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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

Thu, 26 Nov 2009 08:00:23 -0700

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/2009/Nov/26/t1259247687gy895ufoaniakx5.htm/, Retrieved Mon, 29 Apr 2024 01:25:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60061, Retrieved Mon, 29 Apr 2024 01:25:57 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [] [2009-11-26 09:49:31] [d181e5359f7da6c8509e4702d1229fb0]
-   PD            [(Partial) Autocorrelation Function] [] [2009-11-26 15:00:23] [5858ea01c9bd81debbf921a11363ad90] [Current]

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Dataseries X:

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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=60061&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=60061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60061&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	0.539132	3.6961	0.000286
2	-0.084104	-0.5766	0.283485
3	-0.485474	-3.3282	0.000852
4	-0.509306	-3.4916	0.000528
5	-0.153806	-1.0544	0.148536
6	0.222409	1.5248	0.06701
7	0.40808	2.7977	0.003719
8	0.281064	1.9269	0.030027
9	-0.032811	-0.2249	0.411501
10	-0.188652	-1.2933	0.101109
11	-0.245291	-1.6816	0.049637
12	-0.246156	-1.6876	0.049061
13	-0.06995	-0.4796	0.316884
14	0.11225	0.7695	0.22271
15	0.138732	0.9511	0.173209
16	0.040288	0.2762	0.391802
17	-0.044295	-0.3037	0.381361
18	-0.083359	-0.5715	0.285199
19	-0.094364	-0.6469	0.260413
20	0.017555	0.1204	0.452358
21	0.111018	0.7611	0.2252
22	0.003426	0.0235	0.49068
23	-0.127978	-0.8774	0.192373
24	-0.156251	-1.0712	0.144774

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.539132 & 3.6961 & 0.000286 \tabularnewline
2 & -0.084104 & -0.5766 & 0.283485 \tabularnewline
3 & -0.485474 & -3.3282 & 0.000852 \tabularnewline
4 & -0.509306 & -3.4916 & 0.000528 \tabularnewline
5 & -0.153806 & -1.0544 & 0.148536 \tabularnewline
6 & 0.222409 & 1.5248 & 0.06701 \tabularnewline
7 & 0.40808 & 2.7977 & 0.003719 \tabularnewline
8 & 0.281064 & 1.9269 & 0.030027 \tabularnewline
9 & -0.032811 & -0.2249 & 0.411501 \tabularnewline
10 & -0.188652 & -1.2933 & 0.101109 \tabularnewline
11 & -0.245291 & -1.6816 & 0.049637 \tabularnewline
12 & -0.246156 & -1.6876 & 0.049061 \tabularnewline
13 & -0.06995 & -0.4796 & 0.316884 \tabularnewline
14 & 0.11225 & 0.7695 & 0.22271 \tabularnewline
15 & 0.138732 & 0.9511 & 0.173209 \tabularnewline
16 & 0.040288 & 0.2762 & 0.391802 \tabularnewline
17 & -0.044295 & -0.3037 & 0.381361 \tabularnewline
18 & -0.083359 & -0.5715 & 0.285199 \tabularnewline
19 & -0.094364 & -0.6469 & 0.260413 \tabularnewline
