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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: Tue, 29 Dec 2009 13:07:39 -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/29/t1262117861zqvksbo9v1x10ri.htm/, Retrieved Tue, 29 Dec 2009 21:17:44 +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/29/t1262117861zqvksbo9v1x10ri.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 «

100.44 100.51 101.00 100.88 100.55 100.83 101.51 102.16 102.39 102.54 102.85 103.47 103.57 103.69 103.50 103.47 103.45 103.48 103.93 103.89 104.40 104.79 104.77 105.13 105.26 104.96 104.75 105.01 105.15 105.20 105.77 105.78 106.26 106.13 106.12 106.57 106.44 106.54 107.10 108.10 108.40 108.84 109.62 110.42 110.67 111.66 112.28 112.87 112.18 112.36 112.16 111.49 111.25 111.36 111.74 111.10 111.33 111.25 111.04 110.97 111.31 111.02 111.07 111.36

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.233449	1.8529	0.034288
2	0.156981	1.246	0.108689
3	0.212517	1.6868	0.048294
4	0.218469	1.734	0.0439
5	-0.082965	-0.6585	0.256305
6	-0.11399	-0.9048	0.184517
7	0.094467	0.7498	0.228081
8	-0.110366	-0.876	0.192179
9	-0.136758	-1.0855	0.140921
10	-0.084374	-0.6697	0.252749
11	0.030731	0.2439	0.404043
12	-0.146362	-1.1617	0.124867
13	-0.207638	-1.6481	0.052158
14	-0.114794	-0.9112	0.182844
15	-0.00995	-0.079	0.468652
16	-0.268433	-2.1306	0.018515
17	-0.096148	-0.7632	0.22411
18	-0.100897	-0.8008	0.213116
19	-0.073202	-0.581	0.281649
20	-0.184349	-1.4632	0.074189
21	0.022583	0.1793	0.429158
22	0.081326	0.6455	0.260472
23	-0.04539	-0.3603	0.359925
24	0.059541	0.4726	0.319067
25	0.044073	0.3498	0.36382
26	0.017362	0.1378	0.445415
27	-0.041575	-0.33	0.37125
28	-0.03962	-0.3145	0.377101
29	-0.009485	-0.0753	0.470114
30	-0.021177	-0.1681	0.433528
31	-0.05313	-0.4217	0.337338
32	0.096595	0.7667	0.223062
33	0.152033	1.2067	0.116025
34	0.06824	0.5416	0.294988
35	0.037898	0.3008	0.382275
36	0.193675	1.5372	0.06462
37	0.032457	0.2576	0.398769
38	-0.000231	-0.0018	0.499273
39	0.039155	0.3108	0.378497
40	0.008715	0.0692	0.472537
41	-0.078744	-0.625	0.26711
42	-0.080644	-0.6401	0.262218
43	-0.014623	-0.1161	0.453983
44	-0.047716	-0.3787	0.353079
45	-0.022356	-0.1774	0.429865
46	-0.053393	-0.4238	0.33658
47	0.067693	0.5373	0.296478
48	-0.008441	-0.067	0.473398
49	-0.047679	-0.3784	0.353187
50	-0.059579	-0.4729	0.31896
51	-0.009227	-0.0732	0.470926
52	3.8e-05	3e-04	0.49988
53	-0.030673	-0.2435	0.40422
54	0.023244	0.1845	0.427111
55	-0.014183	-0.1126	0.455362
56	-0.019336	-0.1535	0.439256
57	0.022733	0.1804	0.428695
58	0.033994	0.2698	0.394091
59	-0.021985	-0.1745	0.431016
60	-0.002994	-0.0238	0.490557

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.233449	1.8529	0.034288
2	0.10839	0.8603	0.196438
3	0.165389	1.3127	0.097017
4	0.140645	1.1163	0.134258
5	-0.210522	-1.671	0.049845
6	-0.151169	-1.1999	0.117342
7	0.130119	1.0328	0.152826
8	-0.118709	-0.9422	0.17484
9	-0.025248	-0.2004	0.420907
10	-0.030651	-0.2433	0.404287
11	0.034254	0.2719	0.393302
12	-0.079764	-0.6331	0.264478
13	-0.156941	-1.2457	0.108747
14	-0.101421	-0.805	0.211922
15	0.100689	0.7992	0.213591
16	-0.208369	-1.6539	0.051563
17	0.064482	0.5118	0.305287
18	-0.144049	-1.1434	0.12861
19	-0.020968	-0.1664	0.434178
20	-0.080454	-0.6386	0.262704
21	0.067912	0.539	0.29588
22	0.015221	0.1208	0.452111
23	-0.001073	-0.0085	0.496616
24	-0.00325	-0.0258	0.489751
25	-0.055278	-0.4388	0.331169
26	-0.148711	-1.1804	0.121148
27	0.029099	0.231	0.409044
28	-0.153693	-1.2199	0.113524
29	0.002543	0.0202	0.491981
30	-0.023779	-0.1887	0.425452
31	-0.045391	-0.3603	0.359923
32	0.065519	0.52	0.30243
33	0.140303	1.1136	0.134836
34	-0.094586	-0.7507	0.227799
35	0.046297	0.3675	0.357251
36	0.01148	0.0911	0.463844
37	-0.065158	-0.5172	0.303423
38	0.014656	0.1163	0.45388
39	-0.025874	-0.2054	0.418974
40	-0.066048	-0.5242	0.300975
41	-0.018138	-0.144	0.442995
42	-0.070275	-0.5578	0.289482
43	-0.024722	-0.1962	0.422534
44	-0.024274	-0.1927	0.423918
45	0.060504	0.4802	0.316362
46	-0.060104	-0.4771	0.317484
47	0.097896	0.777	0.220025
48	-0.055058	-0.437	0.3318
49	-0.01827	-0.145	0.442583
50	-0.062251	-0.4941	0.311476
51	-0.010741	-0.0853	0.466165
52	0.11937	0.9475	0.17351
53	0.040419	0.3208	0.374707
54	-0.066188	-0.5254	0.300592
55	-0.058473	-0.4641	0.322083
56	-0.08289	-0.6579	0.256493
57	0.003929	0.0312	0.48761
58	0.010535	0.0836	0.466812
59	-0.033255	-0.264	0.39634
60	-0.025804	-0.2048	0.419188

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262117861zqvksbo9v1x10ri/1x1be1262117257.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262117861zqvksbo9v1x10ri/1x1be1262117257.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262117861zqvksbo9v1x10ri/2zdqn1262117257.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262117861zqvksbo9v1x10ri/2zdqn1262117257.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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