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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

Wed, 07 Dec 2011 08:35:25 -0500

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/2011/Dec/07/t1323264953ekkz7n2zg564s3c.htm/, Retrieved Thu, 02 May 2024 17:19:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152337, Retrieved Thu, 02 May 2024 17:19:39 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

112

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] [autocorrelatie ] [2011-12-07 13:35:25] [1a4698f17d8e7f554418314cf0e4bd67] [Current]
-   PD        [(Partial) Autocorrelation Function] [autocorrelatie D=1] [2011-12-07 13:50:51] [141ef847e2c5f8e947fe4eabcb0cf143] 
- RMP           [Standard Deviation-Mean Plot] [ST-MP] [2011-12-07 14:22:28] [141ef847e2c5f8e947fe4eabcb0cf143] 
- RMP             [ARIMA Backward Selection] [ARIMA backward ] [2011-12-08 13:48:01] [141ef847e2c5f8e947fe4eabcb0cf143] 
- R                 [ARIMA Backward Selection] [ARIMA backward nieuw] [2011-12-08 14:12:51] [141ef847e2c5f8e947fe4eabcb0cf143] 
- RM                [ARIMA Forecasting] [ARIMA forecasting...] [2011-12-08 14:14:36] [141ef847e2c5f8e947fe4eabcb0cf143] 
- R P                 [ARIMA Forecasting] [Arima forecasting...] [2011-12-21 11:37:56] [141ef847e2c5f8e947fe4eabcb0cf143] 
- R P               [ARIMA Backward Selection] [ARIMA backward nieuw] [2011-12-19 19:26:36] [141ef847e2c5f8e947fe4eabcb0cf143] 
- RMPD                [Skewness and Kurtosis Test] [skewness] [2011-12-22 14:43:07] [141ef847e2c5f8e947fe4eabcb0cf143] 
- RMPD                [Central Tendency] [gemiddelde] [2011-12-22 15:14:40] [141ef847e2c5f8e947fe4eabcb0cf143] 
- RMPD                [Central Tendency] [gemiddelde] [2011-12-22 23:25:55] [141ef847e2c5f8e947fe4eabcb0cf143] 
- RMPD                [Skewness and Kurtosis Test] [kurtosis en skewness] [2011-12-22 23:27:30] [141ef847e2c5f8e947fe4eabcb0cf143] 

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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	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152337&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152337&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.392669	3.0416	0.001744
2	0.177062	1.3715	0.087661
3	0.42537	3.2949	0.000828
4	0.241957	1.8742	0.032888
5	0.287015	2.2232	0.01499
6	0.35641	2.7607	0.00382
7	0.113489	0.8791	0.191431
8	0.089385	0.6924	0.245688
9	0.025267	0.1957	0.422745
10	-0.237506	-1.8397	0.035379
11	0.007961	0.0617	0.475516
12	0.237879	1.8426	0.035164
13	-0.208728	-1.6168	0.055584
14	-0.307307	-2.3804	0.010244
15	-0.132166	-1.0238	0.15503
16	-0.258807	-2.0047	0.024756
17	-0.130749	-1.0128	0.157616

