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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, 22 Dec 2008 09:29:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/22/t12299633738mi2sbs357d2whl.htm/, Retrieved Mon, 22 Dec 2008 17:29:35 +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/2008/Dec/22/t12299633738mi2sbs357d2whl.htm/},
    year = {2008},
}
@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 = {2008},
    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 «

14532,2 15167 16071,1 14827,5 15082 14772,7 16083 14272,5 15223,3 14897,3 13062,6 12603,8 13629,8 14421,1 13978,3 12927,9 13429,9 13470,1 14785,8 14292 14308,8 14013 13240,9 12153,4 14289,7 15669,2 14169,5 14569,8 14469,1 14264,9 15320,9 14433,5 13691,5 14194,1 13519,2 11857,9 14616 15643,4 14077,2 14887,5 14159,9 14643 17192,5 15386,1 14287,1 17526,6 14497 14398,3 16629,6 16670,7 16614,8 16869,2 15663,9 16359,9 18447,7 16889 16505 18320,9 15052,1 15699,8 18135,3 16768,7 18883 19021 18101,9 17776,1 21489,9 17065,3 18690 18953,1 16398,9 16895,7 18553 19270 19422,1 17579,4 18637,3 18076,7 20438,6 18075,2 19563 19899,2 19227,5 17789,6 19220,8 22058,6 21230,8 19504,4 23913,1 23165,7 23574,3 25002 22603,9 23408,6

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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.820543	7.9555	0
2	0.768954	7.4553	0
3	0.766373	7.4303	0
4	0.677312	6.5668	0
5	0.635758	6.1639	0
6	0.621521	6.0259	0
7	0.560434	5.4336	0
8	0.536103	5.1977	1e-06
9	0.517443	5.0168	1e-06
10	0.463069	4.4896	1e-05
11	0.490256	4.7532	4e-06
12	0.540187	5.2373	0
13	0.425218	4.1226	4e-05
14	0.39118	3.7926	0.000132
15	0.402225	3.8997	9e-05
16	0.346243	3.357	0.000569
17	0.350338	3.3967	0.000501
18	0.338855	3.2853	0.000716
19	0.304289	2.9502	0.002004
20	0.287399	2.7864	0.003224
21	0.264582	2.5652	0.005947
22	0.229466	2.2248	0.014245
23	0.264658	2.566	0.005935
24	0.27892	2.7042	0.004064
25	0.216599	2.1	0.019203
26	0.175509	1.7016	0.046066
27	0.161385	1.5647	0.060508
28	0.108068	1.0478	0.148719
29	0.097536	0.9456	0.173376
30	0.056407	0.5469	0.292875
31	0.028525	0.2766	0.391362
32	-0.002269	-0.022	0.491249
33	-0.026687	-0.2587	0.3982
34	-0.05476	-0.5309	0.298365
35	-0.03191	-0.3094	0.378858
36	-0.018125	-0.1757	0.430442
37	-0.070436	-0.6829	0.248175
38	-0.109145	-1.0582	0.146337
39	-0.120643	-1.1697	0.122544
40	-0.147161	-1.4268	0.078478
41	-0.164301	-1.593	0.057263
42	-0.184566	-1.7894	0.038382
43	-0.187767	-1.8205	0.035935
44	-0.21214	-2.0568	0.021239
45	-0.246382	-2.3888	0.009452
46	-0.247375	-2.3984	0.009221
47	-0.249352	-2.4176	0.008777
48	-0.22806	-2.2111	0.014726
49	-0.271961	-2.6368	0.004897
50	-0.304458	-2.9518	0.001994
51	-0.302454	-2.9324	0.002112
52	-0.319582	-3.0985	0.001283
53	-0.334188	-3.2401	0.000826
54	-0.327118	-3.1715	0.001024
55	-0.332561	-3.2243	0.000869
56	-0.335011	-3.2481	0.000806
57	-0.342816	-3.3237	0.000634
58	-0.334281	-3.241	0.000824
59	-0.317124	-3.0746	0.00138
60	-0.280591	-2.7204	0.003884

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.820543	7.9555	0
2	0.292809	2.8389	0.002774
3	0.267498	2.5935	0.00551
4	-0.11778	-1.1419	0.128195
5	0.007559	0.0733	0.470868
6	0.063472	0.6154	0.269893
7	-0.036863	-0.3574	0.360796
8	0.036976	0.3585	0.360387
9	0.016412	0.1591	0.436956
10	-0.053221	-0.516	0.303534
11	0.188683	1.8293	0.035259
12	0.259015	2.5112	0.006869
13	-0.352049	-3.4132	0.000474
14	-0.189924	-1.8414	0.03436
15	0.070455	0.6831	0.248115
16	0.116181	1.1264	0.131429
17	0.12444	1.2065	0.115328
18	-0.102978	-0.9984	0.160321
19	-0.054151	-0.525	0.300403
20	-0.041068	-0.3982	0.345705
21	0.060729	0.5888	0.278709
22	0.022202	0.2153	0.415018
23	0.017569	0.1703	0.432554
24	-0.019238	-0.1865	0.42622
25	0.008168	0.0792	0.468525
26	-0.14602	-1.4157	0.080081
27	-0.104446	-1.0126	0.156915
28	-0.068136	-0.6606	0.25524
29	0.030842	0.299	0.382792
30	-0.064838	-0.6286	0.26556
31	0.031508	0.3055	0.380336
32	-0.044398	-0.4305	0.333926
33	0.070204	0.6806	0.248883
34	-0.038863	-0.3768	0.353588
35	-0.020195	-0.1958	0.422597
36	0.013128	0.1273	0.449494
37	-0.074892	-0.7261	0.23479
38	-0.079657	-0.7723	0.220935
39	-0.019466	-0.1887	0.425354
40	0.02227	0.2159	0.414761
41	-0.029992	-0.2908	0.385928
42	-0.035675	-0.3459	0.365103
43	0.056145	0.5443	0.293746
44	-0.021169	-0.2052	0.418915
45	-0.081035	-0.7857	0.21702
46	0.012976	0.1258	0.450077
47	-0.075411	-0.7311	0.233256
48	0.046358	0.4495	0.327068
49	-0.041735	-0.4046	0.343332
50	-0.043667	-0.4234	0.336496
51	-0.010944	-0.1061	0.457862
52	-0.01152	-0.1117	0.455654
53	0.032833	0.3183	0.375472
54	0.019064	0.1848	0.42688
55	-0.047112	-0.4568	0.324446
56	0.063239	0.6131	0.270637
57	0.063203	0.6128	0.270751
58	-0.032093	-0.3112	0.378186
59	-0.041508	-0.4024	0.34414
60	-0.011221	-0.1088	0.456798

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299633738mi2sbs357d2whl/110ry1229963342.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299633738mi2sbs357d2whl/110ry1229963342.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299633738mi2sbs357d2whl/2nh7v1229963342.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/22/t12299633738mi2sbs357d2whl/2nh7v1229963342.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (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='lags',ylab='ACF')

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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