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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 03 Dec 2011 03:54:59 -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/03/t1322902520xlwxpfrriein1n1.htm/, Retrieved Sun, 28 Apr 2024 21:31:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150377, Retrieved Sun, 28 Apr 2024 21:31:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

132

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] [Partial ACF] [2011-12-03 08:54:59] [10a6f28c51bb1cb94db47cee32729d66] [Current]
- R P         [(Partial) Autocorrelation Function] [P ACF (d=1)] [2011-12-03 09:06:08] [7ec97e350862fea9ec6e4fa3b5b6058f] 
-   P           [(Partial) Autocorrelation Function] [P ACF (d=1)] [2011-12-03 09:07:43] [7ec97e350862fea9ec6e4fa3b5b6058f] 
-   P             [(Partial) Autocorrelation Function] [P ACF (d=D=1)] [2011-12-03 09:10:52] [7ec97e350862fea9ec6e4fa3b5b6058f] 
- R                 [(Partial) Autocorrelation Function] [Partial ACF 3] [2011-12-20 08:42:33] [7ec97e350862fea9ec6e4fa3b5b6058f] 
- RM                [ARIMA Forecasting] [ARIMA Forecasting] [2011-12-20 08:44:13] [7ec97e350862fea9ec6e4fa3b5b6058f] 
- RMP             [Variance Reduction Matrix] [VRM] [2011-12-03 09:14:27] [7ec97e350862fea9ec6e4fa3b5b6058f] 
- R               [(Partial) Autocorrelation Function] [Partial ACF 2] [2011-12-20 08:39:39] [7ec97e350862fea9ec6e4fa3b5b6058f] 
-             [(Partial) Autocorrelation Function] [Partial ACF] [2011-12-20 08:37:10] [7ec97e350862fea9ec6e4fa3b5b6058f] 