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.392669 & 3.0416 & 0.001744 \tabularnewline
2 & 0.177062 & 1.3715 & 0.087661 \tabularnewline
3 & 0.42537 & 3.2949 & 0.000828 \tabularnewline
4 & 0.241957 & 1.8742 & 0.032888 \tabularnewline
5 & 0.287015 & 2.2232 & 0.01499 \tabularnewline
6 & 0.35641 & 2.7607 & 0.00382 \tabularnewline
7 & 0.113489 & 0.8791 & 0.191431 \tabularnewline
8 & 0.089385 & 0.6924 & 0.245688 \tabularnewline
9 & 0.025267 & 0.1957 & 0.422745 \tabularnewline
10 & -0.237506 & -1.8397 & 0.035379 \tabularnewline
11 & 0.007961 & 0.0617 & 0.475516 \tabularnewline
12 & 0.237879 & 1.8426 & 0.035164 \tabularnewline
13 & -0.208728 & -1.6168 & 0.055584 \tabularnewline
14 & -0.307307 & -2.3804 & 0.010244 \tabularnewline
15 & -0.132166 & -1.0238 & 0.15503 \tabularnewline
16 & -0.258807 & -2.0047 & 0.024756 \tabularnewline
17 & -0.130749 & -1.0128 & 0.157616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152337&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]0.392669[/C][C]3.0416[/C][C]0.001744[/C][/ROW]
[ROW][C]2[/C][C]0.177062[/C][C]1.3715[/C][C]0.087661[/C][/ROW]
[ROW][C]3[/C][C]0.42537[/C][C]3.2949[/C][C]0.000828[/C][/ROW]
[ROW][C]4[/C][C]0.241957[/C][C]1.8742[/C][C]0.032888[/C][/ROW]
[ROW][C]5[/C][C]0.287015[/C][C]2.2232[/C][C]0.01499[/C][/ROW]
[ROW][C]6[/C][C]0.35641[/C][C]2.7607[/C][C]0.00382[/C][/ROW]
[ROW][C]7[/C][C]0.113489[/C][C]0.8791[/C][C]0.191431[/C][/ROW]
[ROW][C]8[/C][C]0.089385[/C][C]0.6924[/C][C]0.245688[/C][/ROW]
[ROW][C]9[/C][C]0.025267[/C][C]0.1957[/C][C]0.422745[/C][/ROW]
[ROW][C]10[/C][C]-0.237506[/C][C]-1.8397[/C][C]0.035379[/C][/ROW]
[ROW][C]11[/C][C]0.007961[/C][C]0.0617[/C][C]0.475516[/C][/ROW]
[ROW][C]12[/C][C]0.237879[/C][C]1.8426[/C][C]0.035164[/C][/ROW]
[ROW][C]13[/C][C]-0.208728[/C][C]-1.6168[/C][C]0.055584[/C][/ROW]
[ROW][C]14[/C][C]-0.307307[/C][C]-2.3804[/C][C]0.010244[/C][/ROW]
[ROW][C]15[/C][C]-0.132166[/C][C]-1.0238[/C][C]0.15503[/C][/ROW]
[ROW][C]16[/C][C]-0.258807[/C][C]-2.0047[/C][C]0.024756[/C][/ROW]
[ROW][C]17[/C][C]-0.130749[/C][C]-1.0128[/C][C]0.157616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152337&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	0.392669	3.0416	0.001744
2	0.177062	1.3715	0.087661
3	0.42537	3.2949	0.000828
4	0.241957	1.8742	0.032888
5	0.287015	2.2232	0.01499
6	0.35641	2.7607	0.00382
7	0.113489	0.8791	0.191431
8	0.089385	0.6924	0.245688
9	0.025267	0.1957	0.422745
10	-0.237506	-1.8397	0.035379
11	0.007961	0.0617	0.475516
12	0.237879	1.8426	0.035164
13	-0.208728	-1.6168	0.055584
14	-0.307307	-2.3804	0.010244
15	-0.132166	-1.0238	0.15503
16	-0.258807	-2.0047	0.024756
17	-0.130749	-1.0128	0.157616

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.392669	3.0416	0.001744
2	0.027043	0.2095	0.417394
3	0.410681	3.1811	0.001162
4	-0.076996	-0.5964	0.276574
5	0.288574	2.2353	0.014566
6	0.024799	0.1921	0.424158
7	-0.082807	-0.6414	0.261845
8	-0.085313	-0.6608	0.255625
9	-0.244348	-1.8927	0.031612
10	-0.374665	-2.9021	0.002588
11	0.131369	1.0176	0.156481
12	0.33441	2.5903	0.006009
13	-0.207001	-1.6034	0.057047
14	-0.181218	-1.4037	0.082781
15	-0.038871	-0.3011	0.382193
16	-0.028294	-0.2192	0.413633
17	0.056775	0.4398	0.330839

