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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 14:21:56 +0000

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/2010/Dec/03/t1291386035hzhgaeb38ku1svd.htm/, Retrieved Tue, 07 May 2024 06:01:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104820, Retrieved Tue, 07 May 2024 06:01:39 +0000

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127

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]
-   PD      [(Partial) Autocorrelation Function] [Stationarity in t...] [2010-12-03 14:21:56] [18ef3d986e8801a4b28404e69e5bf56b] [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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104820&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104820&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104820&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.220721	-2.0823	0.020094
2	0.131963	1.2449	0.108212
3	0.086186	0.8131	0.209173
4	0.098863	0.9327	0.176757
5	0.03574	0.3372	0.368389
6	-0.104947	-0.9901	0.162413
7	0.113782	1.0734	0.142993
8	0.03116	0.294	0.384734
9	-0.190511	-1.7973	0.037842
10	0.041749	0.3939	0.347314
11	0.060971	0.5752	0.283303
12	-0.399716	-3.7709	0.000146
13	0.199285	1.88	0.031686
14	-0.224483	-2.1178	0.018492
15	0.056078	0.529	0.299048
16	-0.216147	-2.0391	0.022202
17	-0.053115	-0.5011	0.308774
18	0.080445	0.7589	0.224953
19	-0.099113	-0.935	0.176151
20	0.030483	0.2876	0.38717

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.220721 & -2.0823 & 0.020094 \tabularnewline
2 & 0.131963 & 1.2449 & 0.108212 \tabularnewline
3 & 0.086186 & 0.8131 & 0.209173 \tabularnewline
4 & 0.098863 & 0.9327 & 0.176757 \tabularnewline
5 & 0.03574 & 0.3372 & 0.368389 \tabularnewline
6 & -0.104947 & -0.9901 & 0.162413 \tabularnewline
7 & 0.113782 & 1.0734 & 0.142993 \tabularnewline
8 & 0.03116 & 0.294 & 0.384734 \tabularnewline
9 & -0.190511 & -1.7973 & 0.037842 \tabularnewline
10 & 0.041749 & 0.3939 & 0.347314 \tabularnewline
11 & 0.060971 & 0.5752 & 0.283303 \tabularnewline
12 & -0.399716 & -3.7709 & 0.000146 \tabularnewline
13 & 0.199285 & 1.88 & 0.031686 \tabularnewline
14 & -0.224483 & -2.1178 & 0.018492 \tabularnewline
15 & 0.056078 & 0.529 & 0.299048 \tabularnewline
16 & -0.216147 & -2.0391 & 0.022202 \tabularnewline
