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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

Sun, 10 Dec 2017 14:49:52 +0100

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/2017/Dec/10/t1512913849c2kjtd9aqwvaoay.htm/, Retrieved Wed, 15 May 2024 01:10:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308924, Retrieved Wed, 15 May 2024 01:10:44 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

100

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2017-12-10 13:49:52] [a8eb7d5a2159f1476456749db34f2e15] [Current]

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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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308924&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308924&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.349668	-4.9327	1e-06
2	-0.134918	-1.9032	0.029226
3	0.040757	0.575	0.282986
4	0.009911	0.1398	0.444478
5	-0.06547	-0.9236	0.178414
6	0.019418	0.2739	0.392214
7	0.034213	0.4826	0.314944
8	-0.049846	-0.7032	0.241386
9	0.04481	0.6321	0.264018
10	0.022388	0.3158	0.376237
11	0.12537	1.7686	0.039249
12	-0.359186	-5.0669	0
13	0.046835	0.6607	0.254787
14	0.135324	1.909	0.028852
15	0.003875	0.0547	0.478228
16	-0.040017	-0.5645	0.286523
17	0.026472	0.3734	0.354609
18	0.121118	1.7086	0.044543
19	-0.136521	-1.9259	0.027773
20	0.008044	0.1135	0.454885
21	-0.015615	-0.2203	0.41294
22	0.052069	0.7345	0.231748
23	-0.026075	-0.3678	0.356692

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.349668 & -4.9327 & 1e-06 \tabularnewline
2 & -0.134918 & -1.9032 & 0.029226 \tabularnewline
3 & 0.040757 & 0.575 & 0.282986 \tabularnewline
4 & 0.009911 & 0.1398 & 0.444478 \tabularnewline
5 & -0.06547 & -0.9236 & 0.178414 \tabularnewline
6 & 0.019418 & 0.2739 & 0.392214 \tabularnewline
7 & 0.034213 & 0.4826 & 0.314944 \tabularnewline
8 & -0.049846 & -0.7032 & 0.241386 \tabularnewline
9 & 0.04481 & 0.6321 & 0.264018 \tabularnewline
10 & 0.022388 & 0.3158 & 0.376237 \tabularnewline
11 & 0.12537 & 1.7686 & 0.039249 \tabularnewline
12 & -0.359186 & -5.0669 & 0 \tabularnewline
13 & 0.046835 & 0.6607 & 0.254787 \tabularnewline
14 & 0.135324 & 1.909 & 0.028852 \tabularnewline
15 & 0.003875 & 0.0547 & 0.478228 \tabularnewline
16 & -0.040017 & -0.5645 & 0.286523 \tabularnewline
17 & 0.026472 & 0.3734 & 0.354609 \tabularnewline
18 & 0.121118 & 1.7086 & 0.044543 \tabularnewline
19 & -0.136521 & -1.9259 & 0.027773 \tabularnewline
20 & 0.008044 & 0.1135 & 0.454885 \tabularnewline
