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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

Fri, 12 Dec 2008 04:32:48 -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/2008/Dec/12/t1229081607o3xzl4qnhqv62u2.htm/, Retrieved Tue, 14 May 2024 23:27:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32572, Retrieved Tue, 14 May 2024 23:27:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-     [Variance Reduction Matrix] [VRM - vaste rente...] [2008-12-12 10:51:08] [c5a66f1c8528a963efc2b82a8519f117]
- RM D  [Standard Deviation-Mean Plot] [SDMP inschrijving...] [2008-12-12 11:03:14] [c5a66f1c8528a963efc2b82a8519f117]
- RM      [Variance Reduction Matrix] [VRM - inschrijvin...] [2008-12-12 11:08:27] [c5a66f1c8528a963efc2b82a8519f117]
- RMP       [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:14:36] [c5a66f1c8528a963efc2b82a8519f117]
-   P           [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:32:48] [b4fc5040f26b33db57f84cfb8d1d2b82] [Current]
-                 [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:37:19] [c5a66f1c8528a963efc2b82a8519f117] 
- RM                [ARIMA Backward Selection] [ARIMA backward se...] [2008-12-12 11:51:13] [c5a66f1c8528a963efc2b82a8519f117] 
- RM                  [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-12 11:57:42] [c5a66f1c8528a963efc2b82a8519f117] 
F                       [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-12 12:06:55] [c5a66f1c8528a963efc2b82a8519f117] 
-  MPD                    [ARIMA Forecasting] [ARIMA forecasting...] [2009-12-16 20:44:06] [37a8d600db9abe09a2528d150ccff095] 
-  MPD                    [ARIMA Forecasting] [Arima forecast - ...] [2009-12-16 20:56:07] [37a8d600db9abe09a2528d150ccff095] 
-  MPD                [ARIMA Backward Selection] [Arima backward se...] [2009-12-16 15:42:38] [37a8d600db9abe09a2528d150ccff095] 
-  MPD              [(Partial) Autocorrelation Function] [ACF en PACF - uit...] [2009-12-11 15:34:04] [37a8d600db9abe09a2528d150ccff095] 

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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	'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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32572&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32572&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.194019	1.3581	0.090321
2	0.232072	1.6245	0.055342
3	0.124337	0.8704	0.194174
4	0.088123	0.6169	0.27009
5	0.025422	0.178	0.429747
6	0.040722	0.2851	0.388402
7	-0.104866	-0.7341	0.233205
8	0.018862	0.132	0.447749
9	-0.014135	-0.0989	0.460792
10	-0.150633	-1.0544	0.148428
11	-0.25804	-1.8063	0.038509
12	-0.106983	-0.7489	0.228755
13	-0.166168	-1.1632	0.125195
14	-0.005041	-0.0353	0.485997
15	-0.065545	-0.4588	0.324197
16	-0.067719	-0.474	0.318792
17	0.016773	0.1174	0.453506

