11 & 5.1e-05 & 6e-04 & 0.499771 \tabularnewline
12 & -0.11109 & -1.242 & 0.108276 \tabularnewline
13 & 0.086942 & 0.972 & 0.166454 \tabularnewline
14 & 0.023667 & 0.2646 & 0.395876 \tabularnewline
15 & 0.0015 & 0.0168 & 0.493323 \tabularnewline
16 & -0.104227 & -1.1653 & 0.123059 \tabularnewline
17 & 0.176851 & 1.9773 & 0.025107 \tabularnewline
18 & -0.160588 & -1.7954 & 0.037501 \tabularnewline
19 & 0.020938 & 0.2341 & 0.407646 \tabularnewline
20 & 0.093401 & 1.0443 & 0.149191 \tabularnewline
21 & -0.07678 & -0.8584 & 0.19615 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299540&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]-0.556787[/C][C]-6.2251[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.080227[/C][C]0.897[/C][C]0.18573[/C][/ROW]
[ROW][C]3[/C][C]-0.002225[/C][C]-0.0249[/C][C]0.490098[/C][/ROW]
[ROW][C]4[/C][C]-0.0055[/C][C]-0.0615[/C][C]0.475534[/C][/ROW]
[ROW][C]5[/C][C]-0.085485[/C][C]-0.9558[/C][C]0.17052[/C][/ROW]
[ROW][C]6[/C][C]0.142393[/C][C]1.592[/C][C]0.056956[/C][/ROW]
[ROW][C]7[/C][C]-0.045188[/C][C]-0.5052[/C][C]0.307146[/C][/ROW]
[ROW][C]8[/C][C]-0.078085[/C][C]-0.873[/C][C]0.192165[/C][/ROW]
[ROW][C]9[/C][C]0.03968[/C][C]0.4436[/C][C]0.329035[/C][/ROW]
[ROW][C]10[/C][C]0.044654[/C][C]0.4992[/C][C]0.309243[/C][/ROW]
[ROW][C]11[/C][C]5.1e-05[/C][C]6e-04[/C][C]0.499771[/C][/ROW]
[ROW][C]12[/C][C]-0.11109[/C][C]-1.242[/C][C]0.108276[/C][/ROW]
[ROW][C]13[/C][C]0.086942[/C][C]0.972[/C][C]0.166454[/C][/ROW]
[ROW][C]14[/C][C]0.023667[/C][C]0.2646[/C][C]0.395876[/C][/ROW]
[ROW][C]15[/C][C]0.0015[/C][C]0.0168[/C][C]0.493323[/C][/ROW]
[ROW][C]16[/C][C]-0.104227[/C][C]-1.1653[/C][C]0.123059[/C][/ROW]
[ROW][C]17[/C][C]0.176851[/C][C]1.9773[/C][C]0.025107[/C][/ROW]
[ROW][C]18[/C][C]-0.160588[/C][C]-1.7954[/C][C]0.037501[/C][/ROW]
[ROW][C]19[/C][C]0.020938[/C][C]0.2341[/C][C]0.407646[/C][/ROW]
[ROW][C]20[/C][C]0.093401[/C][C]1.0443[/C][C]0.149191[/C][/ROW]
[ROW][C]21[/C][C]-0.07678[/C][C]-0.8584[/C][C]0.19615[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299540&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299540&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	-0.556787	-6.2251	0
2	0.080227	0.897	0.18573
3	-0.002225	-0.0249	0.490098
4	-0.0055	-0.0615	0.475534
5	-0.085485	-0.9558	0.17052
6	0.142393	1.592	0.056956
7	-0.045188	-0.5052	0.307146
8	-0.078085	-0.873	0.192165
9	0.03968	0.4436	0.329035
10	0.044654	0.4992	0.309243
11	5.1e-05	6e-04	0.499771
12	-0.11109	-1.242	0.108276
13	0.086942	0.972	0.166454
14	0.023667	0.2646	0.395876
15	0.0015	0.0168	0.493323
16	-0.104227	-1.1653	0.123059
17	0.176851	1.9773	0.025107
18	-0.160588	-1.7954	0.037501
19	0.020938	0.2341	0.407646
20	0.093401	1.0443	0.149191
21	-0.07678	-0.8584	0.19615

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.556787	-6.2251	0
2	-0.333027	-3.7234	0.000148
3	-0.208821	-2.3347	0.010577
4	-0.14389	-1.6087	0.055098
5	-0.252972	-2.8283	0.002726
6	-0.091979	-1.0284	0.152885
7	-0.0048	-0.0537	0.478642
8	-0.120897	-1.3517	0.089461
9	-0.159846	-1.7871	0.038169
10	-0.067233	-0.7517	0.226827
11	0.045834	0.5124	0.304625
12	-0.148441	-1.6596	0.049749
13	-0.170784	-1.9094	0.02925
14	-0.018428	-0.206	0.41855
15	0.095453	1.0672	0.143971
16	-0.132076	-1.4767	0.071142
17	0.027021	0.3021	0.381537
18	0.041468	0.4636	0.32186
19	-0.06077	-0.6794	0.249062
20	-0.029019	-0.3244	0.373074
21	-0.038848	-0.4343	0.332396

