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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Feb 2018 09:29:17 +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/t1517473769duyby6ewslzq2kl.htm/, Retrieved Sun, 28 Apr 2024 21:56:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=313589, Retrieved Sun, 28 Apr 2024 21:56:19 +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 08:29:17] [590d161356c203bfab730abba48e0199] [Current]

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0.0673999230710553
0.0760999147466414
0.0673999158700459
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3.66239571825825
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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=313589&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=313589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313589&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	-0.020962	-0.2964	0.3836
2	0.371277	5.2507	0
3	0.38641	5.4647	0
4	0.082373	1.1649	0.122716
5	0.292275	4.1334	2.6e-05
6	0.144307	2.0408	0.021292
7	-0.034899	-0.4935	0.311086
8	0.093268	1.319	0.094336
9	-0.085172	-1.2045	0.114906
10	-0.114635	-1.6212	0.053277
11	0.021979	0.3108	0.378124
12	-0.481629	-6.8113	0
13	-0.023491	-0.3322	0.370037
14	-0.251004	-3.5497	0.00024
15	-0.214548	-3.0342	0.001366
16	-0.182875	-2.5862	0.005206
17	-0.226447	-3.2024	0.000793
18	-0.148268	-2.0968	0.018633
19	-0.198613	-2.8088	0.002733
20	-0.146061	-2.0656	0.020077
21	-0.05923	-0.8376	0.201619
22	-0.221335	-3.1301	0.001004
23	0.023502	0.3324	0.369982

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.020962 & -0.2964 & 0.3836 \tabularnewline
2 & 0.371277 & 5.2507 & 0 \tabularnewline
3 & 0.38641 & 5.4647 & 0 \tabularnewline
4 & 0.082373 & 1.1649 & 0.122716 \tabularnewline
5 & 0.292275 & 4.1334 & 2.6e-05 \tabularnewline
6 & 0.144307 & 2.0408 & 0.021292 \tabularnewline
7 & -0.034899 & -0.4935 & 0.311086 \tabularnewline
8 & 0.093268 & 1.319 & 0.094336 \tabularnewline
9 & -0.085172 & -1.2045 & 0.114906 \tabularnewline
10 & -0.114635 & -1.6212 & 0.053277 \tabularnewline
11 & 0.021979 & 0.3108 & 0.378124 \tabularnewline
12 & -0.481629 & -6.8113 & 0 \tabularnewline
13 & -0.023491 & -0.3322 & 0.370037 \tabularnewline
14 & -0.251004 & -3.5497 & 0.00024 \tabularnewline
15 & -0.214548 & -3.0342 & 0.001366 \tabularnewline
16 & -0.182875 & -2.5862 & 0.005206 \tabularnewline
17 & -0.226447 & -3.2024 & 0.000793 \tabularnewline
18 & -0.148268 & -2.0968 & 0.018633 \tabularnewline
19 & -0.198613 & -2.8088 & 0.002733 \tabularnewline
