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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

Mon, 13 Dec 2010 19:38:16 +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/13/t1292269039yr2373vdr3cyig6.htm/, Retrieved Mon, 06 May 2024 17:34:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109113, Retrieved Mon, 06 May 2024 17:34:58 +0000

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Original text written by user:

workshop 6

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

127

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   [Spectral Analysis] [Unemployment] [2010-11-29 09:21:38] [b98453cac15ba1066b407e146608df68]
- RMPD      [(Partial) Autocorrelation Function] [tutorial] [2010-12-13 19:38:16] [7b74daa7106fa81c528ad8096e75c3c0] [Current]
- R PD        [(Partial) Autocorrelation Function] [tutorial 9d1] [2010-12-15 16:44:23] [8b2514d8f13517d765015fc185a22b4b] 
-   PD          [(Partial) Autocorrelation Function] [ACF stationair] [2010-12-17 20:36:18] [46df8573ee32a55e1a6edcfb6691f406] 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109113&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109113&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109113&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.035195	-0.763	0.222919
2	-0.007638	-0.1656	0.434274
3	-0.005099	-0.1105	0.456013
4	-0.811432	-17.5914	0
5	0.046278	1.0033	0.158119
6	0.002778	0.0602	0.475997
7	0.046614	1.0106	0.15637
8	0.423649	9.1845	0
9	-0.03039	-0.6588	0.255164
10	0.011673	0.2531	0.400164
11	-0.067863	-1.4712	0.070948
12	-0.084463	-1.8311	0.033859
13	0.005836	0.1265	0.449685
14	-0.01935	-0.4195	0.337523
15	0.060518	1.312	0.095081
16	-0.093869	-2.035	0.021204
17	0.014007	0.3037	0.38076
18	0.015766	0.3418	0.366329
19	-0.038	-0.8238	0.205228
20	0.14541	3.1524	0.000861
21	-0.033124	-0.7181	0.236524
22	-0.006105	-0.1324	0.447379
23	0.018947	0.4108	0.340716
24	-0.132985	-2.883	0.00206
25	0.05683	1.232	0.109276
26	-0.009573	-0.2075	0.417839