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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=150377&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=150377&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150377&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	0.953328	16.8391	0
2	0.882763	15.5927	0
3	0.820671	14.4959	0
4	0.775308	13.6947	0
5	0.746013	13.1772	0
6	0.718955	12.6993	0
7	0.695188	12.2795	0
8	0.67552	11.9321	0
9	0.672009	11.87	0
10	0.685122	12.1017	0
11	0.708534	12.5152	0
12	0.710888	12.5568	0
13	0.647887	11.444	0
14	0.563398	9.9516	0
15	0.487829	8.6168	0
16	0.430982	7.6127	0
17	0.39137	6.913	0
18	0.35542	6.278	0
19	0.32361	5.7161	0
20	0.296614	5.2392	0
21	0.285024	5.0345	0
22	0.290206	5.1261	0
23	0.306861	5.4202	0
24	0.303894	5.3678	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953328 & 16.8391 & 0 \tabularnewline
2 & 0.882763 & 15.5927 & 0 \tabularnewline
3 & 0.820671 & 14.4959 & 0 \tabularnewline
4 & 0.775308 & 13.6947 & 0 \tabularnewline
5 & 0.746013 & 13.1772 & 0 \tabularnewline
6 & 0.718955 & 12.6993 & 0 \tabularnewline
7 & 0.695188 & 12.2795 & 0 \tabularnewline
8 & 0.67552 & 11.9321 & 0 \tabularnewline
9 & 0.672009 & 11.87 & 0 \tabularnewline
10 & 0.685122 & 12.1017 & 0 \tabularnewline
11 & 0.708534 & 12.5152 & 0 \tabularnewline
12 & 0.710888 & 12.5568 & 0 \tabularnewline
13 & 0.647887 & 11.444 & 0 \tabularnewline
14 & 0.563398 & 9.9516 & 0 \tabularnewline
15 & 0.487829 & 8.6168 & 0 \tabularnewline
16 & 0.430982 & 7.6127 & 0 \tabularnewline
17 & 0.39137 & 6.913 & 0 \tabularnewline
18 & 0.35542 & 6.278 & 0 \tabularnewline
19 & 0.32361 & 5.7161 & 0 \tabularnewline
20 & 0.296614 & 5.2392 & 0 \tabularnewline
21 & 0.285024 & 5.0345 & 0 \tabularnewline
22 & 0.290206 & 5.1261 & 0 \tabularnewline
23 & 0.306861 & 5.4202 & 0 \tabularnewline
24 & 0.303894 & 5.3678 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150377&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]0.953328[/C][C]16.8391[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.882763[/C][C]15.5927[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.820671[/C][C]14.4959[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.775308[/C][C]13.6947[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.746013[/C][C]13.1772[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.718955[/C][C]12.6993[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.695188[/C][C]12.2795[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.67552[/C][C]11.9321[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.672009[/C][C]11.87[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.685122[/C][C]12.1017[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.708534[/C][C]12.5152[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.710888[/C][C]12.5568[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.647887[/C][C]11.444[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.563398[/C][C]9.9516[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.487829[/C][C]8.6168[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.430982[/C][C]7.6127[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.39137[/C][C]6.913[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.35542[/C][C]6.278[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.32361[/C][C]5.7161[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.296614[/C][C]5.2392[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.285024[/C][C]5.0345[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.290206[/C][C]5.1261[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.306861[/C][C]5.4202[/C][C]0[/C][/ROW]
[ROW][C]24[/C][C]0.303894[/C][C]5.3678[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150377&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150377&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	0.953328	16.8391	0
2	0.882763	15.5927	0
3	0.820671	14.4959	0
4	0.775308	13.6947	0
5	0.746013	13.1772	0
6	0.718955	12.6993	0
7	0.695188	12.2795	0
8	0.67552	11.9321	0
9	0.672009	11.87	0
10	0.685122	12.1017	0
11	0.708534	12.5152	0
12	0.710888	12.5568	0
13	0.647887	11.444	0
14	0.563398	9.9516	0
15	0.487829	8.6168	0
16	0.430982	7.6127	0
17	0.39137	6.913	0
18	0.35542	6.278	0
19	0.32361	5.7161	0
20	0.296614	5.2392	0
21	0.285024	5.0345	0
22	0.290206	5.1261	0
23	0.306861	5.4202	0
24	0.303894	5.3678	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.953328	16.8391	0
2	-0.285978	-5.0514	0
3	0.132252	2.336	0.010061
4	0.093114	1.6447	0.050517
5	0.093428	1.6503	0.049946
6	-0.039674	-0.7008	0.241979
7	0.07689	1.3582	0.087699
8	0.039877	0.7044	0.240862
9	0.193305	3.4144	0.000362
10	0.127676	2.2552	0.012406
11	0.136637	2.4135	0.008188
12	-0.215254	-3.8022	8.6e-05
13	-0.626847	-11.0723	0
14	-0.006964	-0.123	0.451092
15	0.029423	0.5197	0.301814
16	0.026208	0.4629	0.321873
17	0.035284	0.6232	0.266792
18	0.019447	0.3435	0.365726
19	0.025384	0.4484	0.327095
20	-0.017547	-0.3099	0.378407
21	0.008473	0.1497	0.440563
22	0.009484	0.1675	0.433532
23	0.035919	0.6345	0.263126
24	-0.057767	-1.0204	0.154171

