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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 08:24:33 +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/t1291364604452vbeq97y76awd.htm/, Retrieved Wed, 08 May 2024 00:51:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104534, Retrieved Wed, 08 May 2024 00:51:37 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

210

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]
F    D      [(Partial) Autocorrelation Function] [] [2010-12-03 08:24:33] [dcc54e7e6e8c80b7c45e040080afe6ab] [Current]
- RMPD        [Pearson Correlation] [] [2010-12-10 15:11:22] [1251ac2db27b84d4a3ba43449388906b] 
-   P         [(Partial) Autocorrelation Function] [WS 9 Autocorrelat...] [2010-12-10 23:54:01] [74be16979710d4c4e7c6647856088456] 
-   P         [(Partial) Autocorrelation Function] [WS 9 Cumulatieve ...] [2010-12-10 23:54:01] [8081b8996d5947580de3eb171e82db4f] 

Feedback Forum

2010-12-13 09:56:36 [Stefanie Van Esbroeck] [reply] 
Bij deze berekening valt het mij op dat de student wel time lags heeft ingesteld maar dat hij/zij deze niet groot genoeg heeft ingesteld.Om een duidelijker beeld te vormen en omdat er seizoenaliteit in de tijdreeks aanwezig is, is het beter dat je de time lags instelt op bijvoorbeeld 48. Hieronder kun je een link terugvinden waar dit wel is gebeurd: http://www.freestatistics.org/blog/index.php?v=date/2010/Dec/13/t1292233839ikruvna8zaw0mte.htm/ In deze berekening zal je opmerken dat de waarden positief zijn op de lags 12,24,36 en 48. Je interpretatie van de output is wel correct. Je merkt goed op dat de gegevens geen lange termijn trend bevatten en dat je dan in je volgende berekening de klein d gelijk moet stellen aan 0. Ook je interpretatie over de seizoenaliteit is correct.

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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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104534&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104534&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104534&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.070319	0.5967	0.276298
2	-0.233976	-1.9854	0.025457
3	0.068112	0.5779	0.282551
4	-0.142495	-1.2091	0.115287
5	-0.211961	-1.7985	0.038141
6	0.068913	0.5847	0.280274
7	-0.1007	-0.8545	0.19784
8	-0.052042	-0.4416	0.330054
9	0.118247	1.0034	0.159524
10	-0.112644	-0.9558	0.171181
11	0.114018	0.9675	0.168272
12	0.46381	3.9356	9.5e-05
13	-0.037397	-0.3173	0.375959
14	-0.269423	-2.2861	0.012595
15	0.056802	0.482	0.31564
16	-0.133191	-1.1302	0.131079
17	-0.178608	-1.5155	0.067008
18	0.045474	0.3859	0.35037