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.035195 & -0.763 & 0.222919 \tabularnewline
2 & -0.007638 & -0.1656 & 0.434274 \tabularnewline
3 & -0.005099 & -0.1105 & 0.456013 \tabularnewline
4 & -0.811432 & -17.5914 & 0 \tabularnewline
5 & 0.046278 & 1.0033 & 0.158119 \tabularnewline
6 & 0.002778 & 0.0602 & 0.475997 \tabularnewline
7 & 0.046614 & 1.0106 & 0.15637 \tabularnewline
8 & 0.423649 & 9.1845 & 0 \tabularnewline
9 & -0.03039 & -0.6588 & 0.255164 \tabularnewline
10 & 0.011673 & 0.2531 & 0.400164 \tabularnewline
11 & -0.067863 & -1.4712 & 0.070948 \tabularnewline
12 & -0.084463 & -1.8311 & 0.033859 \tabularnewline
13 & 0.005836 & 0.1265 & 0.449685 \tabularnewline
14 & -0.01935 & -0.4195 & 0.337523 \tabularnewline
15 & 0.060518 & 1.312 & 0.095081 \tabularnewline
16 & -0.093869 & -2.035 & 0.021204 \tabularnewline
17 & 0.014007 & 0.3037 & 0.38076 \tabularnewline
18 & 0.015766 & 0.3418 & 0.366329 \tabularnewline
19 & -0.038 & -0.8238 & 0.205228 \tabularnewline
20 & 0.14541 & 3.1524 & 0.000861 \tabularnewline
21 & -0.033124 & -0.7181 & 0.236524 \tabularnewline
22 & -0.006105 & -0.1324 & 0.447379 \tabularnewline
23 & 0.018947 & 0.4108 & 0.340716 \tabularnewline
24 & -0.132985 & -2.883 & 0.00206 \tabularnewline
25 & 0.05683 & 1.232 & 0.109276 \tabularnewline
26 & -0.009573 & -0.2075 & 0.417839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109113&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]-0.035195[/C][C]-0.763[/C][C]0.222919[/C][/ROW]
[ROW][C]2[/C][C]-0.007638[/C][C]-0.1656[/C][C]0.434274[/C][/ROW]
[ROW][C]3[/C][C]-0.005099[/C][C]-0.1105[/C][C]0.456013[/C][/ROW]
[ROW][C]4[/C][C]-0.811432[/C][C]-17.5914[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.046278[/C][C]1.0033[/C][C]0.158119[/C][/ROW]
[ROW][C]6[/C][C]0.002778[/C][C]0.0602[/C][C]0.475997[/C][/ROW]
[ROW][C]7[/C][C]0.046614[/C][C]1.0106[/C][C]0.15637[/C][/ROW]
[ROW][C]8[/C][C]0.423649[/C][C]9.1845[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.03039[/C][C]-0.6588[/C][C]0.255164[/C][/ROW]
[ROW][C]10[/C][C]0.011673[/C][C]0.2531[/C][C]0.400164[/C][/ROW]
[ROW][C]11[/C][C]-0.067863[/C][C]-1.4712[/C][C]0.070948[/C][/ROW]
[ROW][C]12[/C][C]-0.084463[/C][C]-1.8311[/C][C]0.033859[/C][/ROW]
[ROW][C]13[/C][C]0.005836[/C][C]0.1265[/C][C]0.449685[/C][/ROW]
[ROW][C]14[/C][C]-0.01935[/C][C]-0.4195[/C][C]0.337523[/C][/ROW]
[ROW][C]15[/C][C]0.060518[/C][C]1.312[/C][C]0.095081[/C][/ROW]
[ROW][C]16[/C][C]-0.093869[/C][C]-2.035[/C][C]0.021204[/C][/ROW]
[ROW][C]17[/C][C]0.014007[/C][C]0.3037[/C][C]0.38076[/C][/ROW]
[ROW][C]18[/C][C]0.015766[/C][C]0.3418[/C][C]0.366329[/C][/ROW]
[ROW][C]19[/C][C]-0.038[/C][C]-0.8238[/C][C]0.205228[/C][/ROW]
[ROW][C]20[/C][C]0.14541[/C][C]3.1524[/C][C]0.000861[/C][/ROW]
[ROW][C]21[/C][C]-0.033124[/C][C]-0.7181[/C][C]0.236524[/C][/ROW]
[ROW][C]22[/C][C]-0.006105[/C][C]-0.1324[/C][C]0.447379[/C][/ROW]
[ROW][C]23[/C][C]0.018947[/C][C]0.4108[/C][C]0.340716[/C][/ROW]
[ROW][C]24[/C][C]-0.132985[/C][C]-2.883[/C][C]0.00206[/C][/ROW]
[ROW][C]25[/C][C]0.05683[/C][C]1.232[/C][C]0.109276[/C][/ROW]
[ROW][C]26[/C][C]-0.009573[/C][C]-0.2075[/C][C]0.417839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109113&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109113&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	-0.035195	-0.763	0.222919
2	-0.007638	-0.1656	0.434274
3	-0.005099	-0.1105	0.456013
4	-0.811432	-17.5914	0
5	0.046278	1.0033	0.158119
6	0.002778	0.0602	0.475997
7	0.046614	1.0106	0.15637
8	0.423649	9.1845	0
9	-0.03039	-0.6588	0.255164
10	0.011673	0.2531	0.400164
11	-0.067863	-1.4712	0.070948
12	-0.084463	-1.8311	0.033859
13	0.005836	0.1265	0.449685
14	-0.01935	-0.4195	0.337523
15	0.060518	1.312	0.095081
16	-0.093869	-2.035	0.021204
17	0.014007	0.3037	0.38076
18	0.015766	0.3418	0.366329
19	-0.038	-0.8238	0.205228
20	0.14541	3.1524	0.000861
21	-0.033124	-0.7181	0.236524
22	-0.006105	-0.1324	0.447379
23	0.018947	0.4108	0.340716
24	-0.132985	-2.883	0.00206
25	0.05683	1.232	0.109276
26	-0.009573	-0.2075	0.417839

