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Author's title

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

Sun, 19 Dec 2010 14:09:42 +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/19/t1292767651icrhfdoomddrzdv.htm/, Retrieved Sun, 05 May 2024 05:23:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112400, Retrieved Sun, 05 May 2024 05:23:20 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

126

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

-     [(Partial) Autocorrelation Function] [paperuit_ACF2] [2010-12-19 12:48:24] [7e261c986c934df955dd3ac53e9d45c6]
-   P     [(Partial) Autocorrelation Function] [paperuit_ACF2] [2010-12-19 14:09:42] [13dfa60174f50d862e8699db2153bfc5] [Current]
-   P       [(Partial) Autocorrelation Function] [ACFbis_uitvoerbelgie] [2010-12-22 14:38:38] [8441f95c4a5787a301bc621ebc7904ca] 
-             [(Partial) Autocorrelation Function] [Kristof Nagels] [2010-12-24 15:04:14] [8441f95c4a5787a301bc621ebc7904ca] 
-   P       [(Partial) Autocorrelation Function] [paperACF_uit2] [2010-12-24 14:26:30] [74be16979710d4c4e7c6647856088456] 
-             [(Partial) Autocorrelation Function] [Kristof Nagels] [2010-12-24 15:05:06] [8441f95c4a5787a301bc621ebc7904ca] 

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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=112400&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=112400&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112400&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	-0.438076	-4.5526	7e-06
2	0.030242	0.3143	0.376956
3	0.404597	4.2047	2.7e-05
4	-0.274521	-2.8529	0.002597
5	0.124592	1.2948	0.099076
6	0.177055	1.84	0.034257
7	-0.320724	-3.3331	0.000589
8	0.170874	1.7758	0.039293
9	-0.011469	-0.1192	0.452672
10	-0.201362	-2.0926	0.019363
11	0.100801	1.0476	0.148591
12	-0.082721	-0.8597	0.19594
13	-0.172	-1.7875	0.038333
14	0.091078	0.9465	0.173001
15	0.014308	0.1487	0.441035
16	-0.192638	-2.002	0.023898
17	0.118789	1.2345	0.10985
18	-0.00345	-0.0359	0.485734
19	-0.124613	-1.295	0.099038
20	0.148991	1.5484	0.06223