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.194019 & 1.3581 & 0.090321 \tabularnewline
2 & 0.232072 & 1.6245 & 0.055342 \tabularnewline
3 & 0.124337 & 0.8704 & 0.194174 \tabularnewline
4 & 0.088123 & 0.6169 & 0.27009 \tabularnewline
5 & 0.025422 & 0.178 & 0.429747 \tabularnewline
6 & 0.040722 & 0.2851 & 0.388402 \tabularnewline
7 & -0.104866 & -0.7341 & 0.233205 \tabularnewline
8 & 0.018862 & 0.132 & 0.447749 \tabularnewline
9 & -0.014135 & -0.0989 & 0.460792 \tabularnewline
10 & -0.150633 & -1.0544 & 0.148428 \tabularnewline
11 & -0.25804 & -1.8063 & 0.038509 \tabularnewline
12 & -0.106983 & -0.7489 & 0.228755 \tabularnewline
13 & -0.166168 & -1.1632 & 0.125195 \tabularnewline
14 & -0.005041 & -0.0353 & 0.485997 \tabularnewline
15 & -0.065545 & -0.4588 & 0.324197 \tabularnewline
16 & -0.067719 & -0.474 & 0.318792 \tabularnewline
17 & 0.016773 & 0.1174 & 0.453506 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32572&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]0.194019[/C][C]1.3581[/C][C]0.090321[/C][/ROW]
[ROW][C]2[/C][C]0.232072[/C][C]1.6245[/C][C]0.055342[/C][/ROW]
[ROW][C]3[/C][C]0.124337[/C][C]0.8704[/C][C]0.194174[/C][/ROW]
[ROW][C]4[/C][C]0.088123[/C][C]0.6169[/C][C]0.27009[/C][/ROW]
[ROW][C]5[/C][C]0.025422[/C][C]0.178[/C][C]0.429747[/C][/ROW]
[ROW][C]6[/C][C]0.040722[/C][C]0.2851[/C][C]0.388402[/C][/ROW]
[ROW][C]7[/C][C]-0.104866[/C][C]-0.7341[/C][C]0.233205[/C][/ROW]
[ROW][C]8[/C][C]0.018862[/C][C]0.132[/C][C]0.447749[/C][/ROW]
[ROW][C]9[/C][C]-0.014135[/C][C]-0.0989[/C][C]0.460792[/C][/ROW]
[ROW][C]10[/C][C]-0.150633[/C][C]-1.0544[/C][C]0.148428[/C][/ROW]
[ROW][C]11[/C][C]-0.25804[/C][C]-1.8063[/C][C]0.038509[/C][/ROW]
[ROW][C]12[/C][C]-0.106983[/C][C]-0.7489[/C][C]0.228755[/C][/ROW]
[ROW][C]13[/C][C]-0.166168[/C][C]-1.1632[/C][C]0.125195[/C][/ROW]
[ROW][C]14[/C][C]-0.005041[/C][C]-0.0353[/C][C]0.485997[/C][/ROW]
[ROW][C]15[/C][C]-0.065545[/C][C]-0.4588[/C][C]0.324197[/C][/ROW]
[ROW][C]16[/C][C]-0.067719[/C][C]-0.474[/C][C]0.318792[/C][/ROW]
[ROW][C]17[/C][C]0.016773[/C][C]0.1174[/C][C]0.453506[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32572&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	0.194019	1.3581	0.090321
2	0.232072	1.6245	0.055342
3	0.124337	0.8704	0.194174
4	0.088123	0.6169	0.27009
5	0.025422	0.178	0.429747
6	0.040722	0.2851	0.388402
7	-0.104866	-0.7341	0.233205
8	0.018862	0.132	0.447749
9	-0.014135	-0.0989	0.460792
10	-0.150633	-1.0544	0.148428
11	-0.25804	-1.8063	0.038509
12	-0.106983	-0.7489	0.228755
13	-0.166168	-1.1632	0.125195
14	-0.005041	-0.0353	0.485997
15	-0.065545	-0.4588	0.324197
16	-0.067719	-0.474	0.318792
17	0.016773	0.1174	0.453506

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.194019	1.3581	0.090321
2	0.202033	1.4142	0.081808
3	0.05331	0.3732	0.355316
4	0.016186	0.1133	0.455127
5	-0.028115	-0.1968	0.422397
6	0.015121	0.1058	0.458069
7	-0.128965	-0.9028	0.185536
8	0.045125	0.3159	0.376719
9	0.022029	0.1542	0.439041
10	-0.161367	-1.1296	0.132079
11	-0.235755	-1.6503	0.052641
12	0.01555	0.1089	0.456882
13	-0.03167	-0.2217	0.412737
14	0.085568	0.599	0.275973
15	0.000391	0.0027	0.498912
16	-0.052925	-0.3705	0.356311
17	0.024412	0.1709	0.43251

