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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 28 Dec 2009 12:44:12 -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/Dec/28/t12620298788s6s3rqla246v5n.htm/, Retrieved Mon, 28 Dec 2009 20:51:20 +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/Dec/28/t12620298788s6s3rqla246v5n.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 «

40.22 44.23 45.85 53.38 53.26 51.8 55.3 57.81 63.96 63.77 59.15 56.12 57.42 63.52 61.71 63.01 68.18 72.03 69.75 74.41 74.33 64.24 60.03 59.44 62.5 55.04 58.34 61.92 67.65 67.68 70.3 75.26 71.44 76.36 81.71 92.6 90.6 92.23 94.09 102.79 109.65 124.05 132.69 135.81 116.07 101.42 75.73 55.48 43.8 45.29 44.01 47.48 51.07 57.84 69.04 65.61 72.87 68.41 73.25 77.43

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	0.439697	3.3774	0.00065
2	0.319616	2.455	0.008527
3	0.073929	0.5679	0.286143
4	0.000936	0.0072	0.497145
5	-0.171581	-1.3179	0.09631
6	-0.337756	-2.5944	0.005968
7	-0.166942	-1.2823	0.102375
8	-0.236769	-1.8187	0.03702
9	-0.143721	-1.1039	0.13705
10	-0.04786	-0.3676	0.357237
11	0.052368	0.4022	0.344478
12	-0.07075	-0.5434	0.294436
13	-0.099699	-0.7658	0.223424
14	-0.033024	-0.2537	0.400319
15	0.008295	0.0637	0.474707
16	-0.019728	-0.1515	0.440037
17	-0.101613	-0.7805	0.219108
18	-0.062238	-0.4781	0.317188
19	-0.069225	-0.5317	0.298454
20	-0.101402	-0.7789	0.21958
21	0.030692	0.2358	0.40722
22	0.029365	0.2256	0.411162
23	0.166132	1.2761	0.103464
24	0.033351	0.2562	0.399352
25	0.228496	1.7551	0.042216
26	0.175159	1.3454	0.091819
27	0.115954	0.8907	0.188365
28	-0.005232	-0.0402	0.484038
29	-0.093565	-0.7187	0.237585
30	-0.027842	-0.2139	0.415697
31	-0.15734	-1.2086	0.115828
32	-0.01045	-0.0803	0.468146
33	-0.045409	-0.3488	0.364244
34	0.024331	0.1869	0.426195
35	0.003856	0.0296	0.488237
36	0.091737	0.7046	0.241901
37	0.089625	0.6884	0.246943
38	0.023798	0.1828	0.427793
39	-0.027907	-0.2144	0.415502
40	-0.058102	-0.4463	0.32851
41	-0.047212	-0.3626	0.359083
42	-0.081548	-0.6264	0.26674
43	-0.081254	-0.6241	0.267476
44	-0.154535	-1.187	0.119991
45	-0.122019	-0.9372	0.176227
46	-0.029955	-0.2301	0.409409
47	-0.061322	-0.471	0.319682
48	0.033914	0.2605	0.397692
49	-0.02028	-0.1558	0.438373
50	0.072383	0.556	0.290163
51	0.069614	0.5347	0.297429
52	0.028257	0.217	0.414462
53	0.059009	0.4533	0.326012
54	-0.033609	-0.2582	0.398594
55	0.028517	0.219	0.413687
56	0.00023	0.0018	0.499299
57	0.012876	0.0989	0.460774
58	0.007754	0.0596	0.476353
59	NA	NA	NA
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.439697	3.3774	0.00065
2	0.156549	1.2025	0.116992
3	-0.14416	-1.1073	0.136327
4	-0.041382	-0.3179	0.375856
5	-0.167759	-1.2886	0.101287
6	-0.267123	-2.0518	0.022317
7	0.16482	1.266	0.105244
8	-0.125938	-0.9674	0.168658
9	-0.059589	-0.4577	0.324422
10	0.127046	0.9759	0.16656
11	-0.029351	-0.2254	0.411204
12	-0.279387	-2.146	0.017998
13	-0.025603	-0.1967	0.422386
14	0.009639	0.074	0.470615
15	0.007031	0.054	0.478556
16	0.022152	0.1702	0.432737
17	-0.175553	-1.3484	0.091335
18	-0.142978	-1.0982	0.138281
19	0.019335	0.1485	0.441221
20	-0.145532	-1.1178	0.134081
21	0.12241	0.9403	0.175462
22	0.017898	0.1375	0.44556
23	0.092807	0.7129	0.239371
24	-0.161368	-1.2395	0.110035
25	0.154508	1.1868	0.120031
26	-0.054843	-0.4213	0.337549
27	-0.000605	-0.0046	0.498155
28	-0.037332	-0.2868	0.387654
29	-0.065097	-0.5	0.309459
30	0.01827	0.1403	0.444438
31	0.010942	0.084	0.466652
32	0.052488	0.4032	0.34414
33	0.004547	0.0349	0.486127
34	-0.004676	-0.0359	0.485734
35	0.036245	0.2784	0.390839
36	0.03948	0.3032	0.381384
37	-0.025539	-0.1962	0.422576
38	0.039254	0.3015	0.38204
39	-0.018934	-0.1454	0.442433
40	-0.0459	-0.3526	0.362837
41	0.014655	0.1126	0.455378
42	0.003148	0.0242	0.490395
43	-0.032123	-0.2467	0.402983
44	-0.149801	-1.1506	0.12726
45	0.049653	0.3814	0.352142
46	0.036576	0.2809	0.389868
47	-0.130363	-1.0013	0.160376
48	0.01634	0.1255	0.450274
49	-0.057015	-0.4379	0.331514
50	-0.016084	-0.1235	0.451047
51	0.047372	0.3639	0.358628
52	-0.108516	-0.8335	0.203955
53	-0.078125	-0.6001	0.275372
54	0.105455	0.81	0.210593
55	-0.048475	-0.3723	0.355485
56	0.020548	0.1578	0.437563
57	-0.094877	-0.7288	0.234515
58	-0.039598	-0.3042	0.381039
59	NA	NA	NA
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620298788s6s3rqla246v5n/1ffot1262029449.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620298788s6s3rqla246v5n/1ffot1262029449.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620298788s6s3rqla246v5n/2z1u21262029449.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/28/t12620298788s6s3rqla246v5n/2z1u21262029449.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = -0.6 ; 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 (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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