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.438076 & -4.5526 & 7e-06 \tabularnewline
2 & 0.030242 & 0.3143 & 0.376956 \tabularnewline
3 & 0.404597 & 4.2047 & 2.7e-05 \tabularnewline
4 & -0.274521 & -2.8529 & 0.002597 \tabularnewline
5 & 0.124592 & 1.2948 & 0.099076 \tabularnewline
6 & 0.177055 & 1.84 & 0.034257 \tabularnewline
7 & -0.320724 & -3.3331 & 0.000589 \tabularnewline
8 & 0.170874 & 1.7758 & 0.039293 \tabularnewline
9 & -0.011469 & -0.1192 & 0.452672 \tabularnewline
10 & -0.201362 & -2.0926 & 0.019363 \tabularnewline
11 & 0.100801 & 1.0476 & 0.148591 \tabularnewline
12 & -0.082721 & -0.8597 & 0.19594 \tabularnewline
13 & -0.172 & -1.7875 & 0.038333 \tabularnewline
14 & 0.091078 & 0.9465 & 0.173001 \tabularnewline
15 & 0.014308 & 0.1487 & 0.441035 \tabularnewline
16 & -0.192638 & -2.002 & 0.023898 \tabularnewline
17 & 0.118789 & 1.2345 & 0.10985 \tabularnewline
18 & -0.00345 & -0.0359 & 0.485734 \tabularnewline
19 & -0.124613 & -1.295 & 0.099038 \tabularnewline
20 & 0.148991 & 1.5484 & 0.06223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112400&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]-0.438076[/C][C]-4.5526[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.030242[/C][C]0.3143[/C][C]0.376956[/C][/ROW]
[ROW][C]3[/C][C]0.404597[/C][C]4.2047[/C][C]2.7e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.274521[/C][C]-2.8529[/C][C]0.002597[/C][/ROW]
[ROW][C]5[/C][C]0.124592[/C][C]1.2948[/C][C]0.099076[/C][/ROW]
[ROW][C]6[/C][C]0.177055[/C][C]1.84[/C][C]0.034257[/C][/ROW]
[ROW][C]7[/C][C]-0.320724[/C][C]-3.3331[/C][C]0.000589[/C][/ROW]
[ROW][C]8[/C][C]0.170874[/C][C]1.7758[/C][C]0.039293[/C][/ROW]
[ROW][C]9[/C][C]-0.011469[/C][C]-0.1192[/C][C]0.452672[/C][/ROW]
[ROW][C]10[/C][C]-0.201362[/C][C]-2.0926[/C][C]0.019363[/C][/ROW]
[ROW][C]11[/C][C]0.100801[/C][C]1.0476[/C][C]0.148591[/C][/ROW]
[ROW][C]12[/C][C]-0.082721[/C][C]-0.8597[/C][C]0.19594[/C][/ROW]
[ROW][C]13[/C][C]-0.172[/C][C]-1.7875[/C][C]0.038333[/C][/ROW]
[ROW][C]14[/C][C]0.091078[/C][C]0.9465[/C][C]0.173001[/C][/ROW]
[ROW][C]15[/C][C]0.014308[/C][C]0.1487[/C][C]0.441035[/C][/ROW]
[ROW][C]16[/C][C]-0.192638[/C][C]-2.002[/C][C]0.023898[/C][/ROW]
[ROW][C]17[/C][C]0.118789[/C][C]1.2345[/C][C]0.10985[/C][/ROW]
[ROW][C]18[/C][C]-0.00345[/C][C]-0.0359[/C][C]0.485734[/C][/ROW]
[ROW][C]19[/C][C]-0.124613[/C][C]-1.295[/C][C]0.099038[/C][/ROW]
[ROW][C]20[/C][C]0.148991[/C][C]1.5484[/C][C]0.06223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112400&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112400&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	-0.438076	-4.5526	7e-06
2	0.030242	0.3143	0.376956
3	0.404597	4.2047	2.7e-05
4	-0.274521	-2.8529	0.002597
5	0.124592	1.2948	0.099076
6	0.177055	1.84	0.034257
7	-0.320724	-3.3331	0.000589
8	0.170874	1.7758	0.039293
9	-0.011469	-0.1192	0.452672
10	-0.201362	-2.0926	0.019363
11	0.100801	1.0476	0.148591
12	-0.082721	-0.8597	0.19594
13	-0.172	-1.7875	0.038333
14	0.091078	0.9465	0.173001
15	0.014308	0.1487	0.441035
16	-0.192638	-2.002	0.023898
17	0.118789	1.2345	0.10985
18	-0.00345	-0.0359	0.485734
19	-0.124613	-1.295	0.099038
20	0.148991	1.5484	0.06223

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.438076	-4.5526	7e-06
2	-0.200062	-2.0791	0.019988
3	0.429075	4.4591	1e-05
4	0.14322	1.4884	0.069782
5	0.041913	0.4356	0.332009
6	0.089319	0.9282	0.177679
7	-0.221013	-2.2968	0.011778
8	-0.181518	-1.8864	0.030964
9	-0.107979	-1.1222	0.132143
10	-0.059088	-0.6141	0.270235
11	-0.060424	-0.6279	0.265682
12	-0.031387	-0.3262	0.372459
13	-0.127193	-1.3218	0.09451
14	-0.122229	-1.2702	0.103363
15	0.166808	1.7335	0.042929
16	0.034532	0.3589	0.360199
17	-0.028652	-0.2978	0.383228
18	-0.000568	-0.0059	0.497652
19	-0.072214	-0.7505	0.227301
20	-0.065055	-0.6761	0.250221

