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paper d=D=0

*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: Fri, 04 Dec 2009 07:37:18 -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/04/t1259937543qvhoyvctshlfvcu.htm/, Retrieved Fri, 04 Dec 2009 15:39:06 +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/04/t1259937543qvhoyvctshlfvcu.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 «

4716.99 4926.65 4920.10 5170.09 5246.24 5283.61 4979.05 4825.20 4695.12 4711.54 4727.22 4384.96 4378.75 4472.93 4564.07 4310.54 4171.38 4049.38 3591.37 3720.46 4107.23 4101.71 4162.34 4136.22 4125.88 4031.48 3761.36 3408.56 3228.47 3090.45 2741.14 2980.44 3104.33 3181.57 2863.86 2898.01 3112.33 3254.33 3513.47 3587.61 3727.45 3793.34 3817.58 3845.13 3931.86 4197.52 4307.13 4229.43 4362.28 4217.34 4361.28 4327.74 4417.65 4557.68 4650.35 4967.18 5123.42 5290.85 5535.66 5514.06 5493.88 5694.83 5850.41 6116.64 6175.00 6513.58 6383.78 6673.66 6936.61 7300.68 7392.93 7497.31 7584.71 7160.79 7196.19 7245.63 7347.51 7425.75 7778.51 7822.33 8181.22 8371.47 8347.71 8672.11 8802.79 9138.46 9123.29 9023.21 8850.41 8864.58 9163.74 8516.66 8553.44 7555.20 7851.22 7442.00 7992.53 8264.04 7517.39 7200.40 7193.69 6193.58 5104.21 4800.46 4461.61 4398.59 4243.63 4293.82

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.985309	10.2396	0
2	0.965788	10.0368	0
3	0.939809	9.7668	0
4	0.911137	9.4688	0
5	0.880097	9.1462	0
6	0.84911	8.8242	0
7	0.820085	8.5226	0
8	0.790491	8.215	0
9	0.759967	7.8978	0
10	0.726579	7.5508	0
11	0.693904	7.2113	0
12	0.655422	6.8113	0
13	0.614081	6.3817	0
14	0.572968	5.9545	0
15	0.530607	5.5142	0
16	0.490843	5.101	1e-06
17	0.44933	4.6696	4e-06
18	0.410039	4.2613	2.2e-05
19	0.368889	3.8336	0.000106
20	0.327782	3.4064	0.000463
21	0.287774	2.9906	0.001724
22	0.250322	2.6014	0.005293
23	0.213472	2.2185	0.014308
24	0.177341	1.843	0.034037
25	0.143279	1.489	0.069701
26	0.107644	1.1187	0.132883
27	0.073222	0.7609	0.224174
28	0.037475	0.3894	0.348856
29	0.000589	0.0061	0.497562
30	-0.037021	-0.3847	0.350597
31	-0.07423	-0.7714	0.22107
32	-0.110059	-1.1438	0.127624
33	-0.144823	-1.505	0.067616
34	-0.177314	-1.8427	0.034057
35	-0.207853	-2.1601	0.016489
36	-0.234481	-2.4368	0.008226
37	-0.258866	-2.6902	0.004138
38	-0.279968	-2.9095	0.002198
39	-0.298548	-3.1026	0.001224
40	-0.31647	-3.2889	0.000679
41	-0.33265	-3.457	0.000391
42	-0.347824	-3.6147	0.000229
43	-0.362073	-3.7628	0.000137
44	-0.375562	-3.903	8.3e-05
45	-0.388057	-4.0328	5.2e-05
46	-0.399259	-4.1492	3.3e-05
47	-0.408559	-4.2459	2.3e-05
48	-0.41652	-4.3286	1.7e-05
49	-0.422151	-4.3871	1.3e-05
50	-0.426643	-4.4338	1.1e-05
51	-0.42944	-4.4629	1e-05
52	-0.430816	-4.4772	9e-06
53	-0.431744	-4.4868	9e-06
54	-0.430793	-4.4769	9e-06
55	-0.428335	-4.4514	1e-05
56	-0.424269	-4.4091	1.2e-05
57	-0.417828	-4.3422	1.6e-05
58	-0.409044	-4.2509	2.3e-05
59	-0.399509	-4.1518	3.3e-05
60	-0.389398	-4.0467	4.9e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.985309	10.2396	0
2	-0.17296	-1.7975	0.037529
3	-0.210631	-2.1889	0.015377
4	-0.048562	-0.5047	0.307409
5	-0.040217	-0.4179	0.338409
6	0.024719	0.2569	0.398877
7	0.075242	0.7819	0.217982
8	-0.060717	-0.631	0.26469
9	-0.077918	-0.8098	0.209932
10	-0.11544	-1.1997	0.116443
11	0.043553	0.4526	0.325866
12	-0.196007	-2.037	0.02205
13	-0.081421	-0.8461	0.199671
14	0.079061	0.8216	0.20655
15	-0.054165	-0.5629	0.287335
16	0.077022	0.8004	0.212608
17	-0.103338	-1.0739	0.142627
18	-0.004543	-0.0472	0.481217
19	-0.10603	-1.1019	0.136479
20	-0.025839	-0.2685	0.394403
21	0.08807	0.9153	0.181049
22	0.050229	0.522	0.301371
23	-0.035213	-0.3659	0.357561
24	-0.00795	-0.0826	0.467155
25	-0.0268	-0.2785	0.390575
26	-0.105293	-1.0942	0.138142
27	-0.018486	-0.1921	0.424008
28	-0.03106	-0.3228	0.373739
29	-0.091883	-0.9549	0.170888
30	-0.039979	-0.4155	0.339308
31	0.044128	0.4586	0.323724
32	-0.033398	-0.3471	0.364604
33	-0.051032	-0.5303	0.298483
34	-0.011435	-0.1188	0.452812
35	0.018195	0.1891	0.425189
36	0.046133	0.4794	0.316302
37	0.057899	0.6017	0.274315
38	0.049413	0.5135	0.304319
39	-0.009012	-0.0937	0.462777
40	-0.064302	-0.6682	0.252701
41	0.010608	0.1102	0.45621
42	0.014364	0.1493	0.440809
43	-0.056367	-0.5858	0.279623
44	-0.001486	-0.0154	0.493853
45	-0.014171	-0.1473	0.441596
46	-0.022843	-0.2374	0.406403
47	-0.013847	-0.1439	0.442924
48	-0.018705	-0.1944	0.423117
49	-0.007239	-0.0752	0.470085
50	-0.08159	-0.8479	0.199184
51	0.052723	0.5479	0.292441
52	0.022911	0.2381	0.406129
53	-0.053943	-0.5606	0.288119
54	0.045477	0.4726	0.318723
55	0.017876	0.1858	0.426486
56	0.006312	0.0656	0.473909
57	0.059877	0.6223	0.267541
58	0.054289	0.5642	0.286899
59	-0.030027	-0.312	0.377804
60	-0.070813	-0.7359	0.231692

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937543qvhoyvctshlfvcu/1rhuh1259937434.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937543qvhoyvctshlfvcu/1rhuh1259937434.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937543qvhoyvctshlfvcu/2f0o41259937434.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259937543qvhoyvctshlfvcu/2f0o41259937434.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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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