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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, 21 Dec 2010 18:59:10 +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/21/t1292957819aqmi982em1dwyqf.htm/, Retrieved Tue, 21 Dec 2010 19:57:00 +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/21/t1292957819aqmi982em1dwyqf.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 «

2981.85 3080.58 3106.22 3119.31 3061.26 3097.31 3161.69 3257.16 3277.01 3295.32 3363.99 3494.17 3667.03 3813.06 3917.96 3895.51 3801.06 3570.12 3701.61 3862.27 3970.10 4138.52 4199.75 4290.89 4443.91 4502.64 4356.98 4591.27 4696.96 4621.40 4562.84 4202.52 4296.49 4435.23 4105.18 4116.68 3844.49 3720.98 3674.40 3857.62 3801.06 3504.37 3032.60 3047.03 2962.34 2197.82 2014.45 1862.83 1905.41 1810.99 1670.07 1864.44 2052.02 2029.60 2070.83 2293.41 2443.27 2513.17 2466.92 2502.66 2539.91

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.284856	2.2065	0.015594
2	0.075037	0.5812	0.28163
3	0.223361	1.7301	0.044373
4	0.242925	1.8817	0.032366
5	0.261059	2.0222	0.023813
6	-0.028876	-0.2237	0.411886
7	-0.045413	-0.3518	0.363123
8	0.151645	1.1746	0.12239
9	0.028579	0.2214	0.412777
10	-0.168079	-1.3019	0.098958
11	0.118005	0.9141	0.182171
12	-0.020106	-0.1557	0.43838
13	-0.054262	-0.4203	0.337879
14	0.028481	0.2206	0.413071
15	-0.076448	-0.5922	0.277983
16	0.043198	0.3346	0.369543
17	-0.128343	-0.9941	0.162074
18	-0.196738	-1.5239	0.06639
19	0.003857	0.0299	0.488133
20	-0.097051	-0.7518	0.227569
21	-0.17561	-1.3603	0.089417
22	-0.18669	-1.4461	0.076677
23	-0.174961	-1.3552	0.090211
24	-0.13038	-1.0099	0.158295
25	-0.079168	-0.6132	0.27102
26	-0.121719	-0.9428	0.174775
27	-0.032175	-0.2492	0.402019
28	0.042737	0.331	0.370885
29	-0.043928	-0.3403	0.367423
30	-0.041417	-0.3208	0.374732
31	-0.06774	-0.5247	0.300859
32	-0.015997	-0.1239	0.450899
33	-0.043715	-0.3386	0.368042
34	-0.080318	-0.6221	0.268103
35	-0.109648	-0.8493	0.199538
36	-0.02888	-0.2237	0.411874
37	0.000908	0.007	0.497206
38	-0.025144	-0.1948	0.423118
39	-0.053352	-0.4133	0.340445
40	-0.038518	-0.2984	0.383231
41	0.028649	0.2219	0.412567
42	0.029138	0.2257	0.4111
43	0.015435	0.1196	0.452617
44	-0.006575	-0.0509	0.479775
45	0.03249	0.2517	0.40108
46	0.024291	0.1882	0.425693
47	0.014116	0.1093	0.456647
48	0.012602	0.0976	0.461282
49	0.022006	0.1705	0.432611
50	0.029861	0.2313	0.408932
51	0.010459	0.081	0.46785
52	0.001528	0.0118	0.495298
53	0.009332	0.0723	0.471306
54	0.019769	0.1531	0.439406
55	0.00941	0.0729	0.471068
56	0.002863	0.0222	0.491189
57	-0.000926	-0.0072	0.49715
58	0.003128	0.0242	0.490375
59	0.002449	0.019	0.492464
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.284856	2.2065	0.015594
2	-0.006645	-0.0515	0.479559
3	0.221738	1.7176	0.045516
4	0.138105	1.0698	0.144508
5	0.185547	1.4372	0.077922
6	-0.204606	-1.5849	0.059126
7	-0.062329	-0.4828	0.315499
8	0.075638	0.5859	0.280074
9	-0.067706	-0.5244	0.30095
10	-0.178847	-1.3853	0.085538
11	0.301103	2.3323	0.011528
12	-0.180949	-1.4016	0.083089
13	-0.00198	-0.0153	0.493907
14	0.099823	0.7732	0.221212
15	-0.059314	-0.4594	0.323787
16	-0.072147	-0.5588	0.289172
17	-0.093018	-0.7205	0.237003
18	-0.077516	-0.6004	0.275239
19	-0.007041	-0.0545	0.478342
20	-0.086989	-0.6738	0.251508
21	0.048092	0.3725	0.355409
22	-0.19911	-1.5423	0.064129
23	-0.006912	-0.0535	0.478741
24	-0.065724	-0.5091	0.306276
25	0.045564	0.3529	0.362685
26	0.046427	0.3596	0.360197
27	0.039215	0.3038	0.381181
28	0.103173	0.7992	0.21367
29	-0.00627	-0.0486	0.480713
30	-0.174035	-1.3481	0.091352
31	0.004422	0.0342	0.486396
32	-0.075591	-0.5855	0.280194
33	-0.08953	-0.6935	0.245338
34	0.007566	0.0586	0.476729
35	-0.059627	-0.4619	0.322923
36	0.050152	0.3885	0.349518
37	0.019979	0.1548	0.438767
38	0.082796	0.6413	0.261874
39	-0.14336	-1.1105	0.135615
40	-0.05665	-0.4388	0.331189
41	0.014298	0.1108	0.456092
42	-0.048915	-0.3789	0.353051
43	0.003523	0.0273	0.489159
44	0.030029	0.2326	0.408429
45	-0.041343	-0.3202	0.374948
46	0.010934	0.0847	0.466394
47	-0.050828	-0.3937	0.347595
48	0.01495	0.1158	0.454098
49	0.012902	0.0999	0.460364
50	0.035409	0.2743	0.392408
51	0.011227	0.087	0.465494
52	-0.045353	-0.3513	0.363295
53	-0.050287	-0.3895	0.349135
54	-0.026976	-0.209	0.417596
55	-0.05503	-0.4263	0.335722
56	-0.048043	-0.3721	0.355549
57	-0.092157	-0.7138	0.239045
58	0.065874	0.5103	0.305871
59	-0.00078	-0.006	0.4976
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957819aqmi982em1dwyqf/1epyn1292957946.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957819aqmi982em1dwyqf/1epyn1292957946.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957819aqmi982em1dwyqf/2epyn1292957946.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292957819aqmi982em1dwyqf/2epyn1292957946.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; 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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