17 & -0.053115 & -0.5011 & 0.308774 \tabularnewline
18 & 0.080445 & 0.7589 & 0.224953 \tabularnewline
19 & -0.099113 & -0.935 & 0.176151 \tabularnewline
20 & 0.030483 & 0.2876 & 0.38717 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104820&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]-0.220721[/C][C]-2.0823[/C][C]0.020094[/C][/ROW]
[ROW][C]2[/C][C]0.131963[/C][C]1.2449[/C][C]0.108212[/C][/ROW]
[ROW][C]3[/C][C]0.086186[/C][C]0.8131[/C][C]0.209173[/C][/ROW]
[ROW][C]4[/C][C]0.098863[/C][C]0.9327[/C][C]0.176757[/C][/ROW]
[ROW][C]5[/C][C]0.03574[/C][C]0.3372[/C][C]0.368389[/C][/ROW]
[ROW][C]6[/C][C]-0.104947[/C][C]-0.9901[/C][C]0.162413[/C][/ROW]
[ROW][C]7[/C][C]0.113782[/C][C]1.0734[/C][C]0.142993[/C][/ROW]
[ROW][C]8[/C][C]0.03116[/C][C]0.294[/C][C]0.384734[/C][/ROW]
[ROW][C]9[/C][C]-0.190511[/C][C]-1.7973[/C][C]0.037842[/C][/ROW]
[ROW][C]10[/C][C]0.041749[/C][C]0.3939[/C][C]0.347314[/C][/ROW]
[ROW][C]11[/C][C]0.060971[/C][C]0.5752[/C][C]0.283303[/C][/ROW]
[ROW][C]12[/C][C]-0.399716[/C][C]-3.7709[/C][C]0.000146[/C][/ROW]
[ROW][C]13[/C][C]0.199285[/C][C]1.88[/C][C]0.031686[/C][/ROW]
[ROW][C]14[/C][C]-0.224483[/C][C]-2.1178[/C][C]0.018492[/C][/ROW]
[ROW][C]15[/C][C]0.056078[/C][C]0.529[/C][C]0.299048[/C][/ROW]
[ROW][C]16[/C][C]-0.216147[/C][C]-2.0391[/C][C]0.022202[/C][/ROW]
[ROW][C]17[/C][C]-0.053115[/C][C]-0.5011[/C][C]0.308774[/C][/ROW]
[ROW][C]18[/C][C]0.080445[/C][C]0.7589[/C][C]0.224953[/C][/ROW]
[ROW][C]19[/C][C]-0.099113[/C][C]-0.935[/C][C]0.176151[/C][/ROW]
[ROW][C]20[/C][C]0.030483[/C][C]0.2876[/C][C]0.38717[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104820&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104820&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	-0.220721	-2.0823	0.020094
2	0.131963	1.2449	0.108212
3	0.086186	0.8131	0.209173
4	0.098863	0.9327	0.176757
5	0.03574	0.3372	0.368389
6	-0.104947	-0.9901	0.162413
7	0.113782	1.0734	0.142993
8	0.03116	0.294	0.384734
9	-0.190511	-1.7973	0.037842
10	0.041749	0.3939	0.347314
11	0.060971	0.5752	0.283303
12	-0.399716	-3.7709	0.000146
13	0.199285	1.88	0.031686
14	-0.224483	-2.1178	0.018492
15	0.056078	0.529	0.299048
16	-0.216147	-2.0391	0.022202
17	-0.053115	-0.5011	0.308774
18	0.080445	0.7589	0.224953
19	-0.099113	-0.935	0.176151
20	0.030483	0.2876	0.38717