21 & -0.015615 & -0.2203 & 0.41294 \tabularnewline
22 & 0.052069 & 0.7345 & 0.231748 \tabularnewline
23 & -0.026075 & -0.3678 & 0.356692 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308924&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]-0.349668[/C][C]-4.9327[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.134918[/C][C]-1.9032[/C][C]0.029226[/C][/ROW]
[ROW][C]3[/C][C]0.040757[/C][C]0.575[/C][C]0.282986[/C][/ROW]
[ROW][C]4[/C][C]0.009911[/C][C]0.1398[/C][C]0.444478[/C][/ROW]
[ROW][C]5[/C][C]-0.06547[/C][C]-0.9236[/C][C]0.178414[/C][/ROW]
[ROW][C]6[/C][C]0.019418[/C][C]0.2739[/C][C]0.392214[/C][/ROW]
[ROW][C]7[/C][C]0.034213[/C][C]0.4826[/C][C]0.314944[/C][/ROW]
[ROW][C]8[/C][C]-0.049846[/C][C]-0.7032[/C][C]0.241386[/C][/ROW]
[ROW][C]9[/C][C]0.04481[/C][C]0.6321[/C][C]0.264018[/C][/ROW]
[ROW][C]10[/C][C]0.022388[/C][C]0.3158[/C][C]0.376237[/C][/ROW]
[ROW][C]11[/C][C]0.12537[/C][C]1.7686[/C][C]0.039249[/C][/ROW]
[ROW][C]12[/C][C]-0.359186[/C][C]-5.0669[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.046835[/C][C]0.6607[/C][C]0.254787[/C][/ROW]
[ROW][C]14[/C][C]0.135324[/C][C]1.909[/C][C]0.028852[/C][/ROW]
[ROW][C]15[/C][C]0.003875[/C][C]0.0547[/C][C]0.478228[/C][/ROW]
[ROW][C]16[/C][C]-0.040017[/C][C]-0.5645[/C][C]0.286523[/C][/ROW]
[ROW][C]17[/C][C]0.026472[/C][C]0.3734[/C][C]0.354609[/C][/ROW]
[ROW][C]18[/C][C]0.121118[/C][C]1.7086[/C][C]0.044543[/C][/ROW]
[ROW][C]19[/C][C]-0.136521[/C][C]-1.9259[/C][C]0.027773[/C][/ROW]
[ROW][C]20[/C][C]0.008044[/C][C]0.1135[/C][C]0.454885[/C][/ROW]
[ROW][C]21[/C][C]-0.015615[/C][C]-0.2203[/C][C]0.41294[/C][/ROW]
[ROW][C]22[/C][C]0.052069[/C][C]0.7345[/C][C]0.231748[/C][/ROW]
[ROW][C]23[/C][C]-0.026075[/C][C]-0.3678[/C][C]0.356692[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308924&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	-0.349668	-4.9327	1e-06
2	-0.134918	-1.9032	0.029226
3	0.040757	0.575	0.282986
4	0.009911	0.1398	0.444478
5	-0.06547	-0.9236	0.178414
6	0.019418	0.2739	0.392214
7	0.034213	0.4826	0.314944
8	-0.049846	-0.7032	0.241386
9	0.04481	0.6321	0.264018
10	0.022388	0.3158	0.376237
11	0.12537	1.7686	0.039249
12	-0.359186	-5.0669	0
13	0.046835	0.6607	0.254787
14	0.135324	1.909	0.028852
15	0.003875	0.0547	0.478228
16	-0.040017	-0.5645	0.286523
17	0.026472	0.3734	0.354609
18	0.121118	1.7086	0.044543
19	-0.136521	-1.9259	0.027773
20	0.008044	0.1135	0.454885
21	-0.015615	-0.2203	0.41294
22	0.052069	0.7345	0.231748
23	-0.026075	-0.3678	0.356692