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.953328 & 16.8391 & 0 \tabularnewline
2 & -0.285978 & -5.0514 & 0 \tabularnewline
3 & 0.132252 & 2.336 & 0.010061 \tabularnewline
4 & 0.093114 & 1.6447 & 0.050517 \tabularnewline
5 & 0.093428 & 1.6503 & 0.049946 \tabularnewline
6 & -0.039674 & -0.7008 & 0.241979 \tabularnewline
7 & 0.07689 & 1.3582 & 0.087699 \tabularnewline
8 & 0.039877 & 0.7044 & 0.240862 \tabularnewline
9 & 0.193305 & 3.4144 & 0.000362 \tabularnewline
10 & 0.127676 & 2.2552 & 0.012406 \tabularnewline
11 & 0.136637 & 2.4135 & 0.008188 \tabularnewline
12 & -0.215254 & -3.8022 & 8.6e-05 \tabularnewline
13 & -0.626847 & -11.0723 & 0 \tabularnewline
14 & -0.006964 & -0.123 & 0.451092 \tabularnewline
15 & 0.029423 & 0.5197 & 0.301814 \tabularnewline
16 & 0.026208 & 0.4629 & 0.321873 \tabularnewline
17 & 0.035284 & 0.6232 & 0.266792 \tabularnewline
18 & 0.019447 & 0.3435 & 0.365726 \tabularnewline
19 & 0.025384 & 0.4484 & 0.327095 \tabularnewline
20 & -0.017547 & -0.3099 & 0.378407 \tabularnewline
21 & 0.008473 & 0.1497 & 0.440563 \tabularnewline
22 & 0.009484 & 0.1675 & 0.433532 \tabularnewline
23 & 0.035919 & 0.6345 & 0.263126 \tabularnewline
24 & -0.057767 & -1.0204 & 0.154171 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150377&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]0.953328[/C][C]16.8391[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.285978[/C][C]-5.0514[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.132252[/C][C]2.336[/C][C]0.010061[/C][/ROW]
[ROW][C]4[/C][C]0.093114[/C][C]1.6447[/C][C]0.050517[/C][/ROW]
[ROW][C]5[/C][C]0.093428[/C][C]1.6503[/C][C]0.049946[/C][/ROW]
[ROW][C]6[/C][C]-0.039674[/C][C]-0.7008[/C][C]0.241979[/C][/ROW]
[ROW][C]7[/C][C]0.07689[/C][C]1.3582[/C][C]0.087699[/C][/ROW]
[ROW][C]8[/C][C]0.039877[/C][C]0.7044[/C][C]0.240862[/C][/ROW]
[ROW][C]9[/C][C]0.193305[/C][C]3.4144[/C][C]0.000362[/C][/ROW]
[ROW][C]10[/C][C]0.127676[/C][C]2.2552[/C][C]0.012406[/C][/ROW]
[ROW][C]11[/C][C]0.136637[/C][C]2.4135[/C][C]0.008188[/C][/ROW]
[ROW][C]12[/C][C]-0.215254[/C][C]-3.8022[/C][C]8.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.626847[/C][C]-11.0723[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.006964[/C][C]-0.123[/C][C]0.451092[/C][/ROW]
[ROW][C]15[/C][C]0.029423[/C][C]0.5197[/C][C]0.301814[/C][/ROW]
[ROW][C]16[/C][C]0.026208[/C][C]0.4629[/C][C]0.321873[/C][/ROW]
[ROW][C]17[/C][C]0.035284[/C][C]0.6232[/C][C]0.266792[/C][/ROW]
[ROW][C]18[/C][C]0.019447[/C][C]0.3435[/C][C]0.365726[/C][/ROW]
[ROW][C]19[/C][C]0.025384[/C][C]0.4484[/C][C]0.327095[/C][/ROW]
[ROW][C]20[/C][C]-0.017547[/C][C]-0.3099[/C][C]0.378407[/C][/ROW]
[ROW][C]21[/C][C]0.008473[/C][C]0.1497[/C][C]0.440563[/C][/ROW]
[ROW][C]22[/C][C]0.009484[/C][C]0.1675[/C][C]0.433532[/C][/ROW]
[ROW][C]23[/C][C]0.035919[/C][C]0.6345[/C][C]0.263126[/C][/ROW]
[ROW][C]24[/C][C]-0.057767[/C][C]-1.0204[/C][C]0.154171[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150377&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150377&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	0.953328	16.8391	0
2	-0.285978	-5.0514	0
3	0.132252	2.336	0.010061
4	0.093114	1.6447	0.050517
5	0.093428	1.6503	0.049946
6	-0.039674	-0.7008	0.241979
7	0.07689	1.3582	0.087699
8	0.039877	0.7044	0.240862
9	0.193305	3.4144	0.000362
10	0.127676	2.2552	0.012406
11	0.136637	2.4135	0.008188
12	-0.215254	-3.8022	8.6e-05
13	-0.626847	-11.0723	0
14	-0.006964	-0.123	0.451092
15	0.029423	0.5197	0.301814
16	0.026208	0.4629	0.321873
17	0.035284	0.6232	0.266792
18	0.019447	0.3435	0.365726
19	0.025384	0.4484	0.327095
20	-0.017547	-0.3099	0.378407
21	0.008473	0.1497	0.440563
22	0.009484	0.1675	0.433532
23	0.035919	0.6345	0.263126
24	-0.057767	-1.0204	0.154171

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 = 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 (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