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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2011 14:16:56 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/18/t132423584696xu9ncb9lwh02h.htm/, Retrieved Sun, 05 May 2024 18:23:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157138, Retrieved Sun, 05 May 2024 18:23:43 +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)

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R  D    [(Partial) Autocorrelation Function] [WS IX-aantal over...] [2011-12-06 19:19:57] [74be16979710d4c4e7c6647856088456]
-    D        [(Partial) Autocorrelation Function] [Paper acf] [2011-12-18 19:16:56] [3e388c05c22237d436c48535c44f60bb] [Current]
-   P           [(Partial) Autocorrelation Function] [Paper acf-aanpassing] [2011-12-18 19:18:35] [7c680a04865e75aa8ab422cdbfd97ac3] 

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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	'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157138&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157138&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157138&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.633299	6.205	0
2	0.163048	1.5975	0.056716
3	-0.15032	-1.4728	0.072034
4	-0.377764	-3.7013	0.000179
5	-0.491052	-4.8113	3e-06
6	-0.509885	-4.9958	1e-06
7	-0.452852	-4.437	1.2e-05
8	-0.325671	-3.1909	0.000958
9	-0.122122	-1.1965	0.117215
10	0.174398	1.7087	0.045365
11	0.580408	5.6868	0
12	0.817372	8.0086	0
13	0.543262	5.3229	0
14	0.14727	1.4429	0.076145
15	-0.124412	-1.219	0.112919
16	-0.332354	-3.2564	0.00078
17	-0.427311	-4.1868	3.1e-05
18	-0.437049	-4.2822	2.2e-05
19	-0.390375	-3.8249	0.000116

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.633299 & 6.205 & 0 \tabularnewline
2 & 0.163048 & 1.5975 & 0.056716 \tabularnewline
3 & -0.15032 & -1.4728 & 0.072034 \tabularnewline
4 & -0.377764 & -3.7013 & 0.000179 \tabularnewline
5 & -0.491052 & -4.8113 & 3e-06 \tabularnewline
6 & -0.509885 & -4.9958 & 1e-06 \tabularnewline
7 & -0.452852 & -4.437 & 1.2e-05 \tabularnewline
8 & -0.325671 & -3.1909 & 0.000958 \tabularnewline
9 & -0.122122 & -1.1965 & 0.117215 \tabularnewline
10 & 0.174398 & 1.7087 & 0.045365 \tabularnewline
11 & 0.580408 & 5.6868 & 0 \tabularnewline
12 & 0.817372 & 8.0086 & 0 \tabularnewline
13 & 0.543262 & 5.3229 & 0 \tabularnewline
14 & 0.14727 & 1.4429 & 0.076145 \tabularnewline
15 & -0.124412 & -1.219 & 0.112919 \tabularnewline
16 & -0.332354 & -3.2564 & 0.00078 \tabularnewline
17 & -0.427311 & -4.1868 & 3.1e-05 \tabularnewline
18 & -0.437049 & -4.2822 & 2.2e-05 \tabularnewline
19 & -0.390375 & -3.8249 & 0.000116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157138&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]0.633299[/C][C]6.205[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.163048[/C][C]1.5975[/C][C]0.056716[/C][/ROW]
[ROW][C]3[/C][C]-0.15032[/C][C]-1.4728[/C][C]0.072034[/C][/ROW]
[ROW][C]4[/C][C]-0.377764[/C][C]-3.7013[/C][C]0.000179[/C][/ROW]
[ROW][C]5[/C][C]-0.491052[/C][C]-4.8113[/C][C]3e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.509885[/C][C]-4.9958[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.452852[/C][C]-4.437[/C][C]1.2e-05[/C][/ROW]
[ROW][C]8[/C][C]-0.325671[/C][C]-3.1909[/C][C]0.000958[/C][/ROW]
[ROW][C]9[/C][C]-0.122122[/C][C]-1.1965[/C][C]0.117215[/C][/ROW]
[ROW][C]10[/C][C]0.174398[/C][C]1.7087[/C][C]0.045365[/C][/ROW]
[ROW][C]11[/C][C]0.580408[/C][C]5.6868[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.817372[/C][C]8.0086[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.543262[/C][C]5.3229[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.14727[/C][C]1.4429[/C][C]0.076145[/C][/ROW]
[ROW][C]15[/C][C]-0.124412[/C][C]-1.219[/C][C]0.112919[/C][/ROW]
[ROW][C]16[/C][C]-0.332354[/C][C]-3.2564[/C][C]0.00078[/C][/ROW]
[ROW][C]17[/C][C]-0.427311[/C][C]-4.1868[/C][C]3.1e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.437049[/C][C]-4.2822[/C][C]2.2e-05[/C][/ROW]
[ROW][C]19[/C][C]-0.390375[/C][C]-3.8249[/C][C]0.000116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157138&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157138&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	0.633299	6.205	0
2	0.163048	1.5975	0.056716
3	-0.15032	-1.4728	0.072034
4	-0.377764	-3.7013	0.000179
5	-0.491052	-4.8113	3e-06
6	-0.509885	-4.9958	1e-06
7	-0.452852	-4.437	1.2e-05
8	-0.325671	-3.1909	0.000958
9	-0.122122	-1.1965	0.117215
10	0.174398	1.7087	0.045365
11	0.580408	5.6868	0
12	0.817372	8.0086	0
13	0.543262	5.3229	0
14	0.14727	1.4429	0.076145
15	-0.124412	-1.219	0.112919
16	-0.332354	-3.2564	0.00078
17	-0.427311	-4.1868	3.1e-05
18	-0.437049	-4.2822	2.2e-05
19	-0.390375	-3.8249	0.000116