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.220721	-2.0823	0.020094
2	0.087508	0.8255	0.205634
3	0.139914	1.3199	0.095119
4	0.143586	1.3546	0.089489
5	0.065631	0.6192	0.268696
6	-0.139133	-1.3126	0.096349
7	0.019382	0.1828	0.427667
8	0.07383	0.6965	0.243963
9	-0.183148	-1.7278	0.043745
10	-0.053339	-0.5032	0.308035
11	0.100487	0.948	0.17285
12	-0.410801	-3.8755	0.000102
13	0.120439	1.1362	0.129458
14	-0.085108	-0.8029	0.212083
15	-0.051907	-0.4897	0.312781
16	-0.078416	-0.7398	0.23069
17	-0.088093	-0.8311	0.204081
18	-0.024755	-0.2335	0.407939
19	0.121095	1.1424	0.128175
20	0.059279	0.5592	0.288702

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.220721 & -2.0823 & 0.020094 \tabularnewline
2 & 0.087508 & 0.8255 & 0.205634 \tabularnewline
3 & 0.139914 & 1.3199 & 0.095119 \tabularnewline
4 & 0.143586 & 1.3546 & 0.089489 \tabularnewline
5 & 0.065631 & 0.6192 & 0.268696 \tabularnewline
6 & -0.139133 & -1.3126 & 0.096349 \tabularnewline
7 & 0.019382 & 0.1828 & 0.427667 \tabularnewline
8 & 0.07383 & 0.6965 & 0.243963 \tabularnewline
9 & -0.183148 & -1.7278 & 0.043745 \tabularnewline
10 & -0.053339 & -0.5032 & 0.308035 \tabularnewline
11 & 0.100487 & 0.948 & 0.17285 \tabularnewline
12 & -0.410801 & -3.8755 & 0.000102 \tabularnewline
13 & 0.120439 & 1.1362 & 0.129458 \tabularnewline
14 & -0.085108 & -0.8029 & 0.212083 \tabularnewline
15 & -0.051907 & -0.4897 & 0.312781 \tabularnewline
16 & -0.078416 & -0.7398 & 0.23069 \tabularnewline
17 & -0.088093 & -0.8311 & 0.204081 \tabularnewline
18 & -0.024755 & -0.2335 & 0.407939 \tabularnewline
19 & 0.121095 & 1.1424 & 0.128175 \tabularnewline
20 & 0.059279 & 0.5592 & 0.288702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104820&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]-0.220721[/C][C]-2.0823[/C][C]0.020094[/C][/ROW]
[ROW][C]2[/C][C]0.087508[/C][C]0.8255[/C][C]0.205634[/C][/ROW]
[ROW][C]3[/C][C]0.139914[/C][C]1.3199[/C][C]0.095119[/C][/ROW]
[ROW][C]4[/C][C]0.143586[/C][C]1.3546[/C][C]0.089489[/C][/ROW]
[ROW][C]5[/C][C]0.065631[/C][C]0.6192[/C][C]0.268696[/C][/ROW]
[ROW][C]6[/C][C]-0.139133[/C][C]-1.3126[/C][C]0.096349[/C][/ROW]
[ROW][C]7[/C][C]0.019382[/C][C]0.1828[/C][C]0.427667[/C][/ROW]
[ROW][C]8[/C][C]0.07383[/C][C]0.6965[/C][C]0.243963[/C][/ROW]
[ROW][C]9[/C][C]-0.183148[/C][C]-1.7278[/C][C]0.043745[/C][/ROW]
[ROW][C]10[/C][C]-0.053339[/C][C]-0.5032[/C][C]0.308035[/C][/ROW]
[ROW][C]11[/C][C]0.100487[/C][C]0.948[/C][C]0.17285[/C][/ROW]
[ROW][C]12[/C][C]-0.410801[/C][C]-3.8755[/C][C]0.000102[/C][/ROW]
[ROW][C]13[/C][C]0.120439[/C][C]1.1362[/C][C]0.129458[/C][/ROW]
[ROW][C]14[/C][C]-0.085108[/C][C]-0.8029[/C][C]0.212083[/C][/ROW]
[ROW][C]15[/C][C]-0.051907[/C][C]-0.4897[/C][C]0.312781[/C][/ROW]
[ROW][C]16[/C][C]-0.078416[/C][C]-0.7398[/C][C]0.23069[/C][/ROW]
[ROW][C]17[/C][C]-0.088093[/C][C]-0.8311[/C][C]0.204081[/C][/ROW]
[ROW][C]18[/C][C]-0.024755[/C][C]-0.2335[/C][C]0.407939[/C][/ROW]
[ROW][C]19[/C][C]0.121095[/C][C]1.1424[/C][C]0.128175[/C][/ROW]
[ROW][C]20[/C][C]0.059279[/C][C]0.5592[/C][C]0.288702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104820&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104820&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	-0.220721	-2.0823	0.020094
2	0.087508	0.8255	0.205634
3	0.139914	1.3199	0.095119
4	0.143586	1.3546	0.089489
5	0.065631	0.6192	0.268696
6	-0.139133	-1.3126	0.096349
7	0.019382	0.1828	0.427667
8	0.07383	0.6965	0.243963
9	-0.183148	-1.7278	0.043745
10	-0.053339	-0.5032	0.308035
11	0.100487	0.948	0.17285
12	-0.410801	-3.8755	0.000102
13	0.120439	1.1362	0.129458
14	-0.085108	-0.8029	0.212083
15	-0.051907	-0.4897	0.312781
16	-0.078416	-0.7398	0.23069
17	-0.088093	-0.8311	0.204081
18	-0.024755	-0.2335	0.407939
19	0.121095	1.1424	0.128175
20	0.059279	0.5592	0.288702

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code