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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, 13 Dec 2010 09:39:12 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/13/t1292233095x6bu0zksd8k7m52.htm/, Retrieved Mon, 13 Dec 2010 10:38:15 +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/2010/Dec/13/t1292233095x6bu0zksd8k7m52.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

76.14 75.93 74.49 74.73 75.56 84.19 79.30 74.70 77.09 74.88 77.56 74.08 68.38 71.63 64.65 69.13 58.10 50.28 46.95 41.76 43.91 41.53 54.04 72.69 99.29 114.57 132.55 131.52 122.77 109.05 101.84 93.75 90.82 89.43 91.27 82.15 76.91 70.13 73.67 68.19 65.10 65.10 60.60 57.58 53.40 61.00 58.13 57.95 61.97 71.81 72.51 68.29 68.61 68.00 60.93 59.71 62.36 56.47

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	7 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.526387	3.9741	1e-04
2	0.396086	2.9904	0.002055
3	0.096836	0.7311	0.233859
4	-0.070348	-0.5311	0.298702
5	-0.258998	-1.9554	0.027723
6	-0.351506	-2.6538	0.005148
7	-0.224009	-1.6912	0.048127
8	-0.197951	-1.4945	0.070281
9	-0.196746	-1.4854	0.071474
10	-0.098971	-0.7472	0.229003
11	-0.055045	-0.4156	0.339639
12	-0.105774	-0.7986	0.213926
13	-0.109247	-0.8248	0.206463
14	-0.048858	-0.3689	0.356796
15	0.006266	0.0473	0.481218
16	-0.075924	-0.5732	0.284378
17	-0.072163	-0.5448	0.294001
18	-0.023457	-0.1771	0.430029
19	0.039851	0.3009	0.382305
20	-0.035669	-0.2693	0.394339
21	0.09403	0.7099	0.240326
22	0.082378	0.6219	0.26823
23	0.171339	1.2936	0.100515
24	0.075596	0.5707	0.285211
25	0.153349	1.1578	0.125896
26	0.093443	0.7055	0.241692
27	0.006432	0.0486	0.480721
28	-0.021342	-0.1611	0.43628
29	-0.046685	-0.3525	0.362896
30	-0.030295	-0.2287	0.409951
31	-0.121556	-0.9177	0.181313
32	-0.070792	-0.5345	0.297548
33	-0.046458	-0.3507	0.363535
34	-0.03231	-0.2439	0.404079
35	-0.009871	-0.0745	0.470427
36	0.004405	0.0333	0.486792
37	0.00465	0.0351	0.486058
38	0.000753	0.0057	0.497742
39	-0.015715	-0.1186	0.452987
40	0.041923	0.3165	0.376386
41	0.011348	0.0857	0.466014
42	-0.01781	-0.1345	0.446754
43	0.012067	0.0911	0.463865
44	0.019043	0.1438	0.443095
45	0.02113	0.1595	0.436908
46	-0.007673	-0.0579	0.477002
47	-0.001084	-0.0082	0.49675
48	0.015367	0.116	0.454023

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.526387	3.9741	1e-04
2	0.164614	1.2428	0.109513
3	-0.233162	-1.7603	0.041858
4	-0.149942	-1.132	0.131179
5	-0.176403	-1.3318	0.094111
6	-0.146531	-1.1063	0.136625
7	0.162241	1.2249	0.112826
8	-0.03734	-0.2819	0.389518
9	-0.234249	-1.7685	0.04116
10	0.011291	0.0852	0.466183
11	-0.021537	-0.1626	0.435705
12	-0.212417	-1.6037	0.057152
13	-0.03557	-0.2685	0.394625
14	0.037836	0.2857	0.388088
15	-0.045948	-0.3469	0.364973
16	-0.185742	-1.4023	0.083121
17	-0.134914	-1.0186	0.156354
18	-0.036771	-0.2776	0.391157
19	0.090611	0.6841	0.248342
20	-0.164368	-1.2409	0.109854
21	0.030282	0.2286	0.40999
22	-0.07942	-0.5996	0.275571
23	0.068428	0.5166	0.303709
24	-0.078397	-0.5919	0.278135
25	0.029428	0.2222	0.412484
26	-0.062465	-0.4716	0.319506
27	-0.044478	-0.3358	0.369127
28	0.00159	0.012	0.495232
29	-0.063065	-0.4761	0.317901
30	0.004889	0.0369	0.485343
31	-0.068532	-0.5174	0.303439
32	-0.013683	-0.1033	0.459041
33	-0.034265	-0.2587	0.398401
34	-0.021693	-0.1638	0.435243
35	0.05464	0.4125	0.340753
36	-0.064016	-0.4833	0.315364
37	-0.089238	-0.6737	0.251603
38	0.017661	0.1333	0.447198
39	0.02045	0.1544	0.438922
40	-0.004636	-0.035	0.486102
41	0.009486	0.0716	0.471577
42	-0.130408	-0.9846	0.1645
43	0.062888	0.4748	0.318373
44	-0.021151	-0.1597	0.436847
45	0.001207	0.0091	0.496379
46	-0.054861	-0.4142	0.340145
47	-0.013522	-0.1021	0.459521
48	-0.021463	-0.162	0.435923

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292233095x6bu0zksd8k7m52/1t9ir1292233143.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292233095x6bu0zksd8k7m52/1t9ir1292233143.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292233095x6bu0zksd8k7m52/2t9ir1292233143.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/13/t1292233095x6bu0zksd8k7m52/2t9ir1292233143.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; 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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