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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 15:18:58 +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/19/t1482157192v1opcfyrv83syer.htm/, Retrieved Fri, 17 May 2024 14:19:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301365, Retrieved Fri, 17 May 2024 14:19:54 +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] [auto 11] [2016-12-19 14:18:58] [06fd994a2f2098873ec640c3e39346e5] [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=301365&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=301365&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301365&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	-0.366584	-3.8968	8.3e-05
2	-0.133025	-1.4141	0.080044
3	0.067436	0.7169	0.237471
4	-0.119463	-1.2699	0.103362
5	0.040701	0.4327	0.333042
6	0.126668	1.3465	0.090418
7	-0.121259	-1.289	0.100015
8	-0.132554	-1.4091	0.08078
9	0.290116	3.084	0.001284
10	-0.196145	-2.085	0.019659
11	0.266645	2.8345	0.002719
12	-0.156899	-1.6679	0.049057
13	-0.287245	-3.0535	0.001411
14	0.162788	1.7305	0.043139
15	0.138597	1.4733	0.071725
16	-0.139641	-1.4844	0.070243
17	0.167853	1.7843	0.038529
18	0.004566	0.0485	0.480688
19	-0.239177	-2.5425	0.00618
20	0.197926	2.104	0.018799
21	-0.039877	-0.4239	0.336223

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.366584 & -3.8968 & 8.3e-05 \tabularnewline
2 & -0.133025 & -1.4141 & 0.080044 \tabularnewline
3 & 0.067436 & 0.7169 & 0.237471 \tabularnewline
4 & -0.119463 & -1.2699 & 0.103362 \tabularnewline
5 & 0.040701 & 0.4327 & 0.333042 \tabularnewline
6 & 0.126668 & 1.3465 & 0.090418 \tabularnewline
7 & -0.121259 & -1.289 & 0.100015 \tabularnewline
8 & -0.132554 & -1.4091 & 0.08078 \tabularnewline
9 & 0.290116 & 3.084 & 0.001284 \tabularnewline
10 & -0.196145 & -2.085 & 0.019659 \tabularnewline
11 & 0.266645 & 2.8345 & 0.002719 \tabularnewline
12 & -0.156899 & -1.6679 & 0.049057 \tabularnewline
13 & -0.287245 & -3.0535 & 0.001411 \tabularnewline
14 & 0.162788 & 1.7305 & 0.043139 \tabularnewline
15 & 0.138597 & 1.4733 & 0.071725 \tabularnewline
16 & -0.139641 & -1.4844 & 0.070243 \tabularnewline
17 & 0.167853 & 1.7843 & 0.038529 \tabularnewline
18 & 0.004566 & 0.0485 & 0.480688 \tabularnewline
19 & -0.239177 & -2.5425 & 0.00618 \tabularnewline
