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Author

*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, 12 Dec 2017 16:37:29 +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/12/t15130930549bu4uudmu6hzlhs.htm/, Retrieved Wed, 15 May 2024 08:16:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=309139, Retrieved Wed, 15 May 2024 08:16:00 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2017-12-12 15:37:29] [867b6df3e80c046baffd373216517d1f] [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=309139&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=309139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309139&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	-0.353213	-4.9827	1e-06
2	-0.123308	-1.7395	0.041749
3	0.010776	0.152	0.439663
4	0.048094	0.6785	0.249136
5	-0.062662	-0.884	0.188892
6	-0.000553	-0.0078	0.49689
7	0.046804	0.6602	0.25493
8	-0.081729	-1.1529	0.12516
9	0.054615	0.7704	0.220975
10	0.025884	0.3651	0.357698
11	0.152639	2.1532	0.016252
12	-0.415182	-5.8569	0
13	0.06743	0.9512	0.171325
14	0.145971	2.0592	0.02039
15	0.055844	0.7878	0.215884
16	-0.13097	-1.8476	0.033075
17	0.022715	0.3204	0.374487
18	0.182378	2.5728	0.005409
19	-0.160752	-2.2677	0.012211
20	0.053726	0.7579	0.224704
21	-0.049736	-0.7016	0.241868
22	0.050751	0.7159	0.237437
23	-0.059539	-0.8399	0.200985

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.353213 & -4.9827 & 1e-06 \tabularnewline
2 & -0.123308 & -1.7395 & 0.041749 \tabularnewline
3 & 0.010776 & 0.152 & 0.439663 \tabularnewline
4 & 0.048094 & 0.6785 & 0.249136 \tabularnewline
5 & -0.062662 & -0.884 & 0.188892 \tabularnewline
6 & -0.000553 & -0.0078 & 0.49689 \tabularnewline
7 & 0.046804 & 0.6602 & 0.25493 \tabularnewline
8 & -0.081729 & -1.1529 & 0.12516 \tabularnewline
9 & 0.054615 & 0.7704 & 0.220975 \tabularnewline
10 & 0.025884 & 0.3651 & 0.357698 \tabularnewline
11 & 0.152639 & 2.1532 & 0.016252 \tabularnewline
12 & -0.415182 & -5.8569 & 0 \tabularnewline
13 & 0.06743 & 0.9512 & 0.171325 \tabularnewline
14 & 0.145971 & 2.0592 & 0.02039 \tabularnewline
15 & 0.055844 & 0.7878 & 0.215884 \tabularnewline
16 & -0.13097 & -1.8476 & 0.033075 \tabularnewline
17 & 0.022715 & 0.3204 & 0.374487 \tabularnewline
18 & 0.182378 & 2.5728 & 0.005409 \tabularnewline
19 & -0.160752 & -2.2677 & 0.012211 \tabularnewline
20 & 0.053726 & 0.7579 & 0.224704 \tabularnewline
21 & -0.049736 & -0.7016 & 0.241868 \tabularnewline