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.194019 & 1.3581 & 0.090321 \tabularnewline
2 & 0.202033 & 1.4142 & 0.081808 \tabularnewline
3 & 0.05331 & 0.3732 & 0.355316 \tabularnewline
4 & 0.016186 & 0.1133 & 0.455127 \tabularnewline
5 & -0.028115 & -0.1968 & 0.422397 \tabularnewline
6 & 0.015121 & 0.1058 & 0.458069 \tabularnewline
7 & -0.128965 & -0.9028 & 0.185536 \tabularnewline
8 & 0.045125 & 0.3159 & 0.376719 \tabularnewline
9 & 0.022029 & 0.1542 & 0.439041 \tabularnewline
10 & -0.161367 & -1.1296 & 0.132079 \tabularnewline
11 & -0.235755 & -1.6503 & 0.052641 \tabularnewline
12 & 0.01555 & 0.1089 & 0.456882 \tabularnewline
13 & -0.03167 & -0.2217 & 0.412737 \tabularnewline
14 & 0.085568 & 0.599 & 0.275973 \tabularnewline
15 & 0.000391 & 0.0027 & 0.498912 \tabularnewline
16 & -0.052925 & -0.3705 & 0.356311 \tabularnewline
17 & 0.024412 & 0.1709 & 0.43251 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32572&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]0.194019[/C][C]1.3581[/C][C]0.090321[/C][/ROW]
[ROW][C]2[/C][C]0.202033[/C][C]1.4142[/C][C]0.081808[/C][/ROW]
[ROW][C]3[/C][C]0.05331[/C][C]0.3732[/C][C]0.355316[/C][/ROW]
[ROW][C]4[/C][C]0.016186[/C][C]0.1133[/C][C]0.455127[/C][/ROW]
[ROW][C]5[/C][C]-0.028115[/C][C]-0.1968[/C][C]0.422397[/C][/ROW]
[ROW][C]6[/C][C]0.015121[/C][C]0.1058[/C][C]0.458069[/C][/ROW]
[ROW][C]7[/C][C]-0.128965[/C][C]-0.9028[/C][C]0.185536[/C][/ROW]
[ROW][C]8[/C][C]0.045125[/C][C]0.3159[/C][C]0.376719[/C][/ROW]
[ROW][C]9[/C][C]0.022029[/C][C]0.1542[/C][C]0.439041[/C][/ROW]
[ROW][C]10[/C][C]-0.161367[/C][C]-1.1296[/C][C]0.132079[/C][/ROW]
[ROW][C]11[/C][C]-0.235755[/C][C]-1.6503[/C][C]0.052641[/C][/ROW]
[ROW][C]12[/C][C]0.01555[/C][C]0.1089[/C][C]0.456882[/C][/ROW]
[ROW][C]13[/C][C]-0.03167[/C][C]-0.2217[/C][C]0.412737[/C][/ROW]
[ROW][C]14[/C][C]0.085568[/C][C]0.599[/C][C]0.275973[/C][/ROW]
[ROW][C]15[/C][C]0.000391[/C][C]0.0027[/C][C]0.498912[/C][/ROW]
[ROW][C]16[/C][C]-0.052925[/C][C]-0.3705[/C][C]0.356311[/C][/ROW]
[ROW][C]17[/C][C]0.024412[/C][C]0.1709[/C][C]0.43251[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32572&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32572&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	0.194019	1.3581	0.090321
2	0.202033	1.4142	0.081808
3	0.05331	0.3732	0.355316
4	0.016186	0.1133	0.455127
5	-0.028115	-0.1968	0.422397
6	0.015121	0.1058	0.458069
7	-0.128965	-0.9028	0.185536
8	0.045125	0.3159	0.376719
9	0.022029	0.1542	0.439041
10	-0.161367	-1.1296	0.132079
11	-0.235755	-1.6503	0.052641
12	0.01555	0.1089	0.456882
13	-0.03167	-0.2217	0.412737
14	0.085568	0.599	0.275973
15	0.000391	0.0027	0.498912
16	-0.052925	-0.3705	0.356311
17	0.024412	0.1709	0.43251

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.3 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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