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.392669 & 3.0416 & 0.001744 \tabularnewline
2 & 0.027043 & 0.2095 & 0.417394 \tabularnewline
3 & 0.410681 & 3.1811 & 0.001162 \tabularnewline
4 & -0.076996 & -0.5964 & 0.276574 \tabularnewline
5 & 0.288574 & 2.2353 & 0.014566 \tabularnewline
6 & 0.024799 & 0.1921 & 0.424158 \tabularnewline
7 & -0.082807 & -0.6414 & 0.261845 \tabularnewline
8 & -0.085313 & -0.6608 & 0.255625 \tabularnewline
9 & -0.244348 & -1.8927 & 0.031612 \tabularnewline
10 & -0.374665 & -2.9021 & 0.002588 \tabularnewline
11 & 0.131369 & 1.0176 & 0.156481 \tabularnewline
12 & 0.33441 & 2.5903 & 0.006009 \tabularnewline
13 & -0.207001 & -1.6034 & 0.057047 \tabularnewline
14 & -0.181218 & -1.4037 & 0.082781 \tabularnewline
15 & -0.038871 & -0.3011 & 0.382193 \tabularnewline
16 & -0.028294 & -0.2192 & 0.413633 \tabularnewline
17 & 0.056775 & 0.4398 & 0.330839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152337&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]0.392669[/C][C]3.0416[/C][C]0.001744[/C][/ROW]
[ROW][C]2[/C][C]0.027043[/C][C]0.2095[/C][C]0.417394[/C][/ROW]
[ROW][C]3[/C][C]0.410681[/C][C]3.1811[/C][C]0.001162[/C][/ROW]
[ROW][C]4[/C][C]-0.076996[/C][C]-0.5964[/C][C]0.276574[/C][/ROW]
[ROW][C]5[/C][C]0.288574[/C][C]2.2353[/C][C]0.014566[/C][/ROW]
[ROW][C]6[/C][C]0.024799[/C][C]0.1921[/C][C]0.424158[/C][/ROW]
[ROW][C]7[/C][C]-0.082807[/C][C]-0.6414[/C][C]0.261845[/C][/ROW]
[ROW][C]8[/C][C]-0.085313[/C][C]-0.6608[/C][C]0.255625[/C][/ROW]
[ROW][C]9[/C][C]-0.244348[/C][C]-1.8927[/C][C]0.031612[/C][/ROW]
[ROW][C]10[/C][C]-0.374665[/C][C]-2.9021[/C][C]0.002588[/C][/ROW]
[ROW][C]11[/C][C]0.131369[/C][C]1.0176[/C][C]0.156481[/C][/ROW]
[ROW][C]12[/C][C]0.33441[/C][C]2.5903[/C][C]0.006009[/C][/ROW]
[ROW][C]13[/C][C]-0.207001[/C][C]-1.6034[/C][C]0.057047[/C][/ROW]
[ROW][C]14[/C][C]-0.181218[/C][C]-1.4037[/C][C]0.082781[/C][/ROW]
[ROW][C]15[/C][C]-0.038871[/C][C]-0.3011[/C][C]0.382193[/C][/ROW]
[ROW][C]16[/C][C]-0.028294[/C][C]-0.2192[/C][C]0.413633[/C][/ROW]
[ROW][C]17[/C][C]0.056775[/C][C]0.4398[/C][C]0.330839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152337&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152337&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	0.392669	3.0416	0.001744
2	0.027043	0.2095	0.417394
3	0.410681	3.1811	0.001162
4	-0.076996	-0.5964	0.276574
5	0.288574	2.2353	0.014566
6	0.024799	0.1921	0.424158
7	-0.082807	-0.6414	0.261845
8	-0.085313	-0.6608	0.255625
9	-0.244348	-1.8927	0.031612
10	-0.374665	-2.9021	0.002588
11	0.131369	1.0176	0.156481
12	0.33441	2.5903	0.006009
13	-0.207001	-1.6034	0.057047
14	-0.181218	-1.4037	0.082781
15	-0.038871	-0.3011	0.382193
16	-0.028294	-0.2192	0.413633
17	0.056775	0.4398	0.330839

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code