Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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

Fri, 21 Dec 2012 05:18:26 -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/2012/Dec/21/t13560851536n9avc3t0oyopbm.htm/, Retrieved Fri, 26 Apr 2024 17:10:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203409, Retrieved Fri, 26 Apr 2024 17:10:04 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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 P     [(Partial) Autocorrelation Function] [ws9_ACF_3] [2012-11-26 21:26:48] [be6dd99035eed41c2358246baf91f928]
-   P         [(Partial) Autocorrelation Function] [Paper_4.4_ACF2d] [2012-12-21 10:18:26] [b38599bd3d78365f281c5a627888d89a] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203409&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]3 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=203409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203409&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.570374	-10.792	0
2	0.184937	3.4992	0.000263
3	-0.122624	-2.3201	0.010447
4	0.059094	1.1181	0.132136
5	-0.033502	-0.6339	0.263277
6	0.069254	1.3103	0.09546
7	-0.107147	-2.0273	0.021685
8	0.060622	1.147	0.126068
9	0.012976	0.2455	0.403095
10	-0.103329	-1.9551	0.025676
11	0.30577	5.7854	0
12	-0.435766	-8.2451	0
13	0.175125	3.3135	0.000508
14	-0.026731	-0.5058	0.306661
15	0.062193	1.1767	0.12004
16	-0.063812	-1.2074	0.114043
17	0.041547	0.7861	0.216165
18	-0.078626	-1.4877	0.068859
19	0.097279	1.8406	0.033254
20	-0.042289	-0.8001	0.21208
21	0.046539	0.8806	0.189572
22	-0.050756	-0.9604	0.168762
23	0.045676	0.8642	0.194021
24	-0.094815	-1.794	0.03683
25	0.156381	2.9589	0.001647

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.570374 & -10.792 & 0 \tabularnewline
2 & 0.184937 & 3.4992 & 0.000263 \tabularnewline
3 & -0.122624 & -2.3201 & 0.010447 \tabularnewline
4 & 0.059094 & 1.1181 & 0.132136 \tabularnewline
5 & -0.033502 & -0.6339 & 0.263277 \tabularnewline
6 & 0.069254 & 1.3103 & 0.09546 \tabularnewline
7 & -0.107147 & -2.0273 & 0.021685 \tabularnewline
8 & 0.060622 & 1.147 & 0.126068 \tabularnewline
9 & 0.012976 & 0.2455 & 0.403095 \tabularnewline
10 & -0.103329 & -1.9551 & 0.025676 \tabularnewline
11 & 0.30577 & 5.7854 & 0 \tabularnewline
12 & -0.435766 & -8.2451 & 0 \tabularnewline
13 & 0.175125 & 3.3135 & 0.000508 \tabularnewline
14 & -0.026731 & -0.5058 & 0.306661 \tabularnewline
15 & 0.062193 & 1.1767 & 0.12004 \tabularnewline
16 & -0.063812 & -1.2074 & 0.114043 \tabularnewline
17 & 0.041547 & 0.7861 & 0.216165 \tabularnewline
18 & -0.078626 & -1.4877 & 0.068859 \tabularnewline
19 & 0.097279 & 1.8406 & 0.033254 \tabularnewline
20 & -0.042289 & -0.8001 & 0.21208 \tabularnewline
