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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, 15 Dec 2008 12:52:36 -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/15/t1229370831bo9c7amx1ikvcxu.htm/, Retrieved Mon, 15 Dec 2008 20:53:53 +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/15/t1229370831bo9c7amx1ikvcxu.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 «

31.88 28.03 27.24 29.14 28.19 28.93 32.28 34.70 33.72 34.26 35.42 34.45 34.16 32.57 28.40 29.15 28.67 28.20 29.25 29.74 26.25 26.81 27.68 27.10 27.04 26.00 25.76 25.93 24.94 21.72 18.16 16.98 16.49 16.52 18.24 16.41 15.71 13.97 12.24 14.75 14.61 15.04 15.50 16.08 15.45 15.14 15.43 15.70 17.57 18.41 17.97 18.39 17.63 17.93 17.80 17.70 18.99 19.83 20.21 20.23 21.10 21.25 21.80 21.83 22.21 22.64 23.53 23.78 23.65 23.92 24.76 26.25 27.68 29.55 29.30 29.25 28.69 26.17 27.09 29.40 30.98 32.96 32.19 31.68 32.49 33.67 32.42 34.38 32.37 30.73 30.33 27.26 25.05 22.25 18.26 18.30

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	0.959633	9.4024	0
2	0.910436	8.9204	0
3	0.863876	8.4642	0
4	0.806832	7.9053	0
5	0.760675	7.4531	0
6	0.718935	7.0441	0
7	0.663253	6.4985	0
8	0.605317	5.9309	0
9	0.552776	5.4161	0
10	0.491544	4.8161	3e-06
11	0.433402	4.2465	2.5e-05
12	0.379743	3.7207	0.000167
13	0.319895	3.1343	0.001143
14	0.266897	2.615	0.00518
15	0.226255	2.2168	0.014497
16	0.173129	1.6963	0.046534
17	0.111033	1.0879	0.139683
18	0.041983	0.4114	0.340866
19	-0.029736	-0.2914	0.385705
20	-0.09439	-0.9248	0.178687
21	-0.142166	-1.3929	0.083429
22	-0.187292	-1.8351	0.034795
23	-0.230163	-2.2551	0.013199
24	-0.270402	-2.6494	0.004715
25	-0.314804	-3.0844	0.001332
26	-0.356474	-3.4927	0.000362
27	-0.392994	-3.8505	0.000106
28	-0.42827	-4.1962	3e-05
29	-0.457648	-4.484	1e-05
30	-0.478505	-4.6884	5e-06
31	-0.493721	-4.8375	3e-06
32	-0.505022	-4.9482	2e-06
33	-0.51405	-5.0366	1e-06
34	-0.521939	-5.1139	1e-06
35	-0.530495	-5.1978	1e-06
36	-0.527545	-5.1689	1e-06
37	-0.524648	-5.1405	1e-06
38	-0.515342	-5.0493	1e-06
39	-0.499104	-4.8902	2e-06
40	-0.49347	-4.835	3e-06
41	-0.487601	-4.7775	3e-06
42	-0.479791	-4.701	4e-06
43	-0.469413	-4.5993	6e-06
44	-0.451085	-4.4197	1.3e-05
45	-0.425206	-4.1662	3.4e-05
46	-0.397299	-3.8927	9.2e-05
47	-0.3664	-3.59	0.000262
48	-0.33586	-3.2907	0.000699
49	-0.311689	-3.0539	0.001462
50	-0.28412	-2.7838	0.003236
51	-0.251195	-2.4612	0.007816
52	-0.217485	-2.1309	0.017826
53	-0.175811	-1.7226	0.044091
54	-0.136758	-1.3399	0.091713
55	-0.099626	-0.9761	0.165727
56	-0.059094	-0.579	0.281973
57	-0.02305	-0.2258	0.410903
58	0.004093	0.0401	0.484046
59	0.03373	0.3305	0.370879
60	0.067083	0.6573	0.256287

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.959633	9.4024	0
2	-0.132232	-1.2956	0.09911
3	0.020026	0.1962	0.422429
4	-0.168621	-1.6521	0.050887
5	0.145767	1.4282	0.078237
6	-0.022712	-0.2225	0.412188
7	-0.182914	-1.7922	0.038127
8	-0.060392	-0.5917	0.277714
9	0.044017	0.4313	0.333617
10	-0.117492	-1.1512	0.126259
11	-0.009338	-0.0915	0.463647
12	-0.03847	-0.3769	0.353531
13	-0.057938	-0.5677	0.28579
14	0.044316	0.4342	0.332555
15	0.077449	0.7588	0.224902
16	-0.198565	-1.9455	0.027318
17	-0.157829	-1.5464	0.062649
18	-0.178103	-1.745	0.042089
19	0.036505	0.3577	0.360685
20	-0.013963	-0.1368	0.445734
21	0.088462	0.8667	0.194121
22	-0.06383	-0.6254	0.266595
23	0.016548	0.1621	0.43577
24	-0.061404	-0.6016	0.274417
25	-0.032164	-0.3151	0.376668
26	-0.05953	-0.5833	0.280539
27	-0.044519	-0.4362	0.331837
28	-0.03857	-0.3779	0.353168
29	0.032592	0.3193	0.375085
30	-0.031989	-0.3134	0.37732
31	0.022073	0.2163	0.414617
32	-0.040267	-0.3945	0.347031
33	0.024935	0.2443	0.403756
34	0.018952	0.1857	0.426541
35	-0.025454	-0.2494	0.401792
36	0.037593	0.3683	0.356719
37	-0.132468	-1.2979	0.098713
38	0.015564	0.1525	0.439557
39	-0.000365	-0.0036	0.498577
40	-0.154067	-1.5095	0.067223
41	0.00235	0.023	0.49084
42	-0.051844	-0.508	0.30632
43	0.081617	0.7997	0.212937
44	0.033224	0.3255	0.372744
45	0.001659	0.0163	0.493532
46	-0.007962	-0.078	0.468992
47	-0.000297	-0.0029	0.498841
48	-0.07308	-0.716	0.237854
49	-0.069516	-0.6811	0.248719
50	0.026287	0.2576	0.398648
51	0.021942	0.215	0.415115
52	0.054446	0.5335	0.297474
53	0.061255	0.6002	0.274904
54	-0.09719	-0.9523	0.171677
55	0.048817	0.4783	0.316761
56	0.066577	0.6523	0.257878
57	-0.001949	-0.0191	0.492401
58	-0.121805	-1.1934	0.117818
59	0.009062	0.0888	0.464719
60	0.017145	0.168	0.433474

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229370831bo9c7amx1ikvcxu/1min81229370754.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229370831bo9c7amx1ikvcxu/1min81229370754.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229370831bo9c7amx1ikvcxu/213i01229370754.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229370831bo9c7amx1ikvcxu/213i01229370754.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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