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paper autocorrelation function d=1

*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Tue, 21 Dec 2010 19:27:46 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck.htm/, Retrieved Tue, 21 Dec 2010 20:26:08 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2350.44 2440.25 2408.64 2472.81 2407.6 2454.62 2448.05 2497.84 2645.64 2756.76 2849.27 2921.44 2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.1 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.4 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.4 3857.62 3801.06 3504.37 3032.6 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.6 2070.83 2293.41 2443.27 2513.17 2466.92 2502.66 2539.91

Output produced by software:

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.295132	2.5043	0.007268
2	0.101431	0.8607	0.196137
3	0.23151	1.9644	0.02667
4	0.248879	2.1118	0.019087
5	0.266135	2.2582	0.013481
6	-0.01559	-0.1323	0.447564
7	-0.026614	-0.2258	0.410988
8	0.162446	1.3784	0.086174
9	0.04683	0.3974	0.346135
10	-0.134051	-1.1375	0.129559
11	0.138397	1.1743	0.122064
12	0.013627	0.1156	0.454136
13	-0.021806	-0.185	0.426862
14	0.067924	0.5764	0.283087
15	-0.0389	-0.3301	0.371151
16	0.073541	0.624	0.267295
17	-0.109017	-0.925	0.179017
18	-0.180004	-1.5274	0.065523
19	0.001926	0.0163	0.493504
20	-0.096799	-0.8214	0.207074
21	-0.159525	-1.3536	0.090047
22	-0.147711	-1.2534	0.107063
23	-0.124178	-1.0537	0.147775
24	-0.089573	-0.7601	0.224852
25	-0.032571	-0.2764	0.391528
26	-0.105053	-0.8914	0.187841
27	-0.008879	-0.0753	0.470075
28	0.057217	0.4855	0.314396
29	-0.026035	-0.2209	0.412893
30	-0.025664	-0.2178	0.414115
31	-0.059349	-0.5036	0.308043
32	-0.014106	-0.1197	0.45253
33	-0.057548	-0.4883	0.313406
34	-0.0909	-0.7713	0.221522
35	-0.137838	-1.1696	0.123011
36	-0.039047	-0.3313	0.370682
37	-0.023306	-0.1978	0.421895
38	-0.064025	-0.5433	0.294311
39	-0.057592	-0.4887	0.313274
40	-0.072294	-0.6134	0.270761
41	0.001073	0.0091	0.49638
42	0.002613	0.0222	0.491187
43	-0.021067	-0.1788	0.429316
44	-0.029634	-0.2514	0.401091
45	-0.069187	-0.5871	0.279496
46	-0.053574	-0.4546	0.325386
47	-0.071731	-0.6087	0.272335
48	-0.056232	-0.4771	0.317351

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.295132	2.5043	0.007268
2	0.015696	0.1332	0.447211
3	0.216301	1.8354	0.03529
4	0.141792	1.2031	0.11643
5	0.178329	1.5132	0.067307
6	-0.198627	-1.6854	0.04812
7	-0.058062	-0.4927	0.31187
8	0.088614	0.7519	0.227277
9	-0.053955	-0.4578	0.324228
10	-0.15817	-1.3421	0.091888
11	0.299278	2.5395	0.006631
12	-0.1451	-1.2312	0.111125
13	-0.018152	-0.154	0.439011
14	0.134261	1.1392	0.12919
15	-0.063127	-0.5357	0.296925
16	-0.059636	-0.506	0.307191
17	-0.111134	-0.943	0.174415
18	-0.079807	-0.6772	0.250229
19	-0.034052	-0.2889	0.386727
20	-0.073894	-0.627	0.266316
21	0.050929	0.4321	0.333463
22	-0.117225	-0.9947	0.161609
23	0.01776	0.1507	0.440318
24	-0.009957	-0.0845	0.466453
25	0.057022	0.4838	0.31498
26	0.009297	0.0789	0.468669
27	0.020272	0.172	0.431955
28	0.092598	0.7857	0.217305
29	-0.001645	-0.014	0.49445
30	-0.144667	-1.2275	0.111809
31	0.030963	0.2627	0.396755
32	-0.029967	-0.2543	0.400002
33	-0.123706	-1.0497	0.148688
34	0.02321	0.1969	0.422212
35	-0.086142	-0.7309	0.233595
36	0.029523	0.2505	0.401454
37	0.02229	0.1891	0.425258
38	0.051928	0.4406	0.330402
39	-0.092612	-0.7858	0.21727
40	-0.07534	-0.6393	0.262334
41	0.029109	0.247	0.402808
42	-0.030935	-0.2625	0.396844
43	-0.024954	-0.2117	0.416452
44	0.02939	0.2494	0.401886
45	-0.117255	-0.9949	0.161549
46	0.030998	0.263	0.396639
47	-0.083922	-0.7121	0.239351
48	0.0168	0.1426	0.443519

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck/1apaf1292959662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck/1apaf1292959662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck/23g9i1292959662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck/23g9i1292959662.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck/33g9i1292959662.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292959568jomxxgu5jp26sck/33g9i1292959662.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; 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 <- 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)

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,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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