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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: Fri, 18 Dec 2009 05:59:19 -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/18/t1261141182vk5054zs6nzk7gt.htm/, Retrieved Fri, 18 Dec 2009 13:59:44 +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/18/t1261141182vk5054zs6nzk7gt.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 «

100.00 110.08 123.28 106.30 114.60 110.22 117.82 138.84 131.13 153.26 148.76 110.75 132.00 138.55 126.50 119.47 152.49 152.46 134.08 162.33 130.46 142.83 148.39 122.88 125.86 133.31 140.97 110.30 123.04 125.99 112.24 136.10 111.86 109.63 135.75 114.39 121.79 101.33 147.01 113.01 101.89 117.85 128.68 117.27 121.55 109.18 127.88 104.92 100.93 116.79 107.50 109.18 128.31 83.80 93.16 103.99 106.33 97.55 111.71 105.43 103.62

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	-0.495808	-3.8405	0.000149
2	-0.122583	-0.9495	0.173081
3	0.2465	1.9094	0.030499
4	-0.078106	-0.605	0.273729
5	-0.045509	-0.3525	0.362846
6	-0.006124	-0.0474	0.481162
7	0.059946	0.4643	0.322043
8	-0.025838	-0.2001	0.421024
9	0.003987	0.0309	0.487731
10	0.174173	1.3491	0.091181
11	-0.365391	-2.8303	0.003159
12	0.27819	2.1548	0.017599
13	-0.039009	-0.3022	0.381786
14	-0.040387	-0.3128	0.377744
15	-0.004217	-0.0327	0.487025
16	-0.026946	-0.2087	0.417686
17	0.079289	0.6142	0.270712
18	-0.016239	-0.1258	0.450161
19	-0.048708	-0.3773	0.353645
20	-0.026028	-0.2016	0.420451
21	0.049499	0.3834	0.351383
22	0.069293	0.5367	0.296715
23	-0.17688	-1.3701	0.08788
24	0.094727	0.7338	0.232978
25	0.012847	0.0995	0.460533
26	-0.007293	-0.0565	0.477568
27	0.025791	0.1998	0.421166
28	-0.101426	-0.7856	0.217583
29	0.070607	0.5469	0.29323
30	0.08408	0.6513	0.258676
31	-0.144888	-1.1223	0.133103
32	0.007825	0.0606	0.475935
33	0.089654	0.6945	0.245037
34	-0.027355	-0.2119	0.416456
35	-0.078414	-0.6074	0.27294
36	0.102182	0.7915	0.215885
37	0.001787	0.0138	0.494502
38	-0.133671	-1.0354	0.152315
39	0.108336	0.8392	0.202354
40	0.011252	0.0872	0.465417
41	-0.14201	-1.1	0.137861
42	0.159211	1.2332	0.111148
43	-0.019155	-0.1484	0.441274
44	-0.069437	-0.5379	0.296333
45	0.046686	0.3616	0.359449
46	-0.032342	-0.2505	0.401521
47	-0.027733	-0.2148	0.415318
48	0.028765	0.2228	0.412219
49	-0.009711	-0.0752	0.470146
50	0.031856	0.2468	0.402971
51	-0.011714	-0.0907	0.464002
52	-0.022777	-0.1764	0.430275
53	-0.001312	-0.0102	0.495962
54	0.020648	0.1599	0.436735
55	-0.018615	-0.1442	0.442916
56	0.009335	0.0723	0.471298
57	0.00443	0.0343	0.486371
58	-0.004344	-0.0337	0.486634
59	-0.000924	-0.0072	0.497156
60	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.495808	-3.8405	0.000149
2	-0.488494	-3.7839	0.000179
3	-0.150062	-1.1624	0.124843
4	-0.046281	-0.3585	0.360617
5	-0.001455	-0.0113	0.495524
6	-0.093605	-0.7251	0.235616
7	-0.035521	-0.2751	0.392074
8	-0.01219	-0.0944	0.462544
9	0.048371	0.3747	0.354611
10	0.343278	2.659	0.005017
11	-0.138149	-1.0701	0.144431
12	0.031964	0.2476	0.402649
13	-0.076604	-0.5934	0.277581
14	0.158984	1.2315	0.111474
15	0.043095	0.3338	0.369843
16	-0.07914	-0.613	0.271091
17	-0.098404	-0.7622	0.224454
18	0.029184	0.2261	0.410964
19	0.070142	0.5433	0.294463
20	-0.11098	-0.8596	0.196702
21	-0.039227	-0.3038	0.381148
22	-0.077873	-0.6032	0.274323
23	-0.021114	-0.1635	0.435319
24	-0.066655	-0.5163	0.303769
25	-0.030079	-0.233	0.408282
26	-0.018958	-0.1469	0.441871
27	0.071317	0.5524	0.291356
28	-0.031295	-0.2424	0.404645
29	-0.007018	-0.0544	0.478413
30	0.147915	1.1457	0.128226
31	-0.027128	-0.2101	0.417138
32	-0.038215	-0.296	0.384121
33	0.00842	0.0652	0.474107
34	0.020332	0.1575	0.437695
35	-0.078735	-0.6099	0.272124
36	0.011829	0.0916	0.463648
37	0.101992	0.79	0.216311
38	-0.068547	-0.531	0.298702
39	-0.151523	-1.1737	0.122579
40	-0.071634	-0.5549	0.290521
41	-0.035624	-0.2759	0.39177
42	0.034727	0.269	0.39443
43	-0.021493	-0.1665	0.434167
44	-0.005035	-0.039	0.484509
45	0.06079	0.4709	0.319719
46	-0.057509	-0.4455	0.328793
47	-0.115471	-0.8944	0.187331
48	-0.036022	-0.279	0.390591
49	-0.056341	-0.4364	0.33205
50	0.055173	0.4274	0.33532
51	0.03846	0.2979	0.3834
52	-0.060142	-0.4659	0.321503
53	-0.002851	-0.0221	0.491227
54	-0.039929	-0.3093	0.379087
55	0.01957	0.1516	0.440009
56	0.094274	0.7302	0.234042
57	0.010779	0.0835	0.466869
58	-0.07388	-0.5723	0.284638
59	-0.014543	-0.1126	0.455342
60	NA	NA	NA

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261141182vk5054zs6nzk7gt/1fzor1261141158.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261141182vk5054zs6nzk7gt/1fzor1261141158.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261141182vk5054zs6nzk7gt/2w2ok1261141158.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261141182vk5054zs6nzk7gt/2w2ok1261141158.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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