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.438076 & -4.5526 & 7e-06 \tabularnewline
2 & -0.200062 & -2.0791 & 0.019988 \tabularnewline
3 & 0.429075 & 4.4591 & 1e-05 \tabularnewline
4 & 0.14322 & 1.4884 & 0.069782 \tabularnewline
5 & 0.041913 & 0.4356 & 0.332009 \tabularnewline
6 & 0.089319 & 0.9282 & 0.177679 \tabularnewline
7 & -0.221013 & -2.2968 & 0.011778 \tabularnewline
8 & -0.181518 & -1.8864 & 0.030964 \tabularnewline
9 & -0.107979 & -1.1222 & 0.132143 \tabularnewline
10 & -0.059088 & -0.6141 & 0.270235 \tabularnewline
11 & -0.060424 & -0.6279 & 0.265682 \tabularnewline
12 & -0.031387 & -0.3262 & 0.372459 \tabularnewline
13 & -0.127193 & -1.3218 & 0.09451 \tabularnewline
14 & -0.122229 & -1.2702 & 0.103363 \tabularnewline
15 & 0.166808 & 1.7335 & 0.042929 \tabularnewline
16 & 0.034532 & 0.3589 & 0.360199 \tabularnewline
17 & -0.028652 & -0.2978 & 0.383228 \tabularnewline
18 & -0.000568 & -0.0059 & 0.497652 \tabularnewline
19 & -0.072214 & -0.7505 & 0.227301 \tabularnewline
20 & -0.065055 & -0.6761 & 0.250221 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112400&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]-0.438076[/C][C]-4.5526[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.200062[/C][C]-2.0791[/C][C]0.019988[/C][/ROW]
[ROW][C]3[/C][C]0.429075[/C][C]4.4591[/C][C]1e-05[/C][/ROW]
[ROW][C]4[/C][C]0.14322[/C][C]1.4884[/C][C]0.069782[/C][/ROW]
[ROW][C]5[/C][C]0.041913[/C][C]0.4356[/C][C]0.332009[/C][/ROW]
[ROW][C]6[/C][C]0.089319[/C][C]0.9282[/C][C]0.177679[/C][/ROW]
[ROW][C]7[/C][C]-0.221013[/C][C]-2.2968[/C][C]0.011778[/C][/ROW]
[ROW][C]8[/C][C]-0.181518[/C][C]-1.8864[/C][C]0.030964[/C][/ROW]
[ROW][C]9[/C][C]-0.107979[/C][C]-1.1222[/C][C]0.132143[/C][/ROW]
[ROW][C]10[/C][C]-0.059088[/C][C]-0.6141[/C][C]0.270235[/C][/ROW]
[ROW][C]11[/C][C]-0.060424[/C][C]-0.6279[/C][C]0.265682[/C][/ROW]
[ROW][C]12[/C][C]-0.031387[/C][C]-0.3262[/C][C]0.372459[/C][/ROW]
[ROW][C]13[/C][C]-0.127193[/C][C]-1.3218[/C][C]0.09451[/C][/ROW]
[ROW][C]14[/C][C]-0.122229[/C][C]-1.2702[/C][C]0.103363[/C][/ROW]
[ROW][C]15[/C][C]0.166808[/C][C]1.7335[/C][C]0.042929[/C][/ROW]
[ROW][C]16[/C][C]0.034532[/C][C]0.3589[/C][C]0.360199[/C][/ROW]
[ROW][C]17[/C][C]-0.028652[/C][C]-0.2978[/C][C]0.383228[/C][/ROW]
[ROW][C]18[/C][C]-0.000568[/C][C]-0.0059[/C][C]0.497652[/C][/ROW]
[ROW][C]19[/C][C]-0.072214[/C][C]-0.7505[/C][C]0.227301[/C][/ROW]
[ROW][C]20[/C][C]-0.065055[/C][C]-0.6761[/C][C]0.250221[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112400&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112400&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	-0.438076	-4.5526	7e-06
2	-0.200062	-2.0791	0.019988
3	0.429075	4.4591	1e-05
4	0.14322	1.4884	0.069782
5	0.041913	0.4356	0.332009
6	0.089319	0.9282	0.177679
7	-0.221013	-2.2968	0.011778
8	-0.181518	-1.8864	0.030964
9	-0.107979	-1.1222	0.132143
10	-0.059088	-0.6141	0.270235
11	-0.060424	-0.6279	0.265682
12	-0.031387	-0.3262	0.372459
13	-0.127193	-1.3218	0.09451
14	-0.122229	-1.2702	0.103363
15	0.166808	1.7335	0.042929
16	0.034532	0.3589	0.360199
17	-0.028652	-0.2978	0.383228
18	-0.000568	-0.0059	0.497652
19	-0.072214	-0.7505	0.227301
20	-0.065055	-0.6761	0.250221

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):

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)
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,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