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.633299	6.205	0
2	-0.397405	-3.8938	9.1e-05
3	-0.085135	-0.8342	0.203133
4	-0.28639	-2.806	0.003036
5	-0.186028	-1.8227	0.035732
6	-0.278862	-2.7323	0.003744
7	-0.285722	-2.7995	0.003094
8	-0.341583	-3.3468	0.000584
9	-0.343239	-3.363	0.000554
10	-0.233618	-2.289	0.012136
11	0.246674	2.4169	0.008771
12	0.341577	3.3468	0.000584
13	-0.276762	-2.7117	0.003966
14	-0.048185	-0.4721	0.318957
15	0.039846	0.3904	0.34855
16	0.014234	0.1395	0.444687
17	0.075912	0.7438	0.229413
18	0.010909	0.1069	0.457549
19	-0.003023	-0.0296	0.488217

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.633299 & 6.205 & 0 \tabularnewline
2 & -0.397405 & -3.8938 & 9.1e-05 \tabularnewline
3 & -0.085135 & -0.8342 & 0.203133 \tabularnewline
4 & -0.28639 & -2.806 & 0.003036 \tabularnewline
5 & -0.186028 & -1.8227 & 0.035732 \tabularnewline
6 & -0.278862 & -2.7323 & 0.003744 \tabularnewline
7 & -0.285722 & -2.7995 & 0.003094 \tabularnewline
8 & -0.341583 & -3.3468 & 0.000584 \tabularnewline
9 & -0.343239 & -3.363 & 0.000554 \tabularnewline
10 & -0.233618 & -2.289 & 0.012136 \tabularnewline
11 & 0.246674 & 2.4169 & 0.008771 \tabularnewline
12 & 0.341577 & 3.3468 & 0.000584 \tabularnewline
13 & -0.276762 & -2.7117 & 0.003966 \tabularnewline
14 & -0.048185 & -0.4721 & 0.318957 \tabularnewline
15 & 0.039846 & 0.3904 & 0.34855 \tabularnewline
16 & 0.014234 & 0.1395 & 0.444687 \tabularnewline
17 & 0.075912 & 0.7438 & 0.229413 \tabularnewline
18 & 0.010909 & 0.1069 & 0.457549 \tabularnewline
19 & -0.003023 & -0.0296 & 0.488217 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157138&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]0.633299[/C][C]6.205[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.397405[/C][C]-3.8938[/C][C]9.1e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.085135[/C][C]-0.8342[/C][C]0.203133[/C][/ROW]
[ROW][C]4[/C][C]-0.28639[/C][C]-2.806[/C][C]0.003036[/C][/ROW]
[ROW][C]5[/C][C]-0.186028[/C][C]-1.8227[/C][C]0.035732[/C][/ROW]
[ROW][C]6[/C][C]-0.278862[/C][C]-2.7323[/C][C]0.003744[/C][/ROW]
[ROW][C]7[/C][C]-0.285722[/C][C]-2.7995[/C][C]0.003094[/C][/ROW]
[ROW][C]8[/C][C]-0.341583[/C][C]-3.3468[/C][C]0.000584[/C][/ROW]
[ROW][C]9[/C][C]-0.343239[/C][C]-3.363[/C][C]0.000554[/C][/ROW]
[ROW][C]10[/C][C]-0.233618[/C][C]-2.289[/C][C]0.012136[/C][/ROW]
[ROW][C]11[/C][C]0.246674[/C][C]2.4169[/C][C]0.008771[/C][/ROW]
[ROW][C]12[/C][C]0.341577[/C][C]3.3468[/C][C]0.000584[/C][/ROW]
[ROW][C]13[/C][C]-0.276762[/C][C]-2.7117[/C][C]0.003966[/C][/ROW]
[ROW][C]14[/C][C]-0.048185[/C][C]-0.4721[/C][C]0.318957[/C][/ROW]
[ROW][C]15[/C][C]0.039846[/C][C]0.3904[/C][C]0.34855[/C][/ROW]
[ROW][C]16[/C][C]0.014234[/C][C]0.1395[/C][C]0.444687[/C][/ROW]
[ROW][C]17[/C][C]0.075912[/C][C]0.7438[/C][C]0.229413[/C][/ROW]
[ROW][C]18[/C][C]0.010909[/C][C]0.1069[/C][C]0.457549[/C][/ROW]
[ROW][C]19[/C][C]-0.003023[/C][C]-0.0296[/C][C]0.488217[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157138&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157138&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	0.633299	6.205	0
2	-0.397405	-3.8938	9.1e-05
3	-0.085135	-0.8342	0.203133
4	-0.28639	-2.806	0.003036
5	-0.186028	-1.8227	0.035732
6	-0.278862	-2.7323	0.003744
7	-0.285722	-2.7995	0.003094
8	-0.341583	-3.3468	0.000584
9	-0.343239	-3.363	0.000554
10	-0.233618	-2.289	0.012136
11	0.246674	2.4169	0.008771
12	0.341577	3.3468	0.000584
13	-0.276762	-2.7117	0.003966
14	-0.048185	-0.4721	0.318957
15	0.039846	0.3904	0.34855
16	0.014234	0.1395	0.444687
17	0.075912	0.7438	0.229413
18	0.010909	0.1069	0.457549
19	-0.003023	-0.0296	0.488217

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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Input Parameters & R Code