20 & 0.197926 & 2.104 & 0.018799 \tabularnewline
21 & -0.039877 & -0.4239 & 0.336223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301365&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]-0.366584[/C][C]-3.8968[/C][C]8.3e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.133025[/C][C]-1.4141[/C][C]0.080044[/C][/ROW]
[ROW][C]3[/C][C]0.067436[/C][C]0.7169[/C][C]0.237471[/C][/ROW]
[ROW][C]4[/C][C]-0.119463[/C][C]-1.2699[/C][C]0.103362[/C][/ROW]
[ROW][C]5[/C][C]0.040701[/C][C]0.4327[/C][C]0.333042[/C][/ROW]
[ROW][C]6[/C][C]0.126668[/C][C]1.3465[/C][C]0.090418[/C][/ROW]
[ROW][C]7[/C][C]-0.121259[/C][C]-1.289[/C][C]0.100015[/C][/ROW]
[ROW][C]8[/C][C]-0.132554[/C][C]-1.4091[/C][C]0.08078[/C][/ROW]
[ROW][C]9[/C][C]0.290116[/C][C]3.084[/C][C]0.001284[/C][/ROW]
[ROW][C]10[/C][C]-0.196145[/C][C]-2.085[/C][C]0.019659[/C][/ROW]
[ROW][C]11[/C][C]0.266645[/C][C]2.8345[/C][C]0.002719[/C][/ROW]
[ROW][C]12[/C][C]-0.156899[/C][C]-1.6679[/C][C]0.049057[/C][/ROW]
[ROW][C]13[/C][C]-0.287245[/C][C]-3.0535[/C][C]0.001411[/C][/ROW]
[ROW][C]14[/C][C]0.162788[/C][C]1.7305[/C][C]0.043139[/C][/ROW]
[ROW][C]15[/C][C]0.138597[/C][C]1.4733[/C][C]0.071725[/C][/ROW]
[ROW][C]16[/C][C]-0.139641[/C][C]-1.4844[/C][C]0.070243[/C][/ROW]
[ROW][C]17[/C][C]0.167853[/C][C]1.7843[/C][C]0.038529[/C][/ROW]
[ROW][C]18[/C][C]0.004566[/C][C]0.0485[/C][C]0.480688[/C][/ROW]
[ROW][C]19[/C][C]-0.239177[/C][C]-2.5425[/C][C]0.00618[/C][/ROW]
[ROW][C]20[/C][C]0.197926[/C][C]2.104[/C][C]0.018799[/C][/ROW]
[ROW][C]21[/C][C]-0.039877[/C][C]-0.4239[/C][C]0.336223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301365&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301365&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	-0.366584	-3.8968	8.3e-05
2	-0.133025	-1.4141	0.080044
3	0.067436	0.7169	0.237471
4	-0.119463	-1.2699	0.103362
5	0.040701	0.4327	0.333042
6	0.126668	1.3465	0.090418
7	-0.121259	-1.289	0.100015
8	-0.132554	-1.4091	0.08078
9	0.290116	3.084	0.001284
10	-0.196145	-2.085	0.019659
11	0.266645	2.8345	0.002719
12	-0.156899	-1.6679	0.049057
13	-0.287245	-3.0535	0.001411
14	0.162788	1.7305	0.043139
15	0.138597	1.4733	0.071725
16	-0.139641	-1.4844	0.070243
17	0.167853	1.7843	0.038529
18	0.004566	0.0485	0.480688
19	-0.239177	-2.5425	0.00618
20	0.197926	2.104	0.018799
21	-0.039877	-0.4239	0.336223