20 & -0.146061 & -2.0656 & 0.020077 \tabularnewline
21 & -0.05923 & -0.8376 & 0.201619 \tabularnewline
22 & -0.221335 & -3.1301 & 0.001004 \tabularnewline
23 & 0.023502 & 0.3324 & 0.369982 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313589&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]-0.020962[/C][C]-0.2964[/C][C]0.3836[/C][/ROW]
[ROW][C]2[/C][C]0.371277[/C][C]5.2507[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.38641[/C][C]5.4647[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.082373[/C][C]1.1649[/C][C]0.122716[/C][/ROW]
[ROW][C]5[/C][C]0.292275[/C][C]4.1334[/C][C]2.6e-05[/C][/ROW]
[ROW][C]6[/C][C]0.144307[/C][C]2.0408[/C][C]0.021292[/C][/ROW]
[ROW][C]7[/C][C]-0.034899[/C][C]-0.4935[/C][C]0.311086[/C][/ROW]
[ROW][C]8[/C][C]0.093268[/C][C]1.319[/C][C]0.094336[/C][/ROW]
[ROW][C]9[/C][C]-0.085172[/C][C]-1.2045[/C][C]0.114906[/C][/ROW]
[ROW][C]10[/C][C]-0.114635[/C][C]-1.6212[/C][C]0.053277[/C][/ROW]
[ROW][C]11[/C][C]0.021979[/C][C]0.3108[/C][C]0.378124[/C][/ROW]
[ROW][C]12[/C][C]-0.481629[/C][C]-6.8113[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.023491[/C][C]-0.3322[/C][C]0.370037[/C][/ROW]
[ROW][C]14[/C][C]-0.251004[/C][C]-3.5497[/C][C]0.00024[/C][/ROW]
[ROW][C]15[/C][C]-0.214548[/C][C]-3.0342[/C][C]0.001366[/C][/ROW]
[ROW][C]16[/C][C]-0.182875[/C][C]-2.5862[/C][C]0.005206[/C][/ROW]
[ROW][C]17[/C][C]-0.226447[/C][C]-3.2024[/C][C]0.000793[/C][/ROW]
[ROW][C]18[/C][C]-0.148268[/C][C]-2.0968[/C][C]0.018633[/C][/ROW]
[ROW][C]19[/C][C]-0.198613[/C][C]-2.8088[/C][C]0.002733[/C][/ROW]
[ROW][C]20[/C][C]-0.146061[/C][C]-2.0656[/C][C]0.020077[/C][/ROW]
[ROW][C]21[/C][C]-0.05923[/C][C]-0.8376[/C][C]0.201619[/C][/ROW]
[ROW][C]22[/C][C]-0.221335[/C][C]-3.1301[/C][C]0.001004[/C][/ROW]
[ROW][C]23[/C][C]0.023502[/C][C]0.3324[/C][C]0.369982[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313589&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	-0.020962	-0.2964	0.3836
2	0.371277	5.2507	0
3	0.38641	5.4647	0
4	0.082373	1.1649	0.122716
5	0.292275	4.1334	2.6e-05
6	0.144307	2.0408	0.021292
7	-0.034899	-0.4935	0.311086
8	0.093268	1.319	0.094336
9	-0.085172	-1.2045	0.114906
10	-0.114635	-1.6212	0.053277
11	0.021979	0.3108	0.378124
12	-0.481629	-6.8113	0
13	-0.023491	-0.3322	0.370037
14	-0.251004	-3.5497	0.00024
15	-0.214548	-3.0342	0.001366
16	-0.182875	-2.5862	0.005206
17	-0.226447	-3.2024	0.000793
18	-0.148268	-2.0968	0.018633
19	-0.198613	-2.8088	0.002733
20	-0.146061	-2.0656	0.020077
21	-0.05923	-0.8376	0.201619
22	-0.221335	-3.1301	0.001004
23	0.023502	0.3324	0.369982