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.070319 & 0.5967 & 0.276298 \tabularnewline
2 & -0.233976 & -1.9854 & 0.025457 \tabularnewline
3 & 0.068112 & 0.5779 & 0.282551 \tabularnewline
4 & -0.142495 & -1.2091 & 0.115287 \tabularnewline
5 & -0.211961 & -1.7985 & 0.038141 \tabularnewline
6 & 0.068913 & 0.5847 & 0.280274 \tabularnewline
7 & -0.1007 & -0.8545 & 0.19784 \tabularnewline
8 & -0.052042 & -0.4416 & 0.330054 \tabularnewline
9 & 0.118247 & 1.0034 & 0.159524 \tabularnewline
10 & -0.112644 & -0.9558 & 0.171181 \tabularnewline
11 & 0.114018 & 0.9675 & 0.168272 \tabularnewline
12 & 0.46381 & 3.9356 & 9.5e-05 \tabularnewline
13 & -0.037397 & -0.3173 & 0.375959 \tabularnewline
14 & -0.269423 & -2.2861 & 0.012595 \tabularnewline
15 & 0.056802 & 0.482 & 0.31564 \tabularnewline
16 & -0.133191 & -1.1302 & 0.131079 \tabularnewline
17 & -0.178608 & -1.5155 & 0.067008 \tabularnewline
18 & 0.045474 & 0.3859 & 0.35037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104534&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]0.070319[/C][C]0.5967[/C][C]0.276298[/C][/ROW]
[ROW][C]2[/C][C]-0.233976[/C][C]-1.9854[/C][C]0.025457[/C][/ROW]
[ROW][C]3[/C][C]0.068112[/C][C]0.5779[/C][C]0.282551[/C][/ROW]
[ROW][C]4[/C][C]-0.142495[/C][C]-1.2091[/C][C]0.115287[/C][/ROW]
[ROW][C]5[/C][C]-0.211961[/C][C]-1.7985[/C][C]0.038141[/C][/ROW]
[ROW][C]6[/C][C]0.068913[/C][C]0.5847[/C][C]0.280274[/C][/ROW]
[ROW][C]7[/C][C]-0.1007[/C][C]-0.8545[/C][C]0.19784[/C][/ROW]
[ROW][C]8[/C][C]-0.052042[/C][C]-0.4416[/C][C]0.330054[/C][/ROW]
[ROW][C]9[/C][C]0.118247[/C][C]1.0034[/C][C]0.159524[/C][/ROW]
[ROW][C]10[/C][C]-0.112644[/C][C]-0.9558[/C][C]0.171181[/C][/ROW]
[ROW][C]11[/C][C]0.114018[/C][C]0.9675[/C][C]0.168272[/C][/ROW]
[ROW][C]12[/C][C]0.46381[/C][C]3.9356[/C][C]9.5e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.037397[/C][C]-0.3173[/C][C]0.375959[/C][/ROW]
[ROW][C]14[/C][C]-0.269423[/C][C]-2.2861[/C][C]0.012595[/C][/ROW]
[ROW][C]15[/C][C]0.056802[/C][C]0.482[/C][C]0.31564[/C][/ROW]
[ROW][C]16[/C][C]-0.133191[/C][C]-1.1302[/C][C]0.131079[/C][/ROW]
[ROW][C]17[/C][C]-0.178608[/C][C]-1.5155[/C][C]0.067008[/C][/ROW]
[ROW][C]18[/C][C]0.045474[/C][C]0.3859[/C][C]0.35037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104534&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104534&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	0.070319	0.5967	0.276298
2	-0.233976	-1.9854	0.025457
3	0.068112	0.5779	0.282551
4	-0.142495	-1.2091	0.115287
5	-0.211961	-1.7985	0.038141
6	0.068913	0.5847	0.280274
7	-0.1007	-0.8545	0.19784
8	-0.052042	-0.4416	0.330054
9	0.118247	1.0034	0.159524
10	-0.112644	-0.9558	0.171181
11	0.114018	0.9675	0.168272
12	0.46381	3.9356	9.5e-05
13	-0.037397	-0.3173	0.375959
14	-0.269423	-2.2861	0.012595
15	0.056802	0.482	0.31564
16	-0.133191	-1.1302	0.131079
17	-0.178608	-1.5155	0.067008
18	0.045474	0.3859	0.35037

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.070319	0.5967	0.276298
2	-0.240108	-2.0374	0.022644
3	0.112403	0.9538	0.171694
4	-0.234004	-1.9856	0.025444
5	-0.139325	-1.1822	0.120506
6	0.004284	0.0363	0.485553
7	-0.202861	-1.7213	0.044743
8	-0.002173	-0.0184	0.492671
9	-0.036368	-0.3086	0.379261
10	-0.176649	-1.4989	0.069134
11	0.179288	1.5213	0.066281
12	0.349542	2.966	0.002046
13	-0.013446	-0.1141	0.45474
14	-0.12453	-1.0567	0.147096
15	0.044219	0.3752	0.354303
16	-0.059446	-0.5044	0.307754
17	-0.030484	-0.2587	0.398315
18	-0.083966	-0.7125	0.239237

