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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: Thu, 03 Dec 2009 11:47:03 -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/03/t1259866238n3pd15d8nunyhwr.htm/, Retrieved Thu, 03 Dec 2009 19:50:41 +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/03/t1259866238n3pd15d8nunyhwr.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 «

12.610 10.862 52.929 56.902 81.776 87.876 82.103 72.846 60.632 33.521 15.342 7.758 8.668 13.082 38.157 58.263 81.153 88.476 72.329 75.845 61.108 37.665 12.755 2.793 12.935 19.533 33.404 52.074 70.735 69.702 61.656 82.993 53.990 32.283 15.686 2.713 12.842 19.244 48.488 54.464 84.192 84.458 85.793 75.163 68.212 49.233 24.302 5.402 15.058 33.559 70.358 85.934 94.452 129.305 113.882 107.256 94.274 57.842 26.611 14.521

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	-0.44346	-3.0402	0.001928
2	-0.100928	-0.6919	0.246194
3	-0.044245	-0.3033	0.38149
4	0.217899	1.4938	0.07095
5	-0.191975	-1.3161	0.097259
6	0.120685	0.8274	0.206104
7	0.013405	0.0919	0.463585
8	-0.166774	-1.1433	0.129343
9	0.185856	1.2742	0.104435
10	-0.120706	-0.8275	0.206062
11	0.100014	0.6857	0.248148
12	-0.116674	-0.7999	0.213903
13	0.031636	0.2169	0.414618
14	0.020025	0.1373	0.445697
15	0.074991	0.5141	0.30479
16	-0.119328	-0.8181	0.208723
17	0.048616	0.3333	0.370197
18	0.002213	0.0152	0.493979
19	-0.054847	-0.376	0.354301
20	-0.010013	-0.0686	0.47278
21	0.115248	0.7901	0.216719
22	-0.042626	-0.2922	0.3857
23	0.004872	0.0334	0.486748
24	-0.192919	-1.3226	0.096187
25	0.291132	1.9959	0.025879
26	-0.073165	-0.5016	0.309147
27	-0.078245	-0.5364	0.297099
28	-0.077314	-0.53	0.299291
29	0.24171	1.6571	0.052082
30	-0.127285	-0.8726	0.193653
31	0.007407	0.0508	0.479857
32	0.055445	0.3801	0.352787
33	-0.186255	-1.2769	0.103955
34	0.121549	0.8333	0.204447
35	0.031891	0.2186	0.413941
36	0.018311	0.1255	0.450319
37	-0.112113	-0.7686	0.222986
38	0.112463	0.771	0.222281
39	-0.118867	-0.8149	0.209617
40	0.10926	0.749	0.228781
41	-0.060051	-0.4117	0.341219
42	-0.005361	-0.0368	0.48542
43	0.00614	0.0421	0.483302
44	0.042385	0.2906	0.386326
45	-0.083179	-0.5702	0.285613
46	0.053177	0.3646	0.358537
47	NA	NA	NA
48	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.44346	-3.0402	0.001928
2	-0.370433	-2.5396	0.007233
3	-0.389339	-2.6692	0.005203
4	-0.083828	-0.5747	0.284118
5	-0.227697	-1.561	0.062615
6	-0.039563	-0.2712	0.393701
7	0.078035	0.535	0.297593
8	-0.181595	-1.245	0.109661
9	0.112757	0.773	0.221689
10	-0.121639	-0.8339	0.204273
11	0.04588	0.3145	0.377253
12	-0.021121	-0.1448	0.442744
13	-0.196314	-1.3459	0.092402
14	0.012475	0.0855	0.466103
15	-0.020338	-0.1394	0.444854
16	-0.058469	-0.4008	0.345177
17	0.073686	0.5052	0.307902
18	-0.090777	-0.6223	0.268365
19	-0.049329	-0.3382	0.368365
20	-0.201734	-1.383	0.086597
21	-0.080701	-0.5533	0.291354
22	0.01928	0.1322	0.447704
23	0.052572	0.3604	0.360075
24	-0.267269	-1.8323	0.036623
25	0.116762	0.8005	0.213731
26	0.040078	0.2748	0.392351
27	-0.013051	-0.0895	0.464544
28	-0.07481	-0.5129	0.305221
29	0.039259	0.2691	0.394497
30	0.087217	0.5979	0.276379
31	0.11131	0.7631	0.224608
32	0.092904	0.6369	0.263635
33	-0.051274	-0.3515	0.363387
34	-0.066256	-0.4542	0.325877
35	-0.043002	-0.2948	0.38472
36	-0.106072	-0.7272	0.235358
37	0.033141	0.2272	0.410625
38	0.023473	0.1609	0.436422
39	-0.035631	-0.2443	0.404041
40	0.009206	0.0631	0.474972
41	-0.036043	-0.2471	0.402953
42	-0.01352	-0.0927	0.463273
43	-0.083417	-0.5719	0.285064
44	-0.054394	-0.3729	0.355447
45	-0.038991	-0.2673	0.3952
46	-0.091228	-0.6254	0.267357
47	NA	NA	NA
48	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866238n3pd15d8nunyhwr/1fng01259866022.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866238n3pd15d8nunyhwr/1fng01259866022.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866238n3pd15d8nunyhwr/2x8n11259866022.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259866238n3pd15d8nunyhwr/2x8n11259866022.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 0.3 ; par3 = 1 ; par4 = 1 ; 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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