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.556787 & -6.2251 & 0 \tabularnewline
2 & -0.333027 & -3.7234 & 0.000148 \tabularnewline
3 & -0.208821 & -2.3347 & 0.010577 \tabularnewline
4 & -0.14389 & -1.6087 & 0.055098 \tabularnewline
5 & -0.252972 & -2.8283 & 0.002726 \tabularnewline
6 & -0.091979 & -1.0284 & 0.152885 \tabularnewline
7 & -0.0048 & -0.0537 & 0.478642 \tabularnewline
8 & -0.120897 & -1.3517 & 0.089461 \tabularnewline
9 & -0.159846 & -1.7871 & 0.038169 \tabularnewline
10 & -0.067233 & -0.7517 & 0.226827 \tabularnewline
11 & 0.045834 & 0.5124 & 0.304625 \tabularnewline
12 & -0.148441 & -1.6596 & 0.049749 \tabularnewline
13 & -0.170784 & -1.9094 & 0.02925 \tabularnewline
14 & -0.018428 & -0.206 & 0.41855 \tabularnewline
15 & 0.095453 & 1.0672 & 0.143971 \tabularnewline
16 & -0.132076 & -1.4767 & 0.071142 \tabularnewline
17 & 0.027021 & 0.3021 & 0.381537 \tabularnewline
18 & 0.041468 & 0.4636 & 0.32186 \tabularnewline
19 & -0.06077 & -0.6794 & 0.249062 \tabularnewline
20 & -0.029019 & -0.3244 & 0.373074 \tabularnewline
21 & -0.038848 & -0.4343 & 0.332396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299540&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]-0.556787[/C][C]-6.2251[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.333027[/C][C]-3.7234[/C][C]0.000148[/C][/ROW]
[ROW][C]3[/C][C]-0.208821[/C][C]-2.3347[/C][C]0.010577[/C][/ROW]
[ROW][C]4[/C][C]-0.14389[/C][C]-1.6087[/C][C]0.055098[/C][/ROW]
[ROW][C]5[/C][C]-0.252972[/C][C]-2.8283[/C][C]0.002726[/C][/ROW]
[ROW][C]6[/C][C]-0.091979[/C][C]-1.0284[/C][C]0.152885[/C][/ROW]
[ROW][C]7[/C][C]-0.0048[/C][C]-0.0537[/C][C]0.478642[/C][/ROW]
[ROW][C]8[/C][C]-0.120897[/C][C]-1.3517[/C][C]0.089461[/C][/ROW]
[ROW][C]9[/C][C]-0.159846[/C][C]-1.7871[/C][C]0.038169[/C][/ROW]
[ROW][C]10[/C][C]-0.067233[/C][C]-0.7517[/C][C]0.226827[/C][/ROW]
[ROW][C]11[/C][C]0.045834[/C][C]0.5124[/C][C]0.304625[/C][/ROW]
[ROW][C]12[/C][C]-0.148441[/C][C]-1.6596[/C][C]0.049749[/C][/ROW]
[ROW][C]13[/C][C]-0.170784[/C][C]-1.9094[/C][C]0.02925[/C][/ROW]
[ROW][C]14[/C][C]-0.018428[/C][C]-0.206[/C][C]0.41855[/C][/ROW]
[ROW][C]15[/C][C]0.095453[/C][C]1.0672[/C][C]0.143971[/C][/ROW]
[ROW][C]16[/C][C]-0.132076[/C][C]-1.4767[/C][C]0.071142[/C][/ROW]
[ROW][C]17[/C][C]0.027021[/C][C]0.3021[/C][C]0.381537[/C][/ROW]
[ROW][C]18[/C][C]0.041468[/C][C]0.4636[/C][C]0.32186[/C][/ROW]
[ROW][C]19[/C][C]-0.06077[/C][C]-0.6794[/C][C]0.249062[/C][/ROW]
[ROW][C]20[/C][C]-0.029019[/C][C]-0.3244[/C][C]0.373074[/C][/ROW]
[ROW][C]21[/C][C]-0.038848[/C][C]-0.4343[/C][C]0.332396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299540&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299540&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	-0.556787	-6.2251	0
2	-0.333027	-3.7234	0.000148
3	-0.208821	-2.3347	0.010577
4	-0.14389	-1.6087	0.055098
5	-0.252972	-2.8283	0.002726
6	-0.091979	-1.0284	0.152885
7	-0.0048	-0.0537	0.478642
8	-0.120897	-1.3517	0.089461
9	-0.159846	-1.7871	0.038169
10	-0.067233	-0.7517	0.226827
11	0.045834	0.5124	0.304625
12	-0.148441	-1.6596	0.049749
13	-0.170784	-1.9094	0.02925
14	-0.018428	-0.206	0.41855
15	0.095453	1.0672	0.143971
16	-0.132076	-1.4767	0.071142
17	0.027021	0.3021	0.381537
18	0.041468	0.4636	0.32186
19	-0.06077	-0.6794	0.249062
20	-0.029019	-0.3244	0.373074
21	-0.038848	-0.4343	0.332396

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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