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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 05 Dec 2010 13:40:03 +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/05/t1291556354kh8140yngu1wxbn.htm/, Retrieved Wed, 01 May 2024 16:06:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105392, Retrieved Wed, 01 May 2024 16:06:53 +0000

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User-defined keywords

Estimated Impact

107

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] [Ws 9 - ACF] [2010-12-05 13:32:17] [603e2f5305d3a2a4e062624458fa1155]
-   P         [(Partial) Autocorrelation Function] [Ws 9 - ACF (d = 1)] [2010-12-05 13:40:03] [0829c729852d8a4b1b0c41cf0848af95] [Current]
-   P           [(Partial) Autocorrelation Function] [Ws 9 - ACF (d = 1)] [2010-12-05 14:08:10] [603e2f5305d3a2a4e062624458fa1155] 

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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=105392&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=105392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105392&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	0.246774	1.8631	0.033802
2	-0.051665	-0.3901	0.348972
3	0.067663	0.5108	0.305717
4	-0.055001	-0.4152	0.33976
5	0.232968	1.7589	0.041983
6	0.197446	1.4907	0.070779
7	-0.264446	-1.9965	0.025331
8	-0.186958	-1.4115	0.081766
9	-0.017229	-0.1301	0.448482
10	-0.084249	-0.6361	0.26364
11	0.039767	0.3002	0.382547
12	-0.164394	-1.2412	0.109817
13	-0.314141	-2.3717	0.010553
14	-0.027717	-0.2093	0.417496
15	0.127645	0.9637	0.169635
16	0.116747	0.8814	0.190897
17	0.046475	0.3509	0.363486

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.246774 & 1.8631 & 0.033802 \tabularnewline
2 & -0.051665 & -0.3901 & 0.348972 \tabularnewline
3 & 0.067663 & 0.5108 & 0.305717 \tabularnewline
4 & -0.055001 & -0.4152 & 0.33976 \tabularnewline
5 & 0.232968 & 1.7589 & 0.041983 \tabularnewline
6 & 0.197446 & 1.4907 & 0.070779 \tabularnewline
7 & -0.264446 & -1.9965 & 0.025331 \tabularnewline
8 & -0.186958 & -1.4115 & 0.081766 \tabularnewline
9 & -0.017229 & -0.1301 & 0.448482 \tabularnewline
10 & -0.084249 & -0.6361 & 0.26364 \tabularnewline
11 & 0.039767 & 0.3002 & 0.382547 \tabularnewline
12 & -0.164394 & -1.2412 & 0.109817 \tabularnewline
13 & -0.314141 & -2.3717 & 0.010553 \tabularnewline
14 & -0.027717 & -0.2093 & 0.417496 \tabularnewline
15 & 0.127645 & 0.9637 & 0.169635 \tabularnewline
16 & 0.116747 & 0.8814 & 0.190897 \tabularnewline
17 & 0.046475 & 0.3509 & 0.363486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105392&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]0.246774[/C][C]1.8631[/C][C]0.033802[/C][/ROW]
[ROW][C]2[/C][C]-0.051665[/C][C]-0.3901[/C][C]0.348972[/C][/ROW]
[ROW][C]3[/C][C]0.067663[/C][C]0.5108[/C][C]0.305717[/C][/ROW]
[ROW][C]4[/C][C]-0.055001[/C][C]-0.4152[/C][C]0.33976[/C][/ROW]
[ROW][C]5[/C][C]0.232968[/C][C]1.7589[/C][C]0.041983[/C][/ROW]
[ROW][C]6[/C][C]0.197446[/C][C]1.4907[/C][C]0.070779[/C][/ROW]
[ROW][C]7[/C][C]-0.264446[/C][C]-1.9965[/C][C]0.025331[/C][/ROW]
[ROW][C]8[/C][C]-0.186958[/C][C]-1.4115[/C][C]0.081766[/C][/ROW]
[ROW][C]9[/C][C]-0.017229[/C][C]-0.1301[/C][C]0.448482[/C][/ROW]
[ROW][C]10[/C][C]-0.084249[/C][C]-0.6361[/C][C]0.26364[/C][/ROW]
[ROW][C]11[/C][C]0.039767[/C][C]0.3002[/C][C]0.382547[/C][/ROW]
[ROW][C]12[/C][C]-0.164394[/C][C]-1.2412[/C][C]0.109817[/C][/ROW]
[ROW][C]13[/C][C]-0.314141[/C][C]-2.3717[/C][C]0.010553[/C][/ROW]
[ROW][C]14[/C][C]-0.027717[/C][C]-0.2093[/C][C]0.417496[/C][/ROW]
[ROW][C]15[/C][C]0.127645[/C][C]0.9637[/C][C]0.169635[/C][/ROW]
[ROW][C]16[/C][C]0.116747[/C][C]0.8814[/C][C]0.190897[/C][/ROW]
[ROW][C]17[/C][C]0.046475[/C][C]0.3509[/C][C]0.363486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105392&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	0.246774	1.8631	0.033802
2	-0.051665	-0.3901	0.348972
3	0.067663	0.5108	0.305717
4	-0.055001	-0.4152	0.33976
5	0.232968	1.7589	0.041983
6	0.197446	1.4907	0.070779
7	-0.264446	-1.9965	0.025331
8	-0.186958	-1.4115	0.081766
9	-0.017229	-0.1301	0.448482
10	-0.084249	-0.6361	0.26364
11	0.039767	0.3002	0.382547
12	-0.164394	-1.2412	0.109817
13	-0.314141	-2.3717	0.010553
14	-0.027717	-0.2093	0.417496
15	0.127645	0.9637	0.169635
16	0.116747	0.8814	0.190897
17	0.046475	0.3509	0.363486