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.020962	-0.2964	0.3836
2	0.371001	5.2467	0
3	0.462984	6.5476	0
4	0.034753	0.4915	0.311813
5	-0.00794	-0.1123	0.455351
6	-0.032947	-0.4659	0.320883
7	-0.246668	-3.4884	0.000299
8	-0.205339	-2.9039	0.00205
9	-0.148098	-2.0944	0.018741
10	-0.117303	-1.6589	0.04935
11	0.122662	1.7347	0.042167
12	-0.389853	-5.5134	0
13	-0.109075	-1.5426	0.06226
14	0.065558	0.9271	0.177487
15	0.274913	3.8879	6.9e-05
16	-0.007743	-0.1095	0.456456
17	-0.035716	-0.5051	0.307021
18	0.067466	0.9541	0.170588
19	-0.174883	-2.4732	0.007112
20	-0.252645	-3.5729	0.000221
21	-0.00072	-0.0102	0.495942
22	-0.131532	-1.8601	0.032166
23	0.117243	1.6581	0.049435

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.020962 & -0.2964 & 0.3836 \tabularnewline
2 & 0.371001 & 5.2467 & 0 \tabularnewline
3 & 0.462984 & 6.5476 & 0 \tabularnewline
4 & 0.034753 & 0.4915 & 0.311813 \tabularnewline
5 & -0.00794 & -0.1123 & 0.455351 \tabularnewline
6 & -0.032947 & -0.4659 & 0.320883 \tabularnewline
7 & -0.246668 & -3.4884 & 0.000299 \tabularnewline
8 & -0.205339 & -2.9039 & 0.00205 \tabularnewline
9 & -0.148098 & -2.0944 & 0.018741 \tabularnewline
10 & -0.117303 & -1.6589 & 0.04935 \tabularnewline
11 & 0.122662 & 1.7347 & 0.042167 \tabularnewline
12 & -0.389853 & -5.5134 & 0 \tabularnewline
13 & -0.109075 & -1.5426 & 0.06226 \tabularnewline
14 & 0.065558 & 0.9271 & 0.177487 \tabularnewline
15 & 0.274913 & 3.8879 & 6.9e-05 \tabularnewline
16 & -0.007743 & -0.1095 & 0.456456 \tabularnewline
17 & -0.035716 & -0.5051 & 0.307021 \tabularnewline
18 & 0.067466 & 0.9541 & 0.170588 \tabularnewline
19 & -0.174883 & -2.4732 & 0.007112 \tabularnewline
20 & -0.252645 & -3.5729 & 0.000221 \tabularnewline
21 & -0.00072 & -0.0102 & 0.495942 \tabularnewline
22 & -0.131532 & -1.8601 & 0.032166 \tabularnewline
23 & 0.117243 & 1.6581 & 0.049435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=313589&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]-0.020962[/C][C]-0.2964[/C][C]0.3836[/C][/ROW]
[ROW][C]2[/C][C]0.371001[/C][C]5.2467[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.462984[/C][C]6.5476[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.034753[/C][C]0.4915[/C][C]0.311813[/C][/ROW]
[ROW][C]5[/C][C]-0.00794[/C][C]-0.1123[/C][C]0.455351[/C][/ROW]
[ROW][C]6[/C][C]-0.032947[/C][C]-0.4659[/C][C]0.320883[/C][/ROW]
[ROW][C]7[/C][C]-0.246668[/C][C]-3.4884[/C][C]0.000299[/C][/ROW]
[ROW][C]8[/C][C]-0.205339[/C][C]-2.9039[/C][C]0.00205[/C][/ROW]
[ROW][C]9[/C][C]-0.148098[/C][C]-2.0944[/C][C]0.018741[/C][/ROW]
[ROW][C]10[/C][C]-0.117303[/C][C]-1.6589[/C][C]0.04935[/C][/ROW]
[ROW][C]11[/C][C]0.122662[/C][C]1.7347[/C][C]0.042167[/C][/ROW]
[ROW][C]12[/C][C]-0.389853[/C][C]-5.5134[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.109075[/C][C]-1.5426[/C][C]0.06226[/C][/ROW]
[ROW][C]14[/C][C]0.065558[/C][C]0.9271[/C][C]0.177487[/C][/ROW]
[ROW][C]15[/C][C]0.274913[/C][C]3.8879[/C][C]6.9e-05[/C][/ROW]
[ROW][C]16[/C][C]-0.007743[/C][C]-0.1095[/C][C]0.456456[/C][/ROW]
[ROW][C]17[/C][C]-0.035716[/C][C]-0.5051[/C][C]0.307021[/C][/ROW]
[ROW][C]18[/C][C]0.067466[/C][C]0.9541[/C][C]0.170588[/C][/ROW]
[ROW][C]19[/C][C]-0.174883[/C][C]-2.4732[/C][C]0.007112[/C][/ROW]
[ROW][C]20[/C][C]-0.252645[/C][C]-3.5729[/C][C]0.000221[/C][/ROW]
[ROW][C]21[/C][C]-0.00072[/C][C]-0.0102[/C][C]0.495942[/C][/ROW]
[ROW][C]22[/C][C]-0.131532[/C][C]-1.8601[/C][C]0.032166[/C][/ROW]
[ROW][C]23[/C][C]0.117243[/C][C]1.6581[/C][C]0.049435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=313589&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=313589&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	-0.020962	-0.2964	0.3836
2	0.371001	5.2467	0
3	0.462984	6.5476	0
4	0.034753	0.4915	0.311813
5	-0.00794	-0.1123	0.455351
6	-0.032947	-0.4659	0.320883
7	-0.246668	-3.4884	0.000299
8	-0.205339	-2.9039	0.00205
9	-0.148098	-2.0944	0.018741
10	-0.117303	-1.6589	0.04935
11	0.122662	1.7347	0.042167
12	-0.389853	-5.5134	0
13	-0.109075	-1.5426	0.06226
14	0.065558	0.9271	0.177487
15	0.274913	3.8879	6.9e-05
16	-0.007743	-0.1095	0.456456
17	-0.035716	-0.5051	0.307021
18	0.067466	0.9541	0.170588
19	-0.174883	-2.4732	0.007112
20	-0.252645	-3.5729	0.000221
21	-0.00072	-0.0102	0.495942
22	-0.131532	-1.8601	0.032166
23	0.117243	1.6581	0.049435

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):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.99 ; 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