21 & 0.046539 & 0.8806 & 0.189572 \tabularnewline
22 & -0.050756 & -0.9604 & 0.168762 \tabularnewline
23 & 0.045676 & 0.8642 & 0.194021 \tabularnewline
24 & -0.094815 & -1.794 & 0.03683 \tabularnewline
25 & 0.156381 & 2.9589 & 0.001647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203409&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]-0.570374[/C][C]-10.792[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.184937[/C][C]3.4992[/C][C]0.000263[/C][/ROW]
[ROW][C]3[/C][C]-0.122624[/C][C]-2.3201[/C][C]0.010447[/C][/ROW]
[ROW][C]4[/C][C]0.059094[/C][C]1.1181[/C][C]0.132136[/C][/ROW]
[ROW][C]5[/C][C]-0.033502[/C][C]-0.6339[/C][C]0.263277[/C][/ROW]
[ROW][C]6[/C][C]0.069254[/C][C]1.3103[/C][C]0.09546[/C][/ROW]
[ROW][C]7[/C][C]-0.107147[/C][C]-2.0273[/C][C]0.021685[/C][/ROW]
[ROW][C]8[/C][C]0.060622[/C][C]1.147[/C][C]0.126068[/C][/ROW]
[ROW][C]9[/C][C]0.012976[/C][C]0.2455[/C][C]0.403095[/C][/ROW]
[ROW][C]10[/C][C]-0.103329[/C][C]-1.9551[/C][C]0.025676[/C][/ROW]
[ROW][C]11[/C][C]0.30577[/C][C]5.7854[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]-0.435766[/C][C]-8.2451[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.175125[/C][C]3.3135[/C][C]0.000508[/C][/ROW]
[ROW][C]14[/C][C]-0.026731[/C][C]-0.5058[/C][C]0.306661[/C][/ROW]
[ROW][C]15[/C][C]0.062193[/C][C]1.1767[/C][C]0.12004[/C][/ROW]
[ROW][C]16[/C][C]-0.063812[/C][C]-1.2074[/C][C]0.114043[/C][/ROW]
[ROW][C]17[/C][C]0.041547[/C][C]0.7861[/C][C]0.216165[/C][/ROW]
[ROW][C]18[/C][C]-0.078626[/C][C]-1.4877[/C][C]0.068859[/C][/ROW]
[ROW][C]19[/C][C]0.097279[/C][C]1.8406[/C][C]0.033254[/C][/ROW]
[ROW][C]20[/C][C]-0.042289[/C][C]-0.8001[/C][C]0.21208[/C][/ROW]
[ROW][C]21[/C][C]0.046539[/C][C]0.8806[/C][C]0.189572[/C][/ROW]
[ROW][C]22[/C][C]-0.050756[/C][C]-0.9604[/C][C]0.168762[/C][/ROW]
[ROW][C]23[/C][C]0.045676[/C][C]0.8642[/C][C]0.194021[/C][/ROW]
[ROW][C]24[/C][C]-0.094815[/C][C]-1.794[/C][C]0.03683[/C][/ROW]
[ROW][C]25[/C][C]0.156381[/C][C]2.9589[/C][C]0.001647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203409&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	-0.570374	-10.792	0
2	0.184937	3.4992	0.000263
3	-0.122624	-2.3201	0.010447
4	0.059094	1.1181	0.132136
5	-0.033502	-0.6339	0.263277
6	0.069254	1.3103	0.09546
7	-0.107147	-2.0273	0.021685
8	0.060622	1.147	0.126068
9	0.012976	0.2455	0.403095
10	-0.103329	-1.9551	0.025676
11	0.30577	5.7854	0
12	-0.435766	-8.2451	0
13	0.175125	3.3135	0.000508
14	-0.026731	-0.5058	0.306661
15	0.062193	1.1767	0.12004
16	-0.063812	-1.2074	0.114043
17	0.041547	0.7861	0.216165
18	-0.078626	-1.4877	0.068859
19	0.097279	1.8406	0.033254
20	-0.042289	-0.8001	0.21208
21	0.046539	0.8806	0.189572
22	-0.050756	-0.9604	0.168762
23	0.045676	0.8642	0.194021
24	-0.094815	-1.794	0.03683
25	0.156381	2.9589	0.001647

