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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: Sun, 13 Dec 2009 03:12:58 -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/13/t1260699278f1wk1v4ulfuu1hc.htm/, Retrieved Sun, 13 Dec 2009 11:14:40 +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/13/t1260699278f1wk1v4ulfuu1hc.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:

KDGP2W21

Dataseries X:

» Textbox « » Textfile « » CSV «

2,14 2,45 2,52 2,3 2,25 2,06 1,99 2,25 2,26 2,36 2,3 2,19 2,31 2,21 2,21 2,26 2,18 2,21 2,33 2,12 2,08 1,97 2,09 2,11 2,24 2,45 2,68 2,73 2,76 2,83 3,16 3,22 3,22 3,34 3,35 3,42 3,58 3,71 3,68 3,83 3,94 3,88 4,03 4,15 4,32 4,4 4,37 4,14 4,11 4,16 3,98 4,13 3,76 3,66 3,85 4,03 4,31 4,58 4,46 4,41 3,84 2,84 2,66 2,17 1,43 1,47 1,29 1,23 1,09 0,94 0,76 0,67

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	0.423079	3.5649	0.000328
2	0.305406	2.5734	0.00608
3	0.34941	2.9442	0.002187
4	-0.019356	-0.1631	0.435454
5	0.038359	0.3232	0.373741
6	0.081887	0.69	0.246223
7	-0.048529	-0.4089	0.341917
8	0.113233	0.9541	0.171631
9	0.082731	0.6971	0.244007
10	0.011956	0.1007	0.46002
11	0.157774	1.3294	0.093981
12	0.070007	0.5899	0.278569
13	0.049695	0.4187	0.338336
14	0.133809	1.1275	0.131665
15	0.013795	0.1162	0.453897
16	0.02122	0.1788	0.4293
17	0.008536	0.0719	0.471432
18	0.001247	0.0105	0.495824
19	-0.049914	-0.4206	0.337664
20	-0.061996	-0.5224	0.301513
21	-0.067173	-0.566	0.286586
22	-0.100786	-0.8492	0.199302
23	-0.027032	-0.2278	0.410239
24	-0.086989	-0.733	0.232992
25	-0.090208	-0.7601	0.224855
26	-0.051732	-0.4359	0.332116
27	-0.087159	-0.7344	0.232557
28	-0.076152	-0.6417	0.261578
29	0.002429	0.0205	0.491863
30	-0.082928	-0.6988	0.24349
31	-0.102875	-0.8668	0.194474
32	-0.044414	-0.3742	0.354669
33	-0.077924	-0.6566	0.256782
34	-0.162985	-1.3733	0.086985
35	-0.142727	-1.2026	0.116556
36	-0.128162	-1.0799	0.141918
37	-0.122315	-1.0306	0.153102
38	-0.148632	-1.2524	0.107268
39	-0.086368	-0.7277	0.234581
40	-0.08541	-0.7197	0.237042
41	-0.009386	-0.0791	0.468592
42	0.042035	0.3542	0.362121
43	-0.043632	-0.3676	0.357116
44	0.007902	0.0666	0.473551
45	-0.015511	-0.1307	0.448191
46	-0.111474	-0.9393	0.175382
47	0.058213	0.4905	0.312643
48	0.022171	0.1868	0.426169
49	-0.014852	-0.1251	0.450382
50	0.055911	0.4711	0.319503
51	-0.08111	-0.6834	0.248275
52	-0.089187	-0.7515	0.227417
53	-0.022944	-0.1933	0.423627
54	-0.075554	-0.6366	0.263208
55	0.04166	0.351	0.363301
56	0.037015	0.3119	0.378017
57	-0.017289	-0.1457	0.442295
58	0.073876	0.6225	0.267808
59	-0.044268	-0.373	0.355125
60	-0.068807	-0.5798	0.281949

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.423079	3.5649	0.000328
2	0.153971	1.2974	0.09935
3	0.21827	1.8392	0.035035
4	-0.325129	-2.7396	0.003887
5	0.072632	0.612	0.271245
6	0.050194	0.4229	0.336807
7	0.011276	0.095	0.462287
8	0.104311	0.8789	0.191199
9	-0.027359	-0.2305	0.409172
10	-0.006651	-0.056	0.477734
11	0.093432	0.7873	0.216871
12	-0.000139	-0.0012	0.499536
13	0.020426	0.1721	0.431918
14	0.022269	0.1876	0.425846
15	-0.028926	-0.2437	0.404068
16	-0.005518	-0.0465	0.481521
17	-0.067427	-0.5681	0.285863
18	0.106589	0.8981	0.186075
19	-0.143546	-1.2095	0.115234
20	-0.013057	-0.11	0.456351
21	-0.049358	-0.4159	0.33937
22	-0.03415	-0.2878	0.387186
23	0.078385	0.6605	0.255541
24	-0.127348	-1.073	0.143441
25	-0.006189	-0.0522	0.479278
26	-0.055627	-0.4687	0.320352
27	0.025593	0.2157	0.414939
28	-0.009835	-0.0829	0.467094
29	0.048492	0.4086	0.342031
30	-0.080281	-0.6765	0.250474
31	-0.072963	-0.6148	0.270326
32	0.0099	0.0834	0.466875
33	0.090721	0.7644	0.223572
34	-0.209555	-1.7657	0.040869
35	-0.029372	-0.2475	0.40262
36	0.00226	0.019	0.492431
37	0.035343	0.2978	0.38336
38	-0.10249	-0.8636	0.19536
39	0.018811	0.1585	0.437255
40	-0.017942	-0.1512	0.440131
41	0.090251	0.7605	0.224746
42	0.075744	0.6382	0.262689
43	-0.136797	-1.1527	0.126455
44	0.021693	0.1828	0.427744
45	-0.008052	-0.0678	0.473048
46	-0.034469	-0.2904	0.386162
47	0.157489	1.327	0.094376
48	0.013714	0.1156	0.454165
49	-0.001613	-0.0136	0.494596
50	-0.118052	-0.9947	0.161625
51	-0.096991	-0.8173	0.208257
52	0.033113	0.279	0.390522
53	3.9e-05	3e-04	0.499869
54	0.076456	0.6442	0.260751
55	-0.021352	-0.1799	0.428866
56	-0.100966	-0.8508	0.198884
57	0.06007	0.5062	0.307156
58	-0.038952	-0.3282	0.371858
59	-0.070175	-0.5913	0.278097
60	-0.070976	-0.5981	0.275855

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260699278f1wk1v4ulfuu1hc/14ftx1260699175.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260699278f1wk1v4ulfuu1hc/14ftx1260699175.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260699278f1wk1v4ulfuu1hc/2h8vj1260699175.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/13/t1260699278f1wk1v4ulfuu1hc/2h8vj1260699175.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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 (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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