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.349668	-4.9327	1e-06
2	-0.293012	-4.1334	2.6e-05
3	-0.15292	-2.1572	0.016094
4	-0.092097	-1.2992	0.097692
5	-0.132948	-1.8755	0.031097
6	-0.089746	-1.266	0.103492
7	-0.038084	-0.5372	0.295849
8	-0.078488	-1.1072	0.134771
9	-0.007842	-0.1106	0.456015
10	0.020323	0.2867	0.387322
11	0.208714	2.9443	0.001811
12	-0.257532	-3.6329	0.000178
13	-0.227667	-3.2116	0.00077
14	-0.10737	-1.5146	0.065724
15	-0.02404	-0.3391	0.367434
16	-0.032386	-0.4569	0.324133
17	-0.05037	-0.7106	0.239097
18	0.146641	2.0686	0.019937
19	0.012511	0.1765	0.430042
20	-0.03286	-0.4635	0.321739
21	-0.059475	-0.839	0.201239
22	0.059422	0.8383	0.201446
23	0.114828	1.6198	0.053424

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.349668 & -4.9327 & 1e-06 \tabularnewline
2 & -0.293012 & -4.1334 & 2.6e-05 \tabularnewline
3 & -0.15292 & -2.1572 & 0.016094 \tabularnewline
4 & -0.092097 & -1.2992 & 0.097692 \tabularnewline
5 & -0.132948 & -1.8755 & 0.031097 \tabularnewline
6 & -0.089746 & -1.266 & 0.103492 \tabularnewline
7 & -0.038084 & -0.5372 & 0.295849 \tabularnewline
8 & -0.078488 & -1.1072 & 0.134771 \tabularnewline
9 & -0.007842 & -0.1106 & 0.456015 \tabularnewline
10 & 0.020323 & 0.2867 & 0.387322 \tabularnewline
11 & 0.208714 & 2.9443 & 0.001811 \tabularnewline
12 & -0.257532 & -3.6329 & 0.000178 \tabularnewline
13 & -0.227667 & -3.2116 & 0.00077 \tabularnewline
14 & -0.10737 & -1.5146 & 0.065724 \tabularnewline
15 & -0.02404 & -0.3391 & 0.367434 \tabularnewline
16 & -0.032386 & -0.4569 & 0.324133 \tabularnewline
17 & -0.05037 & -0.7106 & 0.239097 \tabularnewline
18 & 0.146641 & 2.0686 & 0.019937 \tabularnewline
19 & 0.012511 & 0.1765 & 0.430042 \tabularnewline
20 & -0.03286 & -0.4635 & 0.321739 \tabularnewline
21 & -0.059475 & -0.839 & 0.201239 \tabularnewline
22 & 0.059422 & 0.8383 & 0.201446 \tabularnewline
23 & 0.114828 & 1.6198 & 0.053424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308924&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]-0.349668[/C][C]-4.9327[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.293012[/C][C]-4.1334[/C][C]2.6e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.15292[/C][C]-2.1572[/C][C]0.016094[/C][/ROW]
[ROW][C]4[/C][C]-0.092097[/C][C]-1.2992[/C][C]0.097692[/C][/ROW]
[ROW][C]5[/C][C]-0.132948[/C][C]-1.8755[/C][C]0.031097[/C][/ROW]
[ROW][C]6[/C][C]-0.089746[/C][C]-1.266[/C][C]0.103492[/C][/ROW]
[ROW][C]7[/C][C]-0.038084[/C][C]-0.5372[/C][C]0.295849[/C][/ROW]
[ROW][C]8[/C][C]-0.078488[/C][C]-1.1072[/C][C]0.134771[/C][/ROW]
[ROW][C]9[/C][C]-0.007842[/C][C]-0.1106[/C][C]0.456015[/C][/ROW]
[ROW][C]10[/C][C]0.020323[/C][C]0.2867[/C][C]0.387322[/C][/ROW]
[ROW][C]11[/C][C]0.208714[/C][C]2.9443[/C][C]0.001811[/C][/ROW]
[ROW][C]12[/C][C]-0.257532[/C][C]-3.6329[/C][C]0.000178[/C][/ROW]
[ROW][C]13[/C][C]-0.227667[/C][C]-3.2116[/C][C]0.00077[/C][/ROW]
[ROW][C]14[/C][C]-0.10737[/C][C]-1.5146[/C][C]0.065724[/C][/ROW]
[ROW][C]15[/C][C]-0.02404[/C][C]-0.3391[/C][C]0.367434[/C][/ROW]
[ROW][C]16[/C][C]-0.032386[/C][C]-0.4569[/C][C]0.324133[/C][/ROW]
[ROW][C]17[/C][C]-0.05037[/C][C]-0.7106[/C][C]0.239097[/C][/ROW]
[ROW][C]18[/C][C]0.146641[/C][C]2.0686[/C][C]0.019937[/C][/ROW]
[ROW][C]19[/C][C]0.012511[/C][C]0.1765[/C][C]0.430042[/C][/ROW]
[ROW][C]20[/C][C]-0.03286[/C][C]-0.4635[/C][C]0.321739[/C][/ROW]
[ROW][C]21[/C][C]-0.059475[/C][C]-0.839[/C][C]0.201239[/C][/ROW]
[ROW][C]22[/C][C]0.059422[/C][C]0.8383[/C][C]0.201446[/C][/ROW]
[ROW][C]23[/C][C]0.114828[/C][C]1.6198[/C][C]0.053424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308924&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308924&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	-0.349668	-4.9327	1e-06
2	-0.293012	-4.1334	2.6e-05
3	-0.15292	-2.1572	0.016094
4	-0.092097	-1.2992	0.097692
5	-0.132948	-1.8755	0.031097
6	-0.089746	-1.266	0.103492
7	-0.038084	-0.5372	0.295849
8	-0.078488	-1.1072	0.134771
9	-0.007842	-0.1106	0.456015
10	0.020323	0.2867	0.387322
11	0.208714	2.9443	0.001811
12	-0.257532	-3.6329	0.000178
13	-0.227667	-3.2116	0.00077
14	-0.10737	-1.5146	0.065724
15	-0.02404	-0.3391	0.367434
16	-0.032386	-0.4569	0.324133
17	-0.05037	-0.7106	0.239097
18	0.146641	2.0686	0.019937
19	0.012511	0.1765	0.430042
20	-0.03286	-0.4635	0.321739
21	-0.059475	-0.839	0.201239
22	0.059422	0.8383	0.201446
23	0.114828	1.6198	0.053424

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
par3 <- '1'
par2 <- '0.5'
par1 <- 'Default'
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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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