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.035195	-0.763	0.222919
2	-0.008888	-0.1927	0.423644
3	-0.00569	-0.1234	0.450935
4	-0.812981	-17.625	0
5	-0.045157	-0.979	0.164049
6	-0.048226	-1.0455	0.148159
7	0.039143	0.8486	0.198268
8	-0.689958	-14.9579	0
9	-0.038703	-0.8391	0.200932
10	-0.106837	-2.3162	0.010489
11	-0.020238	-0.4388	0.330522
12	-0.37416	-8.1116	0
13	-0.04667	-1.0118	0.156081
14	-0.130713	-2.8338	0.002399
15	-0.062176	-1.3479	0.089164
16	-0.17828	-3.865	6.3e-05
17	-0.048175	-1.0444	0.148417
18	-0.10485	-2.2731	0.011736
19	-0.094377	-2.046	0.020654
20	0.019204	0.4163	0.338676
21	-0.106078	-2.2997	0.010951
22	-0.02959	-0.6415	0.260756
23	-0.057894	-1.2551	0.105032
24	0.031097	0.6742	0.250271
25	-0.003697	-0.0801	0.468078
26	-0.018706	-0.4055	0.342634

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.035195 & -0.763 & 0.222919 \tabularnewline
2 & -0.008888 & -0.1927 & 0.423644 \tabularnewline
3 & -0.00569 & -0.1234 & 0.450935 \tabularnewline
4 & -0.812981 & -17.625 & 0 \tabularnewline
5 & -0.045157 & -0.979 & 0.164049 \tabularnewline
6 & -0.048226 & -1.0455 & 0.148159 \tabularnewline
7 & 0.039143 & 0.8486 & 0.198268 \tabularnewline
8 & -0.689958 & -14.9579 & 0 \tabularnewline
9 & -0.038703 & -0.8391 & 0.200932 \tabularnewline
10 & -0.106837 & -2.3162 & 0.010489 \tabularnewline
11 & -0.020238 & -0.4388 & 0.330522 \tabularnewline
12 & -0.37416 & -8.1116 & 0 \tabularnewline
13 & -0.04667 & -1.0118 & 0.156081 \tabularnewline
14 & -0.130713 & -2.8338 & 0.002399 \tabularnewline
15 & -0.062176 & -1.3479 & 0.089164 \tabularnewline
16 & -0.17828 & -3.865 & 6.3e-05 \tabularnewline
17 & -0.048175 & -1.0444 & 0.148417 \tabularnewline
18 & -0.10485 & -2.2731 & 0.011736 \tabularnewline
19 & -0.094377 & -2.046 & 0.020654 \tabularnewline
20 & 0.019204 & 0.4163 & 0.338676 \tabularnewline
21 & -0.106078 & -2.2997 & 0.010951 \tabularnewline
22 & -0.02959 & -0.6415 & 0.260756 \tabularnewline
23 & -0.057894 & -1.2551 & 0.105032 \tabularnewline
24 & 0.031097 & 0.6742 & 0.250271 \tabularnewline
25 & -0.003697 & -0.0801 & 0.468078 \tabularnewline
26 & -0.018706 & -0.4055 & 0.342634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109113&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]-0.035195[/C][C]-0.763[/C][C]0.222919[/C][/ROW]
[ROW][C]2[/C][C]-0.008888[/C][C]-0.1927[/C][C]0.423644[/C][/ROW]
[ROW][C]3[/C][C]-0.00569[/C][C]-0.1234[/C][C]0.450935[/C][/ROW]
[ROW][C]4[/C][C]-0.812981[/C][C]-17.625[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.045157[/C][C]-0.979[/C][C]0.164049[/C][/ROW]