22 & 0.050751 & 0.7159 & 0.237437 \tabularnewline
23 & -0.059539 & -0.8399 & 0.200985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309139&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]-0.353213[/C][C]-4.9827[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.123308[/C][C]-1.7395[/C][C]0.041749[/C][/ROW]
[ROW][C]3[/C][C]0.010776[/C][C]0.152[/C][C]0.439663[/C][/ROW]
[ROW][C]4[/C][C]0.048094[/C][C]0.6785[/C][C]0.249136[/C][/ROW]
[ROW][C]5[/C][C]-0.062662[/C][C]-0.884[/C][C]0.188892[/C][/ROW]
[ROW][C]6[/C][C]-0.000553[/C][C]-0.0078[/C][C]0.49689[/C][/ROW]
[ROW][C]7[/C][C]0.046804[/C][C]0.6602[/C][C]0.25493[/C][/ROW]
[ROW][C]8[/C][C]-0.081729[/C][C]-1.1529[/C][C]0.12516[/C][/ROW]
[ROW][C]9[/C][C]0.054615[/C][C]0.7704[/C][C]0.220975[/C][/ROW]
[ROW][C]10[/C][C]0.025884[/C][C]0.3651[/C][C]0.357698[/C][/ROW]
[ROW][C]11[/C][C]0.152639[/C][C]2.1532[/C][C]0.016252[/C][/ROW]
[ROW][C]12[/C][C]-0.415182[/C][C]-5.8569[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.06743[/C][C]0.9512[/C][C]0.171325[/C][/ROW]
[ROW][C]14[/C][C]0.145971[/C][C]2.0592[/C][C]0.02039[/C][/ROW]
[ROW][C]15[/C][C]0.055844[/C][C]0.7878[/C][C]0.215884[/C][/ROW]
[ROW][C]16[/C][C]-0.13097[/C][C]-1.8476[/C][C]0.033075[/C][/ROW]
[ROW][C]17[/C][C]0.022715[/C][C]0.3204[/C][C]0.374487[/C][/ROW]
[ROW][C]18[/C][C]0.182378[/C][C]2.5728[/C][C]0.005409[/C][/ROW]
[ROW][C]19[/C][C]-0.160752[/C][C]-2.2677[/C][C]0.012211[/C][/ROW]
[ROW][C]20[/C][C]0.053726[/C][C]0.7579[/C][C]0.224704[/C][/ROW]
[ROW][C]21[/C][C]-0.049736[/C][C]-0.7016[/C][C]0.241868[/C][/ROW]
[ROW][C]22[/C][C]0.050751[/C][C]0.7159[/C][C]0.237437[/C][/ROW]
[ROW][C]23[/C][C]-0.059539[/C][C]-0.8399[/C][C]0.200985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309139&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	-0.353213	-4.9827	1e-06
2	-0.123308	-1.7395	0.041749
3	0.010776	0.152	0.439663
4	0.048094	0.6785	0.249136
5	-0.062662	-0.884	0.188892
6	-0.000553	-0.0078	0.49689
7	0.046804	0.6602	0.25493
8	-0.081729	-1.1529	0.12516
9	0.054615	0.7704	0.220975
10	0.025884	0.3651	0.357698
11	0.152639	2.1532	0.016252
12	-0.415182	-5.8569	0
13	0.06743	0.9512	0.171325
14	0.145971	2.0592	0.02039
15	0.055844	0.7878	0.215884
16	-0.13097	-1.8476	0.033075
17	0.022715	0.3204	0.374487
18	0.182378	2.5728	0.005409
19	-0.160752	-2.2677	0.012211
20	0.053726	0.7579	0.224704
21	-0.049736	-0.7016	0.241868
22	0.050751	0.7159	0.237437
23	-0.059539	-0.8399	0.200985