20 & 0.017555 & 0.1204 & 0.452358 \tabularnewline
21 & 0.111018 & 0.7611 & 0.2252 \tabularnewline
22 & 0.003426 & 0.0235 & 0.49068 \tabularnewline
23 & -0.127978 & -0.8774 & 0.192373 \tabularnewline
24 & -0.156251 & -1.0712 & 0.144774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60061&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]0.539132[/C][C]3.6961[/C][C]0.000286[/C][/ROW]
[ROW][C]2[/C][C]-0.084104[/C][C]-0.5766[/C][C]0.283485[/C][/ROW]
[ROW][C]3[/C][C]-0.485474[/C][C]-3.3282[/C][C]0.000852[/C][/ROW]
[ROW][C]4[/C][C]-0.509306[/C][C]-3.4916[/C][C]0.000528[/C][/ROW]
[ROW][C]5[/C][C]-0.153806[/C][C]-1.0544[/C][C]0.148536[/C][/ROW]
[ROW][C]6[/C][C]0.222409[/C][C]1.5248[/C][C]0.06701[/C][/ROW]
[ROW][C]7[/C][C]0.40808[/C][C]2.7977[/C][C]0.003719[/C][/ROW]
[ROW][C]8[/C][C]0.281064[/C][C]1.9269[/C][C]0.030027[/C][/ROW]
[ROW][C]9[/C][C]-0.032811[/C][C]-0.2249[/C][C]0.411501[/C][/ROW]
[ROW][C]10[/C][C]-0.188652[/C][C]-1.2933[/C][C]0.101109[/C][/ROW]
[ROW][C]11[/C][C]-0.245291[/C][C]-1.6816[/C][C]0.049637[/C][/ROW]
[ROW][C]12[/C][C]-0.246156[/C][C]-1.6876[/C][C]0.049061[/C][/ROW]
[ROW][C]13[/C][C]-0.06995[/C][C]-0.4796[/C][C]0.316884[/C][/ROW]
[ROW][C]14[/C][C]0.11225[/C][C]0.7695[/C][C]0.22271[/C][/ROW]
[ROW][C]15[/C][C]0.138732[/C][C]0.9511[/C][C]0.173209[/C][/ROW]
[ROW][C]16[/C][C]0.040288[/C][C]0.2762[/C][C]0.391802[/C][/ROW]
[ROW][C]17[/C][C]-0.044295[/C][C]-0.3037[/C][C]0.381361[/C][/ROW]
[ROW][C]18[/C][C]-0.083359[/C][C]-0.5715[/C][C]0.285199[/C][/ROW]
[ROW][C]19[/C][C]-0.094364[/C][C]-0.6469[/C][C]0.260413[/C][/ROW]
[ROW][C]20[/C][C]0.017555[/C][C]0.1204[/C][C]0.452358[/C][/ROW]
[ROW][C]21[/C][C]0.111018[/C][C]0.7611[/C][C]0.2252[/C][/ROW]
[ROW][C]22[/C][C]0.003426[/C][C]0.0235[/C][C]0.49068[/C][/ROW]
[ROW][C]23[/C][C]-0.127978[/C][C]-0.8774[/C][C]0.192373[/C][/ROW]
[ROW][C]24[/C][C]-0.156251[/C][C]-1.0712[/C][C]0.144774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60061&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	0.539132	3.6961	0.000286
2	-0.084104	-0.5766	0.283485
3	-0.485474	-3.3282	0.000852
4	-0.509306	-3.4916	0.000528
5	-0.153806	-1.0544	0.148536
6	0.222409	1.5248	0.06701
7	0.40808	2.7977	0.003719
8	0.281064	1.9269	0.030027
9	-0.032811	-0.2249	0.411501
10	-0.188652	-1.2933	0.101109
11	-0.245291	-1.6816	0.049637
12	-0.246156	-1.6876	0.049061
13	-0.06995	-0.4796	0.316884
14	0.11225	0.7695	0.22271
15	0.138732	0.9511	0.173209
16	0.040288	0.2762	0.391802
17	-0.044295	-0.3037	0.381361
18	-0.083359	-0.5715	0.285199
19	-0.094364	-0.6469	0.260413
20	0.017555	0.1204	0.452358
21	0.111018	0.7611	0.2252
22	0.003426	0.0235	0.49068
23	-0.127978	-0.8774	0.192373
24	-0.156251	-1.0712	0.144774