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.570374	-10.792	0
2	-0.208086	-3.9372	5e-05
3	-0.176429	-3.3382	0.000466
4	-0.111244	-2.1048	0.018001
5	-0.081384	-1.5399	0.062238
6	0.02778	0.5256	0.299738
7	-0.07197	-1.3617	0.087068
8	-0.063875	-1.2086	0.113812
9	0.027877	0.5274	0.299104
10	-0.130258	-2.4646	0.007093
11	0.289718	5.4817	0
12	-0.182367	-3.4505	0.000313
13	-0.28728	-5.4356	0
14	-0.122546	-2.3187	0.010487
15	-0.045696	-0.8646	0.193916
16	-0.066796	-1.2638	0.103554
17	-0.082324	-1.5576	0.060101
18	-0.070529	-1.3345	0.091449
19	-0.066205	-1.2527	0.105575
20	-0.038245	-0.7236	0.234885
21	0.088548	1.6754	0.047363
22	-0.091166	-1.7249	0.042701
23	0.189198	3.5798	0.000196
24	-0.149114	-2.8214	0.002524
25	-0.074302	-1.4059	0.080316

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.570374 & -10.792 & 0 \tabularnewline
2 & -0.208086 & -3.9372 & 5e-05 \tabularnewline
3 & -0.176429 & -3.3382 & 0.000466 \tabularnewline
4 & -0.111244 & -2.1048 & 0.018001 \tabularnewline
5 & -0.081384 & -1.5399 & 0.062238 \tabularnewline
6 & 0.02778 & 0.5256 & 0.299738 \tabularnewline
7 & -0.07197 & -1.3617 & 0.087068 \tabularnewline
8 & -0.063875 & -1.2086 & 0.113812 \tabularnewline
9 & 0.027877 & 0.5274 & 0.299104 \tabularnewline
10 & -0.130258 & -2.4646 & 0.007093 \tabularnewline
11 & 0.289718 & 5.4817 & 0 \tabularnewline
12 & -0.182367 & -3.4505 & 0.000313 \tabularnewline
13 & -0.28728 & -5.4356 & 0 \tabularnewline
14 & -0.122546 & -2.3187 & 0.010487 \tabularnewline
15 & -0.045696 & -0.8646 & 0.193916 \tabularnewline
16 & -0.066796 & -1.2638 & 0.103554 \tabularnewline
17 & -0.082324 & -1.5576 & 0.060101 \tabularnewline
18 & -0.070529 & -1.3345 & 0.091449 \tabularnewline
19 & -0.066205 & -1.2527 & 0.105575 \tabularnewline
20 & -0.038245 & -0.7236 & 0.234885 \tabularnewline
21 & 0.088548 & 1.6754 & 0.047363 \tabularnewline
22 & -0.091166 & -1.7249 & 0.042701 \tabularnewline
23 & 0.189198 & 3.5798 & 0.000196 \tabularnewline
24 & -0.149114 & -2.8214 & 0.002524 \tabularnewline
25 & -0.074302 & -1.4059 & 0.080316 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203409&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]-0.570374[/C][C]-10.792[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.208086[/C][C]-3.9372[/C][C]5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.176429[/C][C]-3.3382[/C][C]0.000466[/C][/ROW]
[ROW][C]4[/C][C]-0.111244[/C][C]-2.1048[/C][C]0.018001[/C][/ROW]
[ROW][C]5[/C][C]-0.081384[/C][C]-1.5399[/C][C]0.062238[/C][/ROW]
[ROW][C]6[/C][C]0.02778[/C][C]0.5256[/C][C]0.299738[/C][/ROW]
[ROW][C]7[/C][C]-0.07197[/C][C]-1.3617[/C][C]0.087068[/C][/ROW]
[ROW][C]8[/C][C]-0.063875[/C][C]-1.2086[/C][C]0.113812[/C][/ROW]
[ROW][C]9[/C][C]0.027877[/C][C]0.5274[/C][C]0.299104[/C][/ROW]
[ROW][C]10[/C][C]-0.130258[/C][C]-2.4646[/C][C]0.007093[/C][/ROW]
[ROW][C]11[/C][C]0.289718[/C][C]5.4817[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]-0.182367[/C][C]-3.4505[/C][C]0.000313[/C][/ROW]
[ROW][C]13[/C][C]-0.28728[/C][C]-5.4356[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.122546[/C][C]-2.3187[/C][C]0.010487[/C][/ROW]
[ROW][C]15[/C][C]-0.045696[/C][C]-0.8646[/C][C]0.193916[/C][/ROW]
[ROW][C]16[/C][C]-0.066796[/C][C]-1.2638[/C][C]0.103554[/C][/ROW]
[ROW][C]17[/C][C]-0.082324[/C][C]-1.5576[/C][C]0.060101[/C][/ROW]
[ROW][C]18[/C][C]-0.070529[/C][C]-1.3345[/C][C]0.091449[/C][/ROW]
[ROW][C]19[/C][C]-0.066205[/C][C]-1.2527[/C][C]0.105575[/C][/ROW]
[ROW][C]20[/C][C]-0.038245[/C][C]-0.7236[/C][C]0.234885[/C][/ROW]
[ROW][C]21[/C][C]0.088548[/C][C]1.6754[/C][C]0.047363[/C][/ROW]
[ROW][C]22[/C][C]-0.091166[/C][C]-1.7249[/C][C]0.042701[/C][/ROW]
[ROW][C]23[/C][C]0.189198[/C][C]3.5798[/C][C]0.000196[/C][/ROW]
[ROW][C]24[/C][C]-0.149114[/C][C]-2.8214[/C][C]0.002524[/C][/ROW]
[ROW][C]25[/C][C]-0.074302[/C][C]-1.4059[/C][C]0.080316[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203409&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	-0.570374	-10.792	0
2	-0.208086	-3.9372	5e-05
3	-0.176429	-3.3382	0.000466
4	-0.111244	-2.1048	0.018001
5	-0.081384	-1.5399	0.062238
6	0.02778	0.5256	0.299738
7	-0.07197	-1.3617	0.087068
8	-0.063875	-1.2086	0.113812
9	0.027877	0.5274	0.299104
10	-0.130258	-2.4646	0.007093
11	0.289718	5.4817	0
12	-0.182367	-3.4505	0.000313
13	-0.28728	-5.4356	0
14	-0.122546	-2.3187	0.010487
15	-0.045696	-0.8646	0.193916
16	-0.066796	-1.2638	0.103554
17	-0.082324	-1.5576	0.060101
18	-0.070529	-1.3345	0.091449
19	-0.066205	-1.2527	0.105575
20	-0.038245	-0.7236	0.234885
21	0.088548	1.6754	0.047363
22	-0.091166	-1.7249	0.042701
23	0.189198	3.5798	0.000196
24	-0.149114	-2.8214	0.002524
25	-0.074302	-1.4059	0.080316

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 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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