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*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: Mon, 27 Dec 2010 13:27:22 +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/27/t1293456292ydpozrl4ut07l0w.htm/, Retrieved Mon, 27 Dec 2010 14:24:55 +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/27/t1293456292ydpozrl4ut07l0w.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 «

35.36 31.19 35.29 33.80 36.38 37.77 34.88 37.07 35.56 34.18 32.05 32.35 34.79 33.75 33.76 36.80 36.57 34.14 33.85 35.10 33.92 33.34 30.69 32.32 32.47 34.71 37.19 35.58 36.04 35.63 32.74 33.31 28.40 27.37 28.20 29.23 28.05 27.70 28.05 28.01 30.73 30.82 30.48 30.92 31.20 31.41 31.96 36.95 35.64 37.18 38.69 39.97 40.36 40.79 42.92 41.21 44.15 44.70 47.42 45.14 46.08 50.59 48.63 47.46 47.30 49.02 51.77 54.15 56.10 52.58 52.56 51.27 57.72 53.46 55.48 59.33 57.32 56.44 58.80 55.64 53.62 54.87 56.15 55.35 52.38 51.27 53.95 56.09 56.34 60.65 58.35 57.18 58.87 66.20 62.25 62.62 54.73 56.20 52.54 63.06 63.53 60.95 53.83 51.20 44.57 44.15 44.04 42.28 38.42 35.41 37.01 39.19 46.50 44.79 47.01 49.15 50.85 54.09 55.40 56.16 54.37 52.34 56.13 51.29 42.95 28.88 38.47 34.83 41.17 40.80 40.00 44.00

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.948965	10.9028	0
2	0.904843	10.3959	0
3	0.851889	9.7875	0
4	0.817332	9.3904	0
5	0.778881	8.9487	0
6	0.744757	8.5566	0
7	0.700897	8.0527	0
8	0.657362	7.5525	0
9	0.624889	7.1794	0
10	0.607938	6.9847	0
11	0.593671	6.8208	0
12	0.575179	6.6083	0
13	0.556561	6.3944	0
14	0.548225	6.2986	0
15	0.53501	6.1468	0
16	0.53248	6.1177	0
17	0.527663	6.0624	0
18	0.513573	5.9005	0
19	0.499032	5.7334	0
20	0.478743	5.5003	0
21	0.462491	5.3136	0
22	0.428765	4.9261	1e-06
23	0.395415	4.543	6e-06
24	0.349738	4.0182	4.9e-05
25	0.314818	3.617	0.000212
26	0.274184	3.1501	0.00101
27	0.251044	2.8843	0.002291
28	0.213175	2.4492	0.007814
29	0.179241	2.0593	0.020714
30	0.131543	1.5113	0.06655
31	0.100399	1.1535	0.125395
32	0.064315	0.7389	0.230632
33	0.03449	0.3963	0.346278
34	-0.001665	-0.0191	0.492385
35	-0.032574	-0.3743	0.354409
36	-0.064007	-0.7354	0.231704
37	-0.08613	-0.9896	0.162099
38	-0.105474	-1.2118	0.113876
39	-0.119846	-1.3769	0.085434
40	-0.13788	-1.5841	0.057779
41	-0.158341	-1.8192	0.035573
42	-0.180306	-2.0716	0.020127
43	-0.203939	-2.3431	0.01031
44	-0.224229	-2.5762	0.005545
45	-0.242603	-2.7873	0.00305
46	-0.266019	-3.0563	0.001356
47	-0.290441	-3.3369	0.00055
48	-0.310986	-3.573	0.000247
49	-0.329939	-3.7907	0.000114
50	-0.34631	-3.9788	5.7e-05
51	-0.358336	-4.117	3.4e-05
52	-0.368657	-4.2355	2.1e-05
53	-0.382241	-4.3916	1.1e-05
54	-0.387261	-4.4493	9e-06
55	-0.400635	-4.6029	5e-06
56	-0.404391	-4.6461	4e-06
57	-0.413742	-4.7535	3e-06
58	-0.410859	-4.7204	3e-06
59	-0.402404	-4.6233	4e-06
60	-0.394876	-4.5368	6e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.948965	10.9028	0
2	0.043318	0.4977	0.309766
3	-0.107651	-1.2368	0.109175
4	0.147715	1.6971	0.046016
5	-0.032925	-0.3783	0.352916
6	-0.008377	-0.0962	0.461734
7	-0.08348	-0.9591	0.169627
8	-0.042299	-0.486	0.313896
9	0.111604	1.2822	0.101004
10	0.128305	1.4741	0.071416
11	0.012644	0.1453	0.442362
12	-0.04241	-0.4873	0.313445
13	0.025158	0.289	0.3865
14	0.119367	1.3714	0.086285
15	-0.072786	-0.8362	0.202264
16	0.061235	0.7035	0.241482
17	0.031024	0.3564	0.361039
18	-0.100578	-1.1556	0.124975
19	0.044957	0.5165	0.30318
20	-0.079937	-0.9184	0.18004
21	-0.002884	-0.0331	0.48681
22	-0.158885	-1.8254	0.035097
23	-0.048456	-0.5567	0.289333
24	-0.095002	-1.0915	0.138524
25	0.035736	0.4106	0.341026
26	-0.054946	-0.6313	0.264475
27	0.083631	0.9608	0.169193
28	-0.143479	-1.6485	0.050819
29	-0.006388	-0.0734	0.470804
30	-0.162606	-1.8682	0.031975
31	0.036326	0.4174	0.338549
32	-0.076961	-0.8842	0.189095
33	-0.07693	-0.8839	0.189191
34	-0.040127	-0.461	0.322769
35	-0.012738	-0.1463	0.441934
36	0.002668	0.0307	0.487796
37	-0.008925	-0.1025	0.459244
38	-0.016222	-0.1864	0.42622
39	0.03337	0.3834	0.351023
40	0.00668	0.0768	0.469468
41	-0.067996	-0.7812	0.218037
42	-0.014432	-0.1658	0.434279
43	-0.067144	-0.7714	0.220917
44	0.041192	0.4733	0.318403
45	0.01114	0.128	0.449176
46	-0.088261	-1.014	0.156208
47	0.034929	0.4013	0.344424
48	-0.020579	-0.2364	0.40673
49	0.051595	0.5928	0.277169
50	-0.042151	-0.4843	0.314498
51	0.118636	1.363	0.087597
52	-0.024045	-0.2763	0.391391
53	0.022042	0.2532	0.400236
54	0.021997	0.2527	0.400434
55	-0.066295	-0.7617	0.223807
56	-0.004165	-0.0479	0.480951
57	0.039593	0.4549	0.324967
58	0.019525	0.2243	0.411425
59	0.138963	1.5966	0.056377
60	-0.057511	-0.6608	0.254962

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456292ydpozrl4ut07l0w/1ik5p1293456439.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456292ydpozrl4ut07l0w/1ik5p1293456439.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456292ydpozrl4ut07l0w/2ttma1293456439.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456292ydpozrl4ut07l0w/2ttma1293456439.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456292ydpozrl4ut07l0w/3ttma1293456439.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293456292ydpozrl4ut07l0w/3ttma1293456439.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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