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.353213	-4.9827	1e-06
2	-0.283428	-3.9982	4.5e-05
3	-0.180428	-2.5453	0.005839
4	-0.070928	-1.0006	0.159128
5	-0.11007	-1.5527	0.061039
6	-0.085378	-1.2044	0.114932
7	-0.018609	-0.2625	0.396599
8	-0.109492	-1.5446	0.062019
9	-0.024033	-0.339	0.367474
10	0.007587	0.107	0.457439
11	0.227847	3.2142	0.000763
12	-0.305003	-4.3026	1.3e-05
13	-0.25747	-3.6321	0.000179
14	-0.116374	-1.6417	0.05112
15	0.042529	0.6	0.27461
16	-0.073174	-1.0323	0.151603
17	-0.106788	-1.5064	0.066772
18	0.160475	2.2638	0.012333
19	0.012086	0.1705	0.432398
20	0.002109	0.0297	0.488149
21	-0.067289	-0.9492	0.171827
22	0.069612	0.982	0.163646
23	0.110386	1.5572	0.060507

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.353213 & -4.9827 & 1e-06 \tabularnewline
2 & -0.283428 & -3.9982 & 4.5e-05 \tabularnewline
3 & -0.180428 & -2.5453 & 0.005839 \tabularnewline
4 & -0.070928 & -1.0006 & 0.159128 \tabularnewline
5 & -0.11007 & -1.5527 & 0.061039 \tabularnewline
6 & -0.085378 & -1.2044 & 0.114932 \tabularnewline
7 & -0.018609 & -0.2625 & 0.396599 \tabularnewline
8 & -0.109492 & -1.5446 & 0.062019 \tabularnewline
9 & -0.024033 & -0.339 & 0.367474 \tabularnewline
10 & 0.007587 & 0.107 & 0.457439 \tabularnewline
11 & 0.227847 & 3.2142 & 0.000763 \tabularnewline
12 & -0.305003 & -4.3026 & 1.3e-05 \tabularnewline
13 & -0.25747 & -3.6321 & 0.000179 \tabularnewline
14 & -0.116374 & -1.6417 & 0.05112 \tabularnewline
15 & 0.042529 & 0.6 & 0.27461 \tabularnewline
16 & -0.073174 & -1.0323 & 0.151603 \tabularnewline
17 & -0.106788 & -1.5064 & 0.066772 \tabularnewline
18 & 0.160475 & 2.2638 & 0.012333 \tabularnewline
19 & 0.012086 & 0.1705 & 0.432398 \tabularnewline
20 & 0.002109 & 0.0297 & 0.488149 \tabularnewline
21 & -0.067289 & -0.9492 & 0.171827 \tabularnewline
22 & 0.069612 & 0.982 & 0.163646 \tabularnewline
23 & 0.110386 & 1.5572 & 0.060507 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=309139&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]-0.353213[/C][C]-4.9827[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.283428[/C][C]-3.9982[/C][C]4.5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.180428[/C][C]-2.5453[/C][C]0.005839[/C][/ROW]
[ROW][C]4[/C][C]-0.070928[/C][C]-1.0006[/C][C]0.159128[/C][/ROW]
[ROW][C]5[/C][C]-0.11007[/C][C]-1.5527[/C][C]0.061039[/C][/ROW]
[ROW][C]6[/C][C]-0.085378[/C][C]-1.2044[/C][C]0.114932[/C][/ROW]
[ROW][C]7[/C][C]-0.018609[/C][C]-0.2625[/C][C]0.396599[/C][/ROW]
[ROW][C]8[/C][C]-0.109492[/C][C]-1.5446[/C][C]0.062019[/C][/ROW]
[ROW][C]9[/C][C]-0.024033[/C][C]-0.339[/C][C]0.367474[/C][/ROW]
[ROW][C]10[/C][C]0.007587[/C][C]0.107[/C][C]0.457439[/C][/ROW]
[ROW][C]11[/C][C]0.227847[/C][C]3.2142[/C][C]0.000763[/C][/ROW]
[ROW][C]12[/C][C]-0.305003[/C][C]-4.3026[/C][C]1.3e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.25747[/C][C]-3.6321[/C][C]0.000179[/C][/ROW]
[ROW][C]14[/C][C]-0.116374[/C][C]-1.6417[/C][C]0.05112[/C][/ROW]
[ROW][C]15[/C][C]0.042529[/C][C]0.6[/C][C]0.27461[/C][/ROW]
[ROW][C]16[/C][C]-0.073174[/C][C]-1.0323[/C][C]0.151603[/C][/ROW]
[ROW][C]17[/C][C]-0.106788[/C][C]-1.5064[/C][C]0.066772[/C][/ROW]
[ROW][C]18[/C][C]0.160475[/C][C]2.2638[/C][C]0.012333[/C][/ROW]
[ROW][C]19[/C][C]0.012086[/C][C]0.1705[/C][C]0.432398[/C][/ROW]
[ROW][C]20[/C][C]0.002109[/C][C]0.0297[/C][C]0.488149[/C][/ROW]
[ROW][C]21[/C][C]-0.067289[/C][C]-0.9492[/C][C]0.171827[/C][/ROW]
[ROW][C]22[/C][C]0.069612[/C][C]0.982[/C][C]0.163646[/C][/ROW]
[ROW][C]23[/C][C]0.110386[/C][C]1.5572[/C][C]0.060507[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=309139&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=309139&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	-0.353213	-4.9827	1e-06
2	-0.283428	-3.9982	4.5e-05
3	-0.180428	-2.5453	0.005839
4	-0.070928	-1.0006	0.159128
5	-0.11007	-1.5527	0.061039
6	-0.085378	-1.2044	0.114932
7	-0.018609	-0.2625	0.396599
8	-0.109492	-1.5446	0.062019
9	-0.024033	-0.339	0.367474
10	0.007587	0.107	0.457439
11	0.227847	3.2142	0.000763
12	-0.305003	-4.3026	1.3e-05
13	-0.25747	-3.6321	0.000179
14	-0.116374	-1.6417	0.05112
15	0.042529	0.6	0.27461
16	-0.073174	-1.0323	0.151603
17	-0.106788	-1.5064	0.066772
18	0.160475	2.2638	0.012333
19	0.012086	0.1705	0.432398
20	0.002109	0.0297	0.488149
21	-0.067289	-0.9492	0.171827
22	0.069612	0.982	0.163646
23	0.110386	1.5572	0.060507

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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