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, 23 Dec 2016 08:37:58 +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/2016/Dec/23/t1482478952hiapd1or0748z5p.htm/, Retrieved Tue, 07 May 2024 08:47:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302751, Retrieved Tue, 07 May 2024 08:47:45 +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)

-       [(Partial) Autocorrelation Function] [] [2016-12-23 07:37:58] [0b5bf205c55efce49027552c8371b570] [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	1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302751&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]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302751&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.974954	10.5006	0
2	0.944759	10.1754	0
3	0.917668	9.8836	0
4	0.891383	9.6005	0
5	0.868794	9.3572	0
6	0.849358	9.1479	0
7	0.829308	8.9319	0
8	0.810339	8.7276	0
9	0.788888	8.4966	0
10	0.760863	8.1947	0
11	0.734208	7.9077	0
12	0.709974	7.6467	0
13	0.684124	7.3682	0
14	0.658171	7.0887	0
15	0.63388	6.8271	0
16	0.610591	6.5763	0
17	0.58933	6.3473	0
18	0.568282	6.1206	0
19	0.544114	5.8603	0
20	0.517879	5.5777	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974954 & 10.5006 & 0 \tabularnewline
2 & 0.944759 & 10.1754 & 0 \tabularnewline
3 & 0.917668 & 9.8836 & 0 \tabularnewline
4 & 0.891383 & 9.6005 & 0 \tabularnewline
5 & 0.868794 & 9.3572 & 0 \tabularnewline
6 & 0.849358 & 9.1479 & 0 \tabularnewline
7 & 0.829308 & 8.9319 & 0 \tabularnewline
8 & 0.810339 & 8.7276 & 0 \tabularnewline
9 & 0.788888 & 8.4966 & 0 \tabularnewline
10 & 0.760863 & 8.1947 & 0 \tabularnewline
11 & 0.734208 & 7.9077 & 0 \tabularnewline
12 & 0.709974 & 7.6467 & 0 \tabularnewline
13 & 0.684124 & 7.3682 & 0 \tabularnewline
14 & 0.658171 & 7.0887 & 0 \tabularnewline
15 & 0.63388 & 6.8271 & 0 \tabularnewline
16 & 0.610591 & 6.5763 & 0 \tabularnewline
17 & 0.58933 & 6.3473 & 0 \tabularnewline
18 & 0.568282 & 6.1206 & 0 \tabularnewline
19 & 0.544114 & 5.8603 & 0 \tabularnewline
20 & 0.517879 & 5.5777 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302751&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]0.974954[/C][C]10.5006[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.944759[/C][C]10.1754[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.917668[/C][C]9.8836[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.891383[/C][C]9.6005[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.868794[/C][C]9.3572[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.849358[/C][C]9.1479[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.829308[/C][C]8.9319[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.810339[/C][C]8.7276[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.788888[/C][C]8.4966[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.760863[/C][C]8.1947[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.734208[/C][C]7.9077[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.709974[/C][C]7.6467[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.684124[/C][C]7.3682[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.658171[/C][C]7.0887[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.63388[/C][C]6.8271[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.610591[/C][C]6.5763[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.58933[/C][C]6.3473[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.568282[/C][C]6.1206[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.544114[/C][C]5.8603[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.517879[/C][C]5.5777[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302751&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	0.974954	10.5006	0
2	0.944759	10.1754	0
3	0.917668	9.8836	0
4	0.891383	9.6005	0
5	0.868794	9.3572	0
6	0.849358	9.1479	0
7	0.829308	8.9319	0
8	0.810339	8.7276	0
9	0.788888	8.4966	0
10	0.760863	8.1947	0
11	0.734208	7.9077	0
12	0.709974	7.6467	0
13	0.684124	7.3682	0
14	0.658171	7.0887	0
15	0.63388	6.8271	0
16	0.610591	6.5763	0
17	0.58933	6.3473	0
18	0.568282	6.1206	0
19	0.544114	5.8603	0
20	0.517879	5.5777	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.974954	10.5006	0
2	-0.116761	-1.2575	0.10554
3	0.05863	0.6315	0.264491
4	-0.012101	-0.1303	0.448267
5	0.064683	0.6967	0.243704
6	0.037213	0.4008	0.344652
7	-0.025358	-0.2731	0.392626
8	0.022886	0.2465	0.402869
9	-0.06422	-0.6917	0.245262
10	-0.12521	-1.3486	0.090053
11	0.034219	0.3686	0.356566
12	0.01172	0.1262	0.449883
13	-0.055785	-0.6008	0.274567
14	-0.026387	-0.2842	0.388384
15	0.009787	0.1054	0.458115
16	0.008872	0.0956	0.462019
17	0.020113	0.2166	0.414441
18	-0.007495	-0.0807	0.467902
19	-0.057028	-0.6142	0.27014
20	-0.055212	-0.5947	0.276616

