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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: Sun, 05 Dec 2010 13:25:23 +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/05/t1291555531a38l0xhtzk5laix.htm/, Retrieved Sun, 05 Dec 2010 14:25:31 +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/05/t1291555531a38l0xhtzk5laix.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 «

1579 2146 2462 3695 4831 5134 6250 5760 6249 2917 1741 2359 1511 2059 2635 2867 4403 5720 4502 5749 5627 2846 1762 2429 1169 2154 2249 2687 4359 5382 4459 6398 4596 3024 1887 2070 1351 2218 2461 3028 4784 4975 4607 6249 4809 3157 1910 2228 1594 2467 2222 3607 4685 4962 5770 5480 5000 3228 1993 2288 1580 2111 2192 3601 4665 4876 5813 5589 5331 3075 2002 2306 1507 1992 2487 3490 4647 5594 5611 5788 6204 3013 1931 2549 1504 2090 2702 2939 4500 6208 6415 5657 5964 3163 1997 2422 1376 2202 2683 3303 5202 5231 4880 7998 4977 3531 2025 2205 1442 2238 2179 3218 5139 4990 4914 6084 5672 3548 1793 2086

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.721997	7.9091	0
2	0.378118	4.1421	3.2e-05
3	0.00147	0.0161	0.493589
4	-0.427046	-4.6781	4e-06
5	-0.715973	-7.8431	0
6	-0.798206	-8.7439	0
7	-0.71598	-7.8432	0
8	-0.385985	-4.2283	2.3e-05
9	0.029647	0.3248	0.372961
10	0.357428	3.9154	7.5e-05
11	0.678533	7.433	0
12	0.84901	9.3004	0
13	0.657996	7.208	0
14	0.358114	3.9229	7.3e-05
15	-0.009708	-0.1063	0.457743
16	-0.390924	-4.2824	1.9e-05
17	-0.621464	-6.8078	0
18	-0.713787	-7.8191	0
19	-0.634949	-6.9555	0
20	-0.333587	-3.6543	0.000192
21	0.002538	0.0278	0.488933
22	0.311611	3.4135	0.000438
23	0.61844	6.7747	0
24	0.728595	7.9814	0
25	0.579497	6.3481	0
26	0.31685	3.4709	0.000361
27	-0.011895	-0.1303	0.448273
28	-0.339402	-3.718	0.000153
29	-0.560649	-6.1416	0
30	-0.632975	-6.9339	0
31	-0.541916	-5.9364	0
32	-0.283434	-3.1049	0.001188
33	-0.000692	-0.0076	0.496984
34	0.278363	3.0493	0.001411
35	0.524252	5.7429	0
36	0.627578	6.8748	0
37	0.516192	5.6546	0
38	0.254208	2.7847	0.003114
39	-0.013812	-0.1513	0.439994
40	-0.278256	-3.0481	0.001416
41	-0.482412	-5.2846	0
42	-0.549872	-6.0235	0
43	-0.466124	-5.1061	1e-06
44	-0.262502	-2.8756	0.002387
45	-0.000387	-0.0042	0.498311
46	0.25155	2.7556	0.003386
47	0.437646	4.7942	2e-06
48	0.539029	5.9048	0
49	0.44569	4.8823	2e-06
50	0.214942	2.3546	0.010084
51	-0.009253	-0.1014	0.459717
52	-0.23888	-2.6168	0.005009
53	-0.42381	-4.6426	4e-06
54	-0.466444	-5.1096	1e-06
55	-0.398872	-4.3694	1.3e-05
56	-0.232515	-2.5471	0.006064
57	0.001561	0.0171	0.493193
58	0.203998	2.2347	0.013645
59	0.363183	3.9785	6e-05
60	0.473205	5.1837	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.721997	7.9091	0
2	-0.299049	-3.2759	0.000689
3	-0.314878	-3.4493	0.000388
4	-0.508132	-5.5663	0
5	-0.343824	-3.7664	0.000129
6	-0.265166	-2.9047	0.002188
7	-0.330766	-3.6234	0.000214
8	-0.012209	-0.1337	0.446917
9	-0.005084	-0.0557	0.477842
10	-0.191771	-2.1007	0.018879
11	0.161486	1.769	0.039718
12	0.343592	3.7639	0.00013
13	-0.160301	-1.756	0.040819
14	-0.050542	-0.5537	0.290421
15	0.025427	0.2785	0.39054
16	0.102107	1.1185	0.132788
17	0.138645	1.5188	0.065724
18	0.050298	0.551	0.291332
19	0.072732	0.7967	0.213588
20	0.018497	0.2026	0.419885
21	-0.11584	-1.269	0.103454
22	0.042491	0.4655	0.321221
23	0.182866	2.0032	0.023704
24	0.037292	0.4085	0.34181
25	-0.092168	-1.0097	0.157346
26	-0.08763	-0.9599	0.169509
27	0.090692	0.9935	0.161237
28	0.015724	0.1722	0.431766
29	-0.123171	-1.3493	0.089895
30	0.131917	1.4451	0.075522
31	0.060084	0.6582	0.25584
32	-0.083436	-0.914	0.181276
33	-0.057407	-0.6289	0.265318
34	0.039238	0.4298	0.334045
35	-0.056313	-0.6169	0.269242
36	0.019394	0.2124	0.416059
37	0.05141	0.5632	0.287187
38	-0.111281	-1.219	0.112614
39	0.034111	0.3737	0.354654
40	0.027416	0.3003	0.382222
41	0.004119	0.0451	0.482041
42	-0.02351	-0.2575	0.398602
43	-0.028106	-0.3079	0.379351
44	-0.054615	-0.5983	0.275391
45	0.031014	0.3397	0.367323
46	0.084467	0.9253	0.178336
47	-0.080816	-0.8853	0.188884
48	-0.02429	-0.2661	0.395317
49	-0.019711	-0.2159	0.414709
50	-0.052721	-0.5775	0.282333
51	0.006345	0.0695	0.472353
52	0.061724	0.6762	0.250122
53	-0.0621	-0.6803	0.248823
54	-0.061369	-0.6723	0.251355
55	0.015428	0.169	0.433039
56	-0.005782	-0.0633	0.474803
57	-0.064841	-0.7103	0.239448
58	-0.035646	-0.3905	0.348437
59	-0.027818	-0.3047	0.380549
60	0.047214	0.5172	0.302984

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291555531a38l0xhtzk5laix/14t2y1291555519.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291555531a38l0xhtzk5laix/14t2y1291555519.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291555531a38l0xhtzk5laix/24t2y1291555519.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/05/t1291555531a38l0xhtzk5laix/24t2y1291555519.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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