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.366584	-3.8968	8.3e-05
2	-0.308924	-3.2839	0.000682
3	-0.140024	-1.4885	0.069705
4	-0.241712	-2.5694	0.005744
5	-0.163794	-1.7412	0.042189
6	0.01242	0.132	0.4476
7	-0.08535	-0.9073	0.183093
8	-0.270895	-2.8797	0.002382
9	0.092882	0.9873	0.16279
10	-0.116125	-1.2344	0.109803
11	0.302084	3.2112	0.000861
12	0.022188	0.2359	0.406984
13	-0.257284	-2.735	0.003623
14	-0.187205	-1.99	0.024502
15	-0.009234	-0.0982	0.460992
16	-0.157643	-1.6758	0.048275
17	0.115724	1.2302	0.110596
18	0.124137	1.3196	0.094819
19	-0.001421	-0.0151	0.493986
20	-0.126158	-1.3411	0.091292
21	-0.0509	-0.5411	0.294762

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.366584 & -3.8968 & 8.3e-05 \tabularnewline
2 & -0.308924 & -3.2839 & 0.000682 \tabularnewline
3 & -0.140024 & -1.4885 & 0.069705 \tabularnewline
4 & -0.241712 & -2.5694 & 0.005744 \tabularnewline
5 & -0.163794 & -1.7412 & 0.042189 \tabularnewline
6 & 0.01242 & 0.132 & 0.4476 \tabularnewline
7 & -0.08535 & -0.9073 & 0.183093 \tabularnewline
8 & -0.270895 & -2.8797 & 0.002382 \tabularnewline
9 & 0.092882 & 0.9873 & 0.16279 \tabularnewline
10 & -0.116125 & -1.2344 & 0.109803 \tabularnewline
11 & 0.302084 & 3.2112 & 0.000861 \tabularnewline
12 & 0.022188 & 0.2359 & 0.406984 \tabularnewline
13 & -0.257284 & -2.735 & 0.003623 \tabularnewline
14 & -0.187205 & -1.99 & 0.024502 \tabularnewline
15 & -0.009234 & -0.0982 & 0.460992 \tabularnewline
16 & -0.157643 & -1.6758 & 0.048275 \tabularnewline
17 & 0.115724 & 1.2302 & 0.110596 \tabularnewline
18 & 0.124137 & 1.3196 & 0.094819 \tabularnewline
19 & -0.001421 & -0.0151 & 0.493986 \tabularnewline
20 & -0.126158 & -1.3411 & 0.091292 \tabularnewline
21 & -0.0509 & -0.5411 & 0.294762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301365&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]-0.366584[/C][C]-3.8968[/C][C]8.3e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.308924[/C][C]-3.2839[/C][C]0.000682[/C][/ROW]
[ROW][C]3[/C][C]-0.140024[/C][C]-1.4885[/C][C]0.069705[/C][/ROW]
[ROW][C]4[/C][C]-0.241712[/C][C]-2.5694[/C][C]0.005744[/C][/ROW]
[ROW][C]5[/C][C]-0.163794[/C][C]-1.7412[/C][C]0.042189[/C][/ROW]
[ROW][C]6[/C][C]0.01242[/C][C]0.132[/C][C]0.4476[/C][/ROW]
[ROW][C]7[/C][C]-0.08535[/C][C]-0.9073[/C][C]0.183093[/C][/ROW]
[ROW][C]8[/C][C]-0.270895[/C][C]-2.8797[/C][C]0.002382[/C][/ROW]
[ROW][C]9[/C][C]0.092882[/C][C]0.9873[/C][C]0.16279[/C][/ROW]
[ROW][C]10[/C][C]-0.116125[/C][C]-1.2344[/C][C]0.109803[/C][/ROW]
[ROW][C]11[/C][C]0.302084[/C][C]3.2112[/C][C]0.000861[/C][/ROW]
[ROW][C]12[/C][C]0.022188[/C][C]0.2359[/C][C]0.406984[/C][/ROW]
[ROW][C]13[/C][C]-0.257284[/C][C]-2.735[/C][C]0.003623[/C][/ROW]
[ROW][C]14[/C][C]-0.187205[/C][C]-1.99[/C][C]0.024502[/C][/ROW]
[ROW][C]15[/C][C]-0.009234[/C][C]-0.0982[/C][C]0.460992[/C][/ROW]
[ROW][C]16[/C][C]-0.157643[/C][C]-1.6758[/C][C]0.048275[/C][/ROW]
[ROW][C]17[/C][C]0.115724[/C][C]1.2302[/C][C]0.110596[/C][/ROW]
[ROW][C]18[/C][C]0.124137[/C][C]1.3196[/C][C]0.094819[/C][/ROW]
[ROW][C]19[/C][C]-0.001421[/C][C]-0.0151[/C][C]0.493986[/C][/ROW]
[ROW][C]20[/C][C]-0.126158[/C][C]-1.3411[/C][C]0.091292[/C][/ROW]
[ROW][C]21[/C][C]-0.0509[/C][C]-0.5411[/C][C]0.294762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301365&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301365&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	-0.366584	-3.8968	8.3e-05
2	-0.308924	-3.2839	0.000682
3	-0.140024	-1.4885	0.069705
4	-0.241712	-2.5694	0.005744
5	-0.163794	-1.7412	0.042189
6	0.01242	0.132	0.4476
7	-0.08535	-0.9073	0.183093
8	-0.270895	-2.8797	0.002382
9	0.092882	0.9873	0.16279
10	-0.116125	-1.2344	0.109803
11	0.302084	3.2112	0.000861
12	0.022188	0.2359	0.406984
13	-0.257284	-2.735	0.003623
14	-0.187205	-1.99	0.024502
15	-0.009234	-0.0982	0.460992
16	-0.157643	-1.6758	0.048275
17	0.115724	1.2302	0.110596
18	0.124137	1.3196	0.094819
19	-0.001421	-0.0151	0.493986
20	-0.126158	-1.3411	0.091292
21	-0.0509	-0.5411	0.294762

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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PDF link

Parameters (Session):

Parameters (R input):

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