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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 22 Dec 2010 15:04:35 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293030198nzej5r4kiy0k708.htm/, Retrieved Mon, 06 May 2024 06:18:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114297, Retrieved Mon, 06 May 2024 06:18:11 +0000

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Estimated Impact

135

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D      [(Partial) Autocorrelation Function] [] [2010-12-22 15:04:35] [7b390cc0228d34e5578246b07143e3df] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114297&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114297&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114297&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.851429	7.0725	0
2	0.731417	6.0756	0
3	0.609884	5.0661	2e-06
4	0.428904	3.5627	0.000335
5	0.254631	2.1151	0.019016
6	0.130557	1.0845	0.140961
7	-0.004399	-0.0365	0.485478
8	-0.08213	-0.6822	0.24869
9	-0.12352	-1.026	0.15423
10	-0.151111	-1.2552	0.106816
11	-0.135243	-1.1234	0.132578
12	-0.085965	-0.7141	0.238793
13	-0.101698	-0.8448	0.20058
14	-0.095259	-0.7913	0.215746
15	-0.096127	-0.7985	0.213662
16	-0.134429	-1.1166	0.134009
17	-0.17441	-1.4488	0.075967
18	-0.225572	-1.8737	0.032601

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851429 & 7.0725 & 0 \tabularnewline
2 & 0.731417 & 6.0756 & 0 \tabularnewline
3 & 0.609884 & 5.0661 & 2e-06 \tabularnewline
4 & 0.428904 & 3.5627 & 0.000335 \tabularnewline
5 & 0.254631 & 2.1151 & 0.019016 \tabularnewline
6 & 0.130557 & 1.0845 & 0.140961 \tabularnewline
7 & -0.004399 & -0.0365 & 0.485478 \tabularnewline
8 & -0.08213 & -0.6822 & 0.24869 \tabularnewline
9 & -0.12352 & -1.026 & 0.15423 \tabularnewline
10 & -0.151111 & -1.2552 & 0.106816 \tabularnewline
11 & -0.135243 & -1.1234 & 0.132578 \tabularnewline
12 & -0.085965 & -0.7141 & 0.238793 \tabularnewline
13 & -0.101698 & -0.8448 & 0.20058 \tabularnewline
14 & -0.095259 & -0.7913 & 0.215746 \tabularnewline
15 & -0.096127 & -0.7985 & 0.213662 \tabularnewline
16 & -0.134429 & -1.1166 & 0.134009 \tabularnewline
17 & -0.17441 & -1.4488 & 0.075967 \tabularnewline
18 & -0.225572 & -1.8737 & 0.032601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114297&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]0.851429[/C][C]7.0725[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.731417[/C][C]6.0756[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.609884[/C][C]5.0661[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.428904[/C][C]3.5627[/C][C]0.000335[/C][/ROW]
[ROW][C]5[/C][C]0.254631[/C][C]2.1151[/C][C]0.019016[/C][/ROW]
[ROW][C]6[/C][C]0.130557[/C][C]1.0845[/C][C]0.140961[/C][/ROW]
[ROW][C]7[/C][C]-0.004399[/C][C]-0.0365[/C][C]0.485478[/C][/ROW]
[ROW][C]8[/C][C]-0.08213[/C][C]-0.6822[/C][C]0.24869[/C][/ROW]
[ROW][C]9[/C][C]-0.12352[/C][C]-1.026[/C][C]0.15423[/C][/ROW]
[ROW][C]10[/C][C]-0.151111[/C][C]-1.2552[/C][C]0.106816[/C][/ROW]
[ROW][C]11[/C][C]-0.135243[/C][C]-1.1234[/C][C]0.132578[/C][/ROW]
[ROW][C]12[/C][C]-0.085965[/C][C]-0.7141[/C][C]0.238793[/C][/ROW]
[ROW][C]13[/C][C]-0.101698[/C][C]-0.8448[/C][C]0.20058[/C][/ROW]
[ROW][C]14[/C][C]-0.095259[/C][C]-0.7913[/C][C]0.215746[/C][/ROW]
[ROW][C]15[/C][C]-0.096127[/C][C]-0.7985[/C][C]0.213662[/C][/ROW]
[ROW][C]16[/C][C]-0.134429[/C][C]-1.1166[/C][C]0.134009[/C][/ROW]
[ROW][C]17[/C][C]-0.17441[/C][C]-1.4488[/C][C]0.075967[/C][/ROW]
[ROW][C]18[/C][C]-0.225572[/C][C]-1.8737[/C][C]0.032601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114297&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114297&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	0.851429	7.0725	0
2	0.731417	6.0756	0
3	0.609884	5.0661	2e-06
4	0.428904	3.5627	0.000335
5	0.254631	2.1151	0.019016
6	0.130557	1.0845	0.140961
7	-0.004399	-0.0365	0.485478
8	-0.08213	-0.6822	0.24869
9	-0.12352	-1.026	0.15423
10	-0.151111	-1.2552	0.106816
11	-0.135243	-1.1234	0.132578
12	-0.085965	-0.7141	0.238793
13	-0.101698	-0.8448	0.20058
14	-0.095259	-0.7913	0.215746
15	-0.096127	-0.7985	0.213662
16	-0.134429	-1.1166	0.134009
17	-0.17441	-1.4488	0.075967
18	-0.225572	-1.8737	0.032601