[ROW][C]6[/C][C]-0.048226[/C][C]-1.0455[/C][C]0.148159[/C][/ROW]
[ROW][C]7[/C][C]0.039143[/C][C]0.8486[/C][C]0.198268[/C][/ROW]
[ROW][C]8[/C][C]-0.689958[/C][C]-14.9579[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.038703[/C][C]-0.8391[/C][C]0.200932[/C][/ROW]
[ROW][C]10[/C][C]-0.106837[/C][C]-2.3162[/C][C]0.010489[/C][/ROW]
[ROW][C]11[/C][C]-0.020238[/C][C]-0.4388[/C][C]0.330522[/C][/ROW]
[ROW][C]12[/C][C]-0.37416[/C][C]-8.1116[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.04667[/C][C]-1.0118[/C][C]0.156081[/C][/ROW]
[ROW][C]14[/C][C]-0.130713[/C][C]-2.8338[/C][C]0.002399[/C][/ROW]
[ROW][C]15[/C][C]-0.062176[/C][C]-1.3479[/C][C]0.089164[/C][/ROW]
[ROW][C]16[/C][C]-0.17828[/C][C]-3.865[/C][C]6.3e-05[/C][/ROW]
[ROW][C]17[/C][C]-0.048175[/C][C]-1.0444[/C][C]0.148417[/C][/ROW]
[ROW][C]18[/C][C]-0.10485[/C][C]-2.2731[/C][C]0.011736[/C][/ROW]
[ROW][C]19[/C][C]-0.094377[/C][C]-2.046[/C][C]0.020654[/C][/ROW]
[ROW][C]20[/C][C]0.019204[/C][C]0.4163[/C][C]0.338676[/C][/ROW]
[ROW][C]21[/C][C]-0.106078[/C][C]-2.2997[/C][C]0.010951[/C][/ROW]
[ROW][C]22[/C][C]-0.02959[/C][C]-0.6415[/C][C]0.260756[/C][/ROW]
[ROW][C]23[/C][C]-0.057894[/C][C]-1.2551[/C][C]0.105032[/C][/ROW]
[ROW][C]24[/C][C]0.031097[/C][C]0.6742[/C][C]0.250271[/C][/ROW]
[ROW][C]25[/C][C]-0.003697[/C][C]-0.0801[/C][C]0.468078[/C][/ROW]
[ROW][C]26[/C][C]-0.018706[/C][C]-0.4055[/C][C]0.342634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109113&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109113&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	-0.035195	-0.763	0.222919
2	-0.008888	-0.1927	0.423644
3	-0.00569	-0.1234	0.450935
4	-0.812981	-17.625	0
5	-0.045157	-0.979	0.164049
6	-0.048226	-1.0455	0.148159
7	0.039143	0.8486	0.198268
8	-0.689958	-14.9579	0
9	-0.038703	-0.8391	0.200932
10	-0.106837	-2.3162	0.010489
11	-0.020238	-0.4388	0.330522
12	-0.37416	-8.1116	0
13	-0.04667	-1.0118	0.156081
14	-0.130713	-2.8338	0.002399
15	-0.062176	-1.3479	0.089164
16	-0.17828	-3.865	6.3e-05
17	-0.048175	-1.0444	0.148417
18	-0.10485	-2.2731	0.011736
19	-0.094377	-2.046	0.020654
20	0.019204	0.4163	0.338676
21	-0.106078	-2.2997	0.010951
22	-0.02959	-0.6415	0.260756
23	-0.057894	-1.2551	0.105032
24	0.031097	0.6742	0.250271
25	-0.003697	-0.0801	0.468078
26	-0.018706	-0.4055	0.342634

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 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; 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 <- 5
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