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workshop 8

*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: Sat, 28 Nov 2009 07:50:29 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/28/t125941986965ulqaq720zwr7w.htm/, Retrieved Sat, 28 Nov 2009 15:51:11 +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/2009/Nov/28/t125941986965ulqaq720zwr7w.htm/},
    year = {2009},
}
@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 = {2009},
    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 «

2.05 2.11 2.09 2.05 2.08 2.06 2.06 2.08 2.07 2.06 2.07 2.06 2.09 2.07 2.09 2.28 2.33 2.35 2.52 2.63 2.58 2.70 2.81 2.97 3.04 3.28 3.33 3.50 3.56 3.57 3.69 3.82 3.79 3.96 4.06 4.05 4.03 3.94 4.02 3.88 4.02 4.03 4.09 3.99 4.01 4.01 4.19 4.30 4.27 3.82 3.15 2.49 1.81 1.26 1.06 0.84 0.78 0.70 0.36 0.35

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.615	4.2162	5.6e-05
2	0.524638	3.5967	0.000386
3	0.290019	1.9883	0.026312
4	0.19429	1.332	0.094645
5	0.09333	0.6398	0.262693
6	0.197241	1.3522	0.091389
7	0.192667	1.3209	0.096472
8	0.216724	1.4858	0.072006
9	0.108527	0.744	0.230283
10	0.044597	0.3057	0.380575
11	0.008927	0.0612	0.475728
12	-0.047807	-0.3278	0.372278
13	0.136797	0.9378	0.176562
14	0.035361	0.2424	0.404754
15	0.158909	1.0894	0.140761
16	0.046178	0.3166	0.376483
17	0.002506	0.0172	0.493182
18	-0.086388	-0.5922	0.278263
19	-0.024175	-0.1657	0.434539
20	-0.12474	-0.8552	0.198397
21	-0.039721	-0.2723	0.393287
22	-0.064206	-0.4402	0.330914
23	-0.01658	-0.1137	0.454992
24	-0.120915	-0.8289	0.205662
25	-0.143174	-0.9816	0.165673
26	-0.144106	-0.9879	0.164121
27	-0.229732	-1.575	0.060986
28	-0.211717	-1.4515	0.076647
29	-0.185338	-1.2706	0.10506
30	-0.175951	-1.2063	0.116877
31	-0.177164	-1.2146	0.115297
32	-0.160313	-1.0991	0.138672
33	-0.201096	-1.3786	0.087265
34	-0.213278	-1.4622	0.075176
35	-0.250842	-1.7197	0.046035
36	-0.192444	-1.3193	0.096725
37	-0.18155	-1.2446	0.109717
38	-0.112837	-0.7736	0.221529
39	-0.076538	-0.5247	0.301124
40	-0.058562	-0.4015	0.344943
41	-0.025753	-0.1766	0.430309
42	-0.018612	-0.1276	0.449506
43	-0.054258	-0.372	0.355793
44	-0.025325	-0.1736	0.431456
45	-0.002523	-0.0173	0.493135
46	-6.7e-05	-5e-04	0.499819
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.615	4.2162	5.6e-05
2	0.235476	1.6143	0.056574
3	-0.172783	-1.1845	0.121078
4	-0.024171	-0.1657	0.434549
5	-0.00027	-0.0019	0.499265
6	0.256778	1.7604	0.042425
7	0.050063	0.3432	0.366484
8	-0.045578	-0.3125	0.378035
9	-0.159365	-1.0926	0.14008
10	-0.058321	-0.3998	0.345548
11	0.129092	0.885	0.190328
12	-0.058636	-0.402	0.344757
13	0.309275	2.1203	0.019645
14	-0.299267	-2.0517	0.022899
15	0.133901	0.918	0.181658
16	-0.116204	-0.7967	0.214829
17	-0.061908	-0.4244	0.336598
18	0.107514	0.7371	0.23237
19	-0.043711	-0.2997	0.382877
20	-0.091274	-0.6257	0.267256
21	-0.102899	-0.7054	0.24201
22	0.112462	0.771	0.222283
23	0.032966	0.226	0.41109
24	-0.170879	-1.1715	0.123655
25	0.012109	0.083	0.467095
26	-0.135052	-0.9259	0.179622
27	0.002608	0.0179	0.492905
28	-0.116308	-0.7974	0.214623
29	0.10168	0.6971	0.244593
30	-0.055553	-0.3809	0.352514
31	-0.061457	-0.4213	0.337717
32	-0.055057	-0.3775	0.353769
33	0.00098	0.0067	0.497335
34	-0.100385	-0.6882	0.247354
35	0.003302	0.0226	0.491018
36	0.012563	0.0861	0.465866
37	0.012417	0.0851	0.466261
38	-0.020818	-0.1427	0.443561
39	0.037682	0.2583	0.398638
40	0.051336	0.3519	0.363227
41	0.063685	0.4366	0.332199
42	-0.034249	-0.2348	0.407692
43	-0.011286	-0.0774	0.469329
44	-0.066337	-0.4548	0.325679
45	0.091784	0.6292	0.26612
46	-0.044332	-0.3039	0.381264
47	NA	NA	NA
48	NA	NA	NA
49	NA	NA	NA
50	NA	NA	NA
51	NA	NA	NA
52	NA	NA	NA
53	NA	NA	NA
54	NA	NA	NA
55	NA	NA	NA
56	NA	NA	NA
57	NA	NA	NA
58	NA	NA	NA
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/28/t125941986965ulqaq720zwr7w/1govr1259419825.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t125941986965ulqaq720zwr7w/1govr1259419825.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t125941986965ulqaq720zwr7w/29afl1259419825.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Nov/28/t125941986965ulqaq720zwr7w/29afl1259419825.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

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('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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