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.539132	3.6961	0.000286
2	-0.528334	-3.6221	0.000357
3	-0.256844	-1.7608	0.042386
4	-0.132599	-0.9091	0.183981
5	0.133876	0.9178	0.181702
6	0.01432	0.0982	0.461106
7	0.101888	0.6985	0.24415
8	-0.034198	-0.2344	0.407828
9	-0.036222	-0.2483	0.402481
10	0.16098	1.1036	0.137687
11	-0.145544	-0.9978	0.161743
12	-0.241944	-1.6587	0.051919
13	0.072802	0.4991	0.310016
14	0.007906	0.0542	0.478503
15	-0.188838	-1.2946	0.10089
16	-0.100719	-0.6905	0.246639
17	0.091349	0.6263	0.267088
18	-0.024166	-0.1657	0.434561
19	-0.034021	-0.2332	0.408297
20	0.15181	1.0408	0.151656
21	-0.046221	-0.3169	0.37637
22	-0.221338	-1.5174	0.06793
23	0.0041	0.0281	0.488848
24	-0.068848	-0.472	0.319557

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.539132 & 3.6961 & 0.000286 \tabularnewline
2 & -0.528334 & -3.6221 & 0.000357 \tabularnewline
3 & -0.256844 & -1.7608 & 0.042386 \tabularnewline
4 & -0.132599 & -0.9091 & 0.183981 \tabularnewline
5 & 0.133876 & 0.9178 & 0.181702 \tabularnewline
6 & 0.01432 & 0.0982 & 0.461106 \tabularnewline
7 & 0.101888 & 0.6985 & 0.24415 \tabularnewline
8 & -0.034198 & -0.2344 & 0.407828 \tabularnewline
9 & -0.036222 & -0.2483 & 0.402481 \tabularnewline
10 & 0.16098 & 1.1036 & 0.137687 \tabularnewline
11 & -0.145544 & -0.9978 & 0.161743 \tabularnewline
12 & -0.241944 & -1.6587 & 0.051919 \tabularnewline
13 & 0.072802 & 0.4991 & 0.310016 \tabularnewline
14 & 0.007906 & 0.0542 & 0.478503 \tabularnewline
15 & -0.188838 & -1.2946 & 0.10089 \tabularnewline
16 & -0.100719 & -0.6905 & 0.246639 \tabularnewline
17 & 0.091349 & 0.6263 & 0.267088 \tabularnewline
18 & -0.024166 & -0.1657 & 0.434561 \tabularnewline
19 & -0.034021 & -0.2332 & 0.408297 \tabularnewline
20 & 0.15181 & 1.0408 & 0.151656 \tabularnewline
21 & -0.046221 & -0.3169 & 0.37637 \tabularnewline
22 & -0.221338 & -1.5174 & 0.06793 \tabularnewline
23 & 0.0041 & 0.0281 & 0.488848 \tabularnewline
24 & -0.068848 & -0.472 & 0.319557 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60061&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]0.539132[/C][C]3.6961[/C][C]0.000286[/C][/ROW]
[ROW][C]2[/C][C]-0.528334[/C][C]-3.6221[/C][C]0.000357[/C][/ROW]
[ROW][C]3[/C][C]-0.256844[/C][C]-1.7608[/C][C]0.042386[/C][/ROW]
[ROW][C]4[/C][C]-0.132599[/C][C]-0.9091[/C][C]0.183981[/C][/ROW]
[ROW][C]5[/C][C]0.133876[/C][C]0.9178[/C][C]0.181702[/C][/ROW]
[ROW][C]6[/C][C]0.01432[/C][C]0.0982[/C][C]0.461106[/C][/ROW]
[ROW][C]7[/C][C]0.101888[/C][C]0.6985[/C][C]0.24415[/C][/ROW]
[ROW][C]8[/C][C]-0.034198[/C][C]-0.2344[/C][C]0.407828[/C][/ROW]
[ROW][C]9[/C][C]-0.036222[/C][C]-0.2483[/C][C]0.402481[/C][/ROW]
[ROW][C]10[/C][C]0.16098[/C][C]1.1036[/C][C]0.137687[/C][/ROW]
[ROW][C]11[/C][C]-0.145544[/C][C]-0.9978[/C][C]0.161743[/C][/ROW]
[ROW][C]12[/C][C]-0.241944[/C][C]-1.6587[/C][C]0.051919[/C][/ROW]
[ROW][C]13[/C][C]0.072802[/C][C]0.4991[/C][C]0.310016[/C][/ROW]
[ROW][C]14[/C][C]0.007906[/C][C]0.0542[/C][C]0.478503[/C][/ROW]
[ROW][C]15[/C][C]-0.188838[/C][C]-1.2946[/C][C]0.10089[/C][/ROW]
[ROW][C]16[/C][C]-0.100719[/C][C]-0.6905[/C][C]0.246639[/C][/ROW]
[ROW][C]17[/C][C]0.091349[/C][C]0.6263[/C][C]0.267088[/C][/ROW]
[ROW][C]18[/C][C]-0.024166[/C][C]-0.1657[/C][C]0.434561[/C][/ROW]
[ROW][C]19[/C][C]-0.034021[/C][C]-0.2332[/C][C]0.408297[/C][/ROW]
[ROW][C]20[/C][C]0.15181[/C][C]1.0408[/C][C]0.151656[/C][/ROW]
[ROW][C]21[/C][C]-0.046221[/C][C]-0.3169[/C][C]0.37637[/C][/ROW]
[ROW][C]22[/C][C]-0.221338[/C][C]-1.5174[/C][C]0.06793[/C][/ROW]
[ROW][C]23[/C][C]0.0041[/C][C]0.0281[/C][C]0.488848[/C][/ROW]
[ROW][C]24[/C][C]-0.068848[/C][C]-0.472[/C][C]0.319557[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60061&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	0.539132	3.6961	0.000286
2	-0.528334	-3.6221	0.000357
3	-0.256844	-1.7608	0.042386
4	-0.132599	-0.9091	0.183981
5	0.133876	0.9178	0.181702
6	0.01432	0.0982	0.461106
7	0.101888	0.6985	0.24415
8	-0.034198	-0.2344	0.407828
9	-0.036222	-0.2483	0.402481
10	0.16098	1.1036	0.137687
11	-0.145544	-0.9978	0.161743
12	-0.241944	-1.6587	0.051919
13	0.072802	0.4991	0.310016
14	0.007906	0.0542	0.478503
15	-0.188838	-1.2946	0.10089
16	-0.100719	-0.6905	0.246639
17	0.091349	0.6263	0.267088
18	-0.024166	-0.1657	0.434561
19	-0.034021	-0.2332	0.408297
20	0.15181	1.0408	0.151656
21	-0.046221	-0.3169	0.37637
22	-0.221338	-1.5174	0.06793
23	0.0041	0.0281	0.488848
24	-0.068848	-0.472	0.319557

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; 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