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.974954 & 10.5006 & 0 \tabularnewline
2 & -0.116761 & -1.2575 & 0.10554 \tabularnewline
3 & 0.05863 & 0.6315 & 0.264491 \tabularnewline
4 & -0.012101 & -0.1303 & 0.448267 \tabularnewline
5 & 0.064683 & 0.6967 & 0.243704 \tabularnewline
6 & 0.037213 & 0.4008 & 0.344652 \tabularnewline
7 & -0.025358 & -0.2731 & 0.392626 \tabularnewline
8 & 0.022886 & 0.2465 & 0.402869 \tabularnewline
9 & -0.06422 & -0.6917 & 0.245262 \tabularnewline
10 & -0.12521 & -1.3486 & 0.090053 \tabularnewline
11 & 0.034219 & 0.3686 & 0.356566 \tabularnewline
12 & 0.01172 & 0.1262 & 0.449883 \tabularnewline
13 & -0.055785 & -0.6008 & 0.274567 \tabularnewline
14 & -0.026387 & -0.2842 & 0.388384 \tabularnewline
15 & 0.009787 & 0.1054 & 0.458115 \tabularnewline
16 & 0.008872 & 0.0956 & 0.462019 \tabularnewline
17 & 0.020113 & 0.2166 & 0.414441 \tabularnewline
18 & -0.007495 & -0.0807 & 0.467902 \tabularnewline
19 & -0.057028 & -0.6142 & 0.27014 \tabularnewline
20 & -0.055212 & -0.5947 & 0.276616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302751&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]0.974954[/C][C]10.5006[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.116761[/C][C]-1.2575[/C][C]0.10554[/C][/ROW]
[ROW][C]3[/C][C]0.05863[/C][C]0.6315[/C][C]0.264491[/C][/ROW]
[ROW][C]4[/C][C]-0.012101[/C][C]-0.1303[/C][C]0.448267[/C][/ROW]
[ROW][C]5[/C][C]0.064683[/C][C]0.6967[/C][C]0.243704[/C][/ROW]
[ROW][C]6[/C][C]0.037213[/C][C]0.4008[/C][C]0.344652[/C][/ROW]
[ROW][C]7[/C][C]-0.025358[/C][C]-0.2731[/C][C]0.392626[/C][/ROW]
[ROW][C]8[/C][C]0.022886[/C][C]0.2465[/C][C]0.402869[/C][/ROW]
[ROW][C]9[/C][C]-0.06422[/C][C]-0.6917[/C][C]0.245262[/C][/ROW]
[ROW][C]10[/C][C]-0.12521[/C][C]-1.3486[/C][C]0.090053[/C][/ROW]
[ROW][C]11[/C][C]0.034219[/C][C]0.3686[/C][C]0.356566[/C][/ROW]
[ROW][C]12[/C][C]0.01172[/C][C]0.1262[/C][C]0.449883[/C][/ROW]
[ROW][C]13[/C][C]-0.055785[/C][C]-0.6008[/C][C]0.274567[/C][/ROW]
[ROW][C]14[/C][C]-0.026387[/C][C]-0.2842[/C][C]0.388384[/C][/ROW]
[ROW][C]15[/C][C]0.009787[/C][C]0.1054[/C][C]0.458115[/C][/ROW]
[ROW][C]16[/C][C]0.008872[/C][C]0.0956[/C][C]0.462019[/C][/ROW]
[ROW][C]17[/C][C]0.020113[/C][C]0.2166[/C][C]0.414441[/C][/ROW]
[ROW][C]18[/C][C]-0.007495[/C][C]-0.0807[/C][C]0.467902[/C][/ROW]
[ROW][C]19[/C][C]-0.057028[/C][C]-0.6142[/C][C]0.27014[/C][/ROW]
[ROW][C]20[/C][C]-0.055212[/C][C]-0.5947[/C][C]0.276616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302751&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302751&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	0.974954	10.5006	0
2	-0.116761	-1.2575	0.10554
3	0.05863	0.6315	0.264491
4	-0.012101	-0.1303	0.448267
5	0.064683	0.6967	0.243704
6	0.037213	0.4008	0.344652
7	-0.025358	-0.2731	0.392626
8	0.022886	0.2465	0.402869
9	-0.06422	-0.6917	0.245262
10	-0.12521	-1.3486	0.090053
11	0.034219	0.3686	0.356566
12	0.01172	0.1262	0.449883
13	-0.055785	-0.6008	0.274567
14	-0.026387	-0.2842	0.388384
15	0.009787	0.1054	0.458115
16	0.008872	0.0956	0.462019
17	0.020113	0.2166	0.414441
18	-0.007495	-0.0807	0.467902
19	-0.057028	-0.6142	0.27014
20	-0.055212	-0.5947	0.276616

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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 <- '0'
par3 <- '1'
par2 <- '1'
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