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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: Wed, 06 Jan 2010 02:56:35 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/06/t1262771950f69so48dns8cwke.htm/, Retrieved Wed, 06 Jan 2010 10:59:12 +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/Jan/06/t1262771950f69so48dns8cwke.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:

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	0.940628	7.9815	0
2	0.866462	7.3522	0
3	0.783385	6.6472	0
4	0.68574	5.8187	0
5	0.592309	5.0259	2e-06
6	0.496746	4.215	3.6e-05
7	0.401727	3.4088	0.000536
8	0.310073	2.6311	0.005202
9	0.234723	1.9917	0.025099
10	0.170783	1.4491	0.07582
11	0.111048	0.9423	0.174601
12	0.072414	0.6145	0.270427
13	0.048797	0.4141	0.340031
14	0.023877	0.2026	0.420008
15	-0.003274	-0.0278	0.488957
16	-0.038	-0.3224	0.374027
17	-0.08226	-0.698	0.243713
18	-0.131536	-1.1161	0.134041
19	-0.184997	-1.5698	0.060428
20	-0.234871	-1.9929	0.025029
21	-0.270949	-2.2991	0.012202
22	-0.308872	-2.6209	0.005346
23	-0.335181	-2.8441	0.002897
24	-0.361063	-3.0637	0.001537
25	-0.380325	-3.2272	0.000941
26	-0.386201	-3.277	0.000808
27	-0.386212	-3.2771	0.000808
28	-0.383685	-3.2557	0.000863
29	-0.382019	-3.2415	0.000901
30	-0.383132	-3.251	0.000875
31	-0.3815	-3.2371	0.000913
32	-0.372664	-3.1622	0.001146
33	-0.364961	-3.0968	0.001394
34	-0.356901	-3.0284	0.001706
35	-0.340278	-2.8874	0.002563
36	-0.320202	-2.717	0.004123
37	-0.29746	-2.524	0.006904
38	-0.27005	-2.2914	0.012433
39	-0.236524	-2.007	0.024254
40	-0.201372	-1.7087	0.045907
41	-0.161556	-1.3708	0.08734
42	-0.124062	-1.0527	0.147999
43	-0.097309	-0.8257	0.205852
44	-0.070012	-0.5941	0.277162
45	-0.04301	-0.3649	0.358109
46	-0.016693	-0.1416	0.443878
47	0.00708	0.0601	0.47613
48	0.018961	0.1609	0.436315
49	0.024886	0.2112	0.416679
50	0.03056	0.2593	0.398068
51	0.027515	0.2335	0.408027
52	0.032102	0.2724	0.393048
53	0.037739	0.3202	0.374861
54	0.048958	0.4154	0.339535
55	0.06131	0.5202	0.30225
56	0.071738	0.6087	0.272314
57	0.08458	0.7177	0.237636
58	0.098409	0.835	0.203232
59	0.106645	0.9049	0.184265
60	0.118492	1.0054	0.159027

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.940628	7.9815	0
2	-0.158988	-1.3491	0.090773
3	-0.103847	-0.8812	0.190578
4	-0.162107	-1.3755	0.086617
5	0.008569	0.0727	0.471119
6	-0.076379	-0.6481	0.259492
7	-0.047592	-0.4038	0.343767
8	-0.05027	-0.4266	0.335489
9	0.082824	0.7028	0.242228
10	0.008454	0.0717	0.471506
11	-0.052484	-0.4453	0.328704
12	0.095798	0.8129	0.209486
13	0.05553	0.4712	0.319466
14	-0.092261	-0.7829	0.218139
15	-0.109872	-0.9323	0.177149
16	-0.11215	-0.9516	0.172236
17	-0.099247	-0.8421	0.20125
18	-0.079804	-0.6772	0.250237
19	-0.082224	-0.6977	0.243808
20	0.021346	0.1811	0.428389
21	0.116684	0.9901	0.162722
22	-0.090353	-0.7667	0.222891
23	0.040775	0.346	0.365182
24	-0.07722	-0.6552	0.257203
25	-0.006897	-0.0585	0.476749
26	-0.019588	-0.1662	0.434229
27	-0.052757	-0.4477	0.327873
28	-0.090821	-0.7706	0.221721
29	-0.062186	-0.5277	0.299676
30	-0.091171	-0.7736	0.220848
31	0.007456	0.0633	0.474864
32	0.094865	0.805	0.211747
33	-0.027045	-0.2295	0.409571
34	-0.011245	-0.0954	0.462125
35	0.050816	0.4312	0.33381
36	-0.027198	-0.2308	0.40907
37	-0.031874	-0.2705	0.393789
38	-0.032074	-0.2722	0.393142
39	0.007205	0.0611	0.475711
40	-0.01317	-0.1118	0.455665
41	-0.002549	-0.0216	0.491403
42	-0.072471	-0.6149	0.270266
43	-0.03199	-0.2714	0.393412
44	0.018695	0.1586	0.4372
45	0.034676	0.2942	0.384714
46	0.044576	0.3782	0.353183
47	-0.005381	-0.0457	0.481855
48	-0.125488	-1.0648	0.145261
49	-0.073062	-0.62	0.268623
50	-0.018768	-0.1593	0.436958
51	-0.09387	-0.7965	0.214176
52	0.080964	0.687	0.247145
53	-0.022103	-0.1876	0.425877
54	0.05656	0.4799	0.316368
55	-0.023963	-0.2033	0.419724
56	-0.022846	-0.1939	0.423418
57	0.036986	0.3138	0.377278
58	0.044242	0.3754	0.35423
59	-0.111334	-0.9447	0.173986
60	0.0055	0.0467	0.481454

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/06/t1262771950f69so48dns8cwke/1e41c1262771792.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/06/t1262771950f69so48dns8cwke/1e41c1262771792.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/06/t1262771950f69so48dns8cwke/2amdo1262771792.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/06/t1262771950f69so48dns8cwke/2amdo1262771792.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; 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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