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.070319 & 0.5967 & 0.276298 \tabularnewline
2 & -0.240108 & -2.0374 & 0.022644 \tabularnewline
3 & 0.112403 & 0.9538 & 0.171694 \tabularnewline
4 & -0.234004 & -1.9856 & 0.025444 \tabularnewline
5 & -0.139325 & -1.1822 & 0.120506 \tabularnewline
6 & 0.004284 & 0.0363 & 0.485553 \tabularnewline
7 & -0.202861 & -1.7213 & 0.044743 \tabularnewline
8 & -0.002173 & -0.0184 & 0.492671 \tabularnewline
9 & -0.036368 & -0.3086 & 0.379261 \tabularnewline
10 & -0.176649 & -1.4989 & 0.069134 \tabularnewline
11 & 0.179288 & 1.5213 & 0.066281 \tabularnewline
12 & 0.349542 & 2.966 & 0.002046 \tabularnewline
13 & -0.013446 & -0.1141 & 0.45474 \tabularnewline
14 & -0.12453 & -1.0567 & 0.147096 \tabularnewline
15 & 0.044219 & 0.3752 & 0.354303 \tabularnewline
16 & -0.059446 & -0.5044 & 0.307754 \tabularnewline
17 & -0.030484 & -0.2587 & 0.398315 \tabularnewline
18 & -0.083966 & -0.7125 & 0.239237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104534&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]0.070319[/C][C]0.5967[/C][C]0.276298[/C][/ROW]
[ROW][C]2[/C][C]-0.240108[/C][C]-2.0374[/C][C]0.022644[/C][/ROW]
[ROW][C]3[/C][C]0.112403[/C][C]0.9538[/C][C]0.171694[/C][/ROW]
[ROW][C]4[/C][C]-0.234004[/C][C]-1.9856[/C][C]0.025444[/C][/ROW]
[ROW][C]5[/C][C]-0.139325[/C][C]-1.1822[/C][C]0.120506[/C][/ROW]
[ROW][C]6[/C][C]0.004284[/C][C]0.0363[/C][C]0.485553[/C][/ROW]
[ROW][C]7[/C][C]-0.202861[/C][C]-1.7213[/C][C]0.044743[/C][/ROW]
[ROW][C]8[/C][C]-0.002173[/C][C]-0.0184[/C][C]0.492671[/C][/ROW]
[ROW][C]9[/C][C]-0.036368[/C][C]-0.3086[/C][C]0.379261[/C][/ROW]
[ROW][C]10[/C][C]-0.176649[/C][C]-1.4989[/C][C]0.069134[/C][/ROW]
[ROW][C]11[/C][C]0.179288[/C][C]1.5213[/C][C]0.066281[/C][/ROW]
[ROW][C]12[/C][C]0.349542[/C][C]2.966[/C][C]0.002046[/C][/ROW]
[ROW][C]13[/C][C]-0.013446[/C][C]-0.1141[/C][C]0.45474[/C][/ROW]
[ROW][C]14[/C][C]-0.12453[/C][C]-1.0567[/C][C]0.147096[/C][/ROW]
[ROW][C]15[/C][C]0.044219[/C][C]0.3752[/C][C]0.354303[/C][/ROW]
[ROW][C]16[/C][C]-0.059446[/C][C]-0.5044[/C][C]0.307754[/C][/ROW]
[ROW][C]17[/C][C]-0.030484[/C][C]-0.2587[/C][C]0.398315[/C][/ROW]
[ROW][C]18[/C][C]-0.083966[/C][C]-0.7125[/C][C]0.239237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104534&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104534&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	0.070319	0.5967	0.276298
2	-0.240108	-2.0374	0.022644
3	0.112403	0.9538	0.171694
4	-0.234004	-1.9856	0.025444
5	-0.139325	-1.1822	0.120506
6	0.004284	0.0363	0.485553
7	-0.202861	-1.7213	0.044743
8	-0.002173	-0.0184	0.492671
9	-0.036368	-0.3086	0.379261
10	-0.176649	-1.4989	0.069134
11	0.179288	1.5213	0.066281
12	0.349542	2.966	0.002046
13	-0.013446	-0.1141	0.45474
14	-0.12453	-1.0567	0.147096
15	0.044219	0.3752	0.354303
16	-0.059446	-0.5044	0.307754
17	-0.030484	-0.2587	0.398315
18	-0.083966	-0.7125	0.239237

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 ;

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