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.246774	1.8631	0.033802
2	-0.119862	-0.9049	0.184654
3	0.120482	0.9096	0.183427
4	-0.123136	-0.9297	0.178235
5	0.333813	2.5202	0.007276
6	-0.005176	-0.0391	0.484483
7	-0.294409	-2.2227	0.015108
8	-0.074415	-0.5618	0.28822
9	0.046266	0.3493	0.364077
10	-0.109227	-0.8246	0.206506
11	-0.012277	-0.0927	0.463237
12	-0.14358	-1.084	0.141464
13	-0.075973	-0.5736	0.284253
14	-0.000727	-0.0055	0.49782
15	0.145112	1.0956	0.138936
16	0.088094	0.6651	0.254335
17	-0.025435	-0.192	0.424199

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.246774 & 1.8631 & 0.033802 \tabularnewline
2 & -0.119862 & -0.9049 & 0.184654 \tabularnewline
3 & 0.120482 & 0.9096 & 0.183427 \tabularnewline
4 & -0.123136 & -0.9297 & 0.178235 \tabularnewline
5 & 0.333813 & 2.5202 & 0.007276 \tabularnewline
6 & -0.005176 & -0.0391 & 0.484483 \tabularnewline
7 & -0.294409 & -2.2227 & 0.015108 \tabularnewline
8 & -0.074415 & -0.5618 & 0.28822 \tabularnewline
9 & 0.046266 & 0.3493 & 0.364077 \tabularnewline
10 & -0.109227 & -0.8246 & 0.206506 \tabularnewline
11 & -0.012277 & -0.0927 & 0.463237 \tabularnewline
12 & -0.14358 & -1.084 & 0.141464 \tabularnewline
13 & -0.075973 & -0.5736 & 0.284253 \tabularnewline
14 & -0.000727 & -0.0055 & 0.49782 \tabularnewline
15 & 0.145112 & 1.0956 & 0.138936 \tabularnewline
16 & 0.088094 & 0.6651 & 0.254335 \tabularnewline
17 & -0.025435 & -0.192 & 0.424199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105392&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]0.246774[/C][C]1.8631[/C][C]0.033802[/C][/ROW]
[ROW][C]2[/C][C]-0.119862[/C][C]-0.9049[/C][C]0.184654[/C][/ROW]
[ROW][C]3[/C][C]0.120482[/C][C]0.9096[/C][C]0.183427[/C][/ROW]
[ROW][C]4[/C][C]-0.123136[/C][C]-0.9297[/C][C]0.178235[/C][/ROW]
[ROW][C]5[/C][C]0.333813[/C][C]2.5202[/C][C]0.007276[/C][/ROW]
[ROW][C]6[/C][C]-0.005176[/C][C]-0.0391[/C][C]0.484483[/C][/ROW]
[ROW][C]7[/C][C]-0.294409[/C][C]-2.2227[/C][C]0.015108[/C][/ROW]
[ROW][C]8[/C][C]-0.074415[/C][C]-0.5618[/C][C]0.28822[/C][/ROW]
[ROW][C]9[/C][C]0.046266[/C][C]0.3493[/C][C]0.364077[/C][/ROW]
[ROW][C]10[/C][C]-0.109227[/C][C]-0.8246[/C][C]0.206506[/C][/ROW]
[ROW][C]11[/C][C]-0.012277[/C][C]-0.0927[/C][C]0.463237[/C][/ROW]
[ROW][C]12[/C][C]-0.14358[/C][C]-1.084[/C][C]0.141464[/C][/ROW]
[ROW][C]13[/C][C]-0.075973[/C][C]-0.5736[/C][C]0.284253[/C][/ROW]
[ROW][C]14[/C][C]-0.000727[/C][C]-0.0055[/C][C]0.49782[/C][/ROW]
[ROW][C]15[/C][C]0.145112[/C][C]1.0956[/C][C]0.138936[/C][/ROW]
[ROW][C]16[/C][C]0.088094[/C][C]0.6651[/C][C]0.254335[/C][/ROW]
[ROW][C]17[/C][C]-0.025435[/C][C]-0.192[/C][C]0.424199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105392&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105392&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	0.246774	1.8631	0.033802
2	-0.119862	-0.9049	0.184654
3	0.120482	0.9096	0.183427
4	-0.123136	-0.9297	0.178235
5	0.333813	2.5202	0.007276
6	-0.005176	-0.0391	0.484483
7	-0.294409	-2.2227	0.015108
8	-0.074415	-0.5618	0.28822
9	0.046266	0.3493	0.364077
10	-0.109227	-0.8246	0.206506
11	-0.012277	-0.0927	0.463237
12	-0.14358	-1.084	0.141464
13	-0.075973	-0.5736	0.284253
14	-0.000727	-0.0055	0.49782
15	0.145112	1.0956	0.138936
16	0.088094	0.6651	0.254335
17	-0.025435	-0.192	0.424199

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code