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.851429	7.0725	0
2	0.023577	0.1958	0.422654
3	-0.06641	-0.5516	0.291488
4	-0.292888	-2.4329	0.008787
5	-0.147382	-1.2242	0.112512
6	0.057535	0.4779	0.31711
7	-0.073031	-0.6066	0.27304
8	0.095662	0.7946	0.214777
9	0.02125	0.1765	0.430202
10	-0.004633	-0.0385	0.484708
11	0.060727	0.5044	0.30778
12	0.066102	0.5491	0.292361
13	-0.234913	-1.9513	0.027539
14	-0.059428	-0.4936	0.311561
15	-0.071379	-0.5929	0.277587
16	-0.057923	-0.4811	0.315969
17	-0.035457	-0.2945	0.384619
18	-0.120923	-1.0045	0.159332

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851429 & 7.0725 & 0 \tabularnewline
2 & 0.023577 & 0.1958 & 0.422654 \tabularnewline
3 & -0.06641 & -0.5516 & 0.291488 \tabularnewline
4 & -0.292888 & -2.4329 & 0.008787 \tabularnewline
5 & -0.147382 & -1.2242 & 0.112512 \tabularnewline
6 & 0.057535 & 0.4779 & 0.31711 \tabularnewline
7 & -0.073031 & -0.6066 & 0.27304 \tabularnewline
8 & 0.095662 & 0.7946 & 0.214777 \tabularnewline
9 & 0.02125 & 0.1765 & 0.430202 \tabularnewline
10 & -0.004633 & -0.0385 & 0.484708 \tabularnewline
11 & 0.060727 & 0.5044 & 0.30778 \tabularnewline
12 & 0.066102 & 0.5491 & 0.292361 \tabularnewline
13 & -0.234913 & -1.9513 & 0.027539 \tabularnewline
14 & -0.059428 & -0.4936 & 0.311561 \tabularnewline
15 & -0.071379 & -0.5929 & 0.277587 \tabularnewline
16 & -0.057923 & -0.4811 & 0.315969 \tabularnewline
17 & -0.035457 & -0.2945 & 0.384619 \tabularnewline
18 & -0.120923 & -1.0045 & 0.159332 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114297&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]0.851429[/C][C]7.0725[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.023577[/C][C]0.1958[/C][C]0.422654[/C][/ROW]
[ROW][C]3[/C][C]-0.06641[/C][C]-0.5516[/C][C]0.291488[/C][/ROW]
[ROW][C]4[/C][C]-0.292888[/C][C]-2.4329[/C][C]0.008787[/C][/ROW]
[ROW][C]5[/C][C]-0.147382[/C][C]-1.2242[/C][C]0.112512[/C][/ROW]
[ROW][C]6[/C][C]0.057535[/C][C]0.4779[/C][C]0.31711[/C][/ROW]
[ROW][C]7[/C][C]-0.073031[/C][C]-0.6066[/C][C]0.27304[/C][/ROW]
[ROW][C]8[/C][C]0.095662[/C][C]0.7946[/C][C]0.214777[/C][/ROW]
[ROW][C]9[/C][C]0.02125[/C][C]0.1765[/C][C]0.430202[/C][/ROW]
[ROW][C]10[/C][C]-0.004633[/C][C]-0.0385[/C][C]0.484708[/C][/ROW]
[ROW][C]11[/C][C]0.060727[/C][C]0.5044[/C][C]0.30778[/C][/ROW]
[ROW][C]12[/C][C]0.066102[/C][C]0.5491[/C][C]0.292361[/C][/ROW]
[ROW][C]13[/C][C]-0.234913[/C][C]-1.9513[/C][C]0.027539[/C][/ROW]
[ROW][C]14[/C][C]-0.059428[/C][C]-0.4936[/C][C]0.311561[/C][/ROW]
[ROW][C]15[/C][C]-0.071379[/C][C]-0.5929[/C][C]0.277587[/C][/ROW]
[ROW][C]16[/C][C]-0.057923[/C][C]-0.4811[/C][C]0.315969[/C][/ROW]
[ROW][C]17[/C][C]-0.035457[/C][C]-0.2945[/C][C]0.384619[/C][/ROW]
[ROW][C]18[/C][C]-0.120923[/C][C]-1.0045[/C][C]0.159332[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114297&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114297&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	0.851429	7.0725	0
2	0.023577	0.1958	0.422654
3	-0.06641	-0.5516	0.291488
4	-0.292888	-2.4329	0.008787
5	-0.147382	-1.2242	0.112512
6	0.057535	0.4779	0.31711
7	-0.073031	-0.6066	0.27304
8	0.095662	0.7946	0.214777
9	0.02125	0.1765	0.430202
10	-0.004633	-0.0385	0.484708
11	0.060727	0.5044	0.30778
12	0.066102	0.5491	0.292361
13	-0.234913	-1.9513	0.027539
14	-0.059428	-0.4936	0.311561
15	-0.071379	-0.5929	0.277587
16	-0.057923	-0.4811	0.315969
17	-0.035457	-0.2945	0.384619
18	-0.120923	-1.0045	0.159332

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code