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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, 12 Jan 2010 04:21:14 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295361ueyinnsq0rfl13h.htm/, Retrieved Tue, 12 Jan 2010 12:22:43 +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/Jan/12/t1263295361ueyinnsq0rfl13h.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 «

277 260.6 291.6 275.4 275.3 231.7 238.8 274.2 277.8 299.1 286.6 232.3 294.1 267.5 309.7 280.7 287.3 235.7 256.4 289 290.8 321.9 291.8 241.4 295.5 258.2 306.1 281.5 283.1 237.4 274.8 299.3 300.4 340.9 318.8 265.7 322.7 281.6 323.5 312.6 310.8 262.8 273.8 320 310.3 342.2 320.1 265.6 327 300.7 346.4 317.3 326.2 270.7 278.2 324.6 321.8 343.5 354 278.2 330.2 307.3 375.9 335.3 339.3 280.3 293.7 341.2 345.1 368.7 369.4 288.4 341 319.1 374.2 344.5 337.3 281 282.2 321 325.4 366.3 380.3 300.7 359.3 327.6 383.6 352.4 329.4 294.5 333.5 334.3 358 396.1 387 307.2 363.9 344.7 397.6 376.8 337.1 299.3 323.1 329.1 347 462 436.5 360.4 415.5 382.1 432.2 424.3 386.7 354.5 375.8 368 402.4 426.5 433.3 338.5 416.8 381.1 445.7 412.4 394 348.2 380.1 373.7 393.6 434.2 430.7 344.5 411.9 370.5 437.3 411.3 385.5 341.3 384.2 373.2 415.8 448.6 454.3 350.3 419.1 398 456.1 430.1 399.8 362.7 384. etc...

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	-0.700886	-9.192	0
2	0.278792	3.6563	0.00017
3	-0.132113	-1.7326	0.042476
4	0.115795	1.5186	0.065345
5	-0.116182	-1.5237	0.064708
6	0.06273	0.8227	0.205909
7	-0.014761	-0.1936	0.423363
8	0.018117	0.2376	0.406236
9	0.040728	0.5341	0.296966
10	-0.18426	-2.4166	0.008357
11	0.377928	4.9565	1e-06
12	-0.479634	-6.2903	0
13	0.379269	4.9741	1e-06
14	-0.307884	-4.0379	4.1e-05
15	0.287775	3.7741	0.00011
16	-0.136467	-1.7897	0.037627
17	-0.004662	-0.0611	0.475659
18	0.012844	0.1684	0.433217
19	0.044592	0.5848	0.279717
20	-0.071857	-0.9424	0.173658
21	0.001534	0.0201	0.491985
22	0.097209	1.2749	0.102034
23	-0.151601	-1.9882	0.024187
24	0.175691	2.3042	0.011205
25	-0.19003	-2.4922	0.006821
26	0.220014	2.8855	0.002205
27	-0.176151	-2.3102	0.011032
28	-0.006433	-0.0844	0.466432
29	0.141722	1.8587	0.032392
30	-0.124045	-1.6268	0.052801
31	0.043644	0.5724	0.283904
32	0.015008	0.1968	0.422098
33	-0.011493	-0.1507	0.440181
34	-0.02329	-0.3054	0.380198
35	0.061285	0.8037	0.211328
36	-0.111774	-1.4659	0.07225
37	0.151899	1.9921	0.023969
38	-0.138094	-1.8111	0.035936
39	0.039437	0.5172	0.302838
40	0.075892	0.9953	0.160491
41	-0.096494	-1.2655	0.103702
42	0.071198	0.9337	0.175871
43	-0.088767	-1.1642	0.122984
44	0.111846	1.4668	0.072122
45	-0.078372	-1.0278	0.152734
46	-0.005726	-0.0751	0.470112
47	0.062179	0.8155	0.207967
48	-0.028696	-0.3763	0.353561
49	-0.044055	-0.5778	0.282087
50	0.065062	0.8533	0.197344
51	0.002468	0.0324	0.487111
52	-0.102211	-1.3405	0.090927
53	0.156451	2.0518	0.020851
54	-0.196638	-2.5789	0.005374
55	0.213773	2.8036	0.002817
56	-0.141692	-1.8583	0.032419
57	0.048156	0.6316	0.264255
58	-0.004533	-0.0595	0.476329
59	-0.000698	-0.0092	0.496353
60	-0.011262	-0.1477	0.441376

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.700886	-9.192	0
2	-0.417584	-5.4766	0
3	-0.351854	-4.6145	4e-06
4	-0.183692	-2.4091	0.008524
5	-0.19361	-2.5392	0.005999
6	-0.235195	-3.0846	0.001188
7	-0.229988	-3.0163	0.001474
8	-0.192584	-2.5257	0.006225
9	0.037735	0.4949	0.310656
10	-0.249195	-3.2682	0.000654
11	0.283936	3.7238	0.000133
12	0.028363	0.372	0.355186
13	0.073801	0.9679	0.167229
14	-0.252702	-3.3142	0.00056
15	-0.247959	-3.2519	0.00069
16	0.077346	1.0144	0.155911
17	-0.015065	-0.1976	0.421803
18	-0.018348	-0.2406	0.405061
19	-0.025053	-0.3286	0.371443
20	0.015491	0.2032	0.419626
21	0.055487	0.7277	0.233891
22	0.001521	0.02	0.492053
23	0.101301	1.3285	0.092879
24	0.015182	0.1991	0.421204
25	-0.007367	-0.0966	0.461569
26	-0.066053	-0.8663	0.193771
27	0.055333	0.7257	0.234509
28	-0.12251	-1.6067	0.054977
29	0.065474	0.8587	0.195855
30	-0.000988	-0.013	0.494841
31	-0.088442	-1.1599	0.123846
32	0.006001	0.0787	0.468681
33	-0.031547	-0.4137	0.339793
34	0.011881	0.1558	0.438181
35	0.016452	0.2158	0.414715
36	-0.009002	-0.1181	0.453078
37	0.02983	0.3912	0.348058
38	0.039867	0.5228	0.300878
39	-0.025251	-0.3312	0.370461
40	-0.074902	-0.9823	0.163658
41	0.027419	0.3596	0.359795
42	0.003387	0.0444	0.48231
43	-0.034938	-0.4582	0.32369
44	0.02151	0.2821	0.389102
45	0.044292	0.5809	0.281041
46	-0.04692	-0.6154	0.269568
47	0.093918	1.2317	0.109867
48	0.017883	0.2345	0.407427
49	0.019723	0.2587	0.398103
50	0.021097	0.2767	0.391175
51	0.070291	0.9219	0.178947
52	-0.080242	-1.0524	0.147054
53	0.034018	0.4461	0.328029
54	-0.095109	-1.2473	0.106985
55	-0.093427	-1.2253	0.111073
56	0.011388	0.1494	0.440723
57	0.042487	0.5572	0.289054
58	0.010099	0.1324	0.447393
59	0.029353	0.385	0.350372
60	0.021742	0.2851	0.387938

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295361ueyinnsq0rfl13h/14k5p1263295272.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295361ueyinnsq0rfl13h/14k5p1263295272.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295361ueyinnsq0rfl13h/2m1991263295272.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/12/t1263295361ueyinnsq0rfl13h/2m1991263295272.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 2 ; 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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