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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: Thu, 17 Dec 2009 20:26:45 +0100

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/17/t1261078052s553syl4tp9ln3a.htm/, Retrieved Thu, 17 Dec 2009 20:27:34 +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/17/t1261078052s553syl4tp9ln3a.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 «

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.477054	-6.2747	0
2	0.134382	1.7675	0.039452
3	-0.110352	-1.4515	0.074232
4	0.053687	0.7061	0.240527
5	-0.119803	-1.5758	0.058453
6	0.042621	0.5606	0.287901
7	0.02792	0.3672	0.356948
8	0.040655	0.5347	0.296761
9	0.020549	0.2703	0.393634
10	-0.135087	-1.7768	0.03868
11	0.259658	3.4153	0.000397
12	-0.460579	-6.058	0
13	0.242301	3.187	0.000853
14	-0.20139	-2.6489	0.004412
15	0.286965	3.7744	0.00011
16	-0.077162	-1.0149	0.155784
17	-0.033297	-0.438	0.330984
18	0.016544	0.2176	0.413998
19	0.023534	0.3095	0.378641
20	-0.085647	-1.1265	0.130754
21	0.007769	0.1022	0.459365
22	0.098324	1.2933	0.098824
23	-0.103989	-1.3678	0.08658
24	0.145569	1.9147	0.028593
25	-0.13307	-1.7503	0.040923
26	0.163112	2.1454	0.016658
27	-0.193419	-2.544	0.005917
28	-0.027551	-0.3624	0.358756
29	0.144486	1.9004	0.029521
30	-0.097736	-1.2855	0.100165
31	0.044356	0.5834	0.280188
32	0.031755	0.4177	0.338353
33	-0.013383	-0.176	0.430239
34	-0.022859	-0.3007	0.382019
35	0.038253	0.5031	0.307754
36	-0.090296	-1.1877	0.118298
37	0.12123	1.5945	0.056321
38	-0.120568	-1.5858	0.057303
39	0.041892	0.551	0.291171
40	0.090768	1.1939	0.117082
41	-0.078207	-1.0287	0.152538
42	0.031939	0.4201	0.33747
43	-0.0731	-0.9615	0.168825
44	0.093204	1.2259	0.110949
45	-0.078623	-1.0341	0.151262
46	-0.001912	-0.0252	0.489981
47	0.073019	0.9604	0.169094
48	-0.028117	-0.3698	0.355984
49	-0.045277	-0.5955	0.276135
50	0.06815	0.8964	0.185651
51	-0.011904	-0.1566	0.437882
52	-0.099604	-1.3101	0.095951
53	0.111647	1.4685	0.071893
54	-0.138021	-1.8154	0.035598
55	0.197012	2.5913	0.005189
56	-0.10282	-1.3524	0.089008
57	0.022449	0.2953	0.384068
58	-0.006155	-0.081	0.467785
59	-0.015521	-0.2041	0.419239
60	-0.018839	-0.2478	0.402295

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.477054	-6.2747	0
2	-0.120657	-1.587	0.05717
3	-0.126212	-1.6601	0.049357
4	-0.055962	-0.7361	0.231346
5	-0.157262	-2.0685	0.020042
6	-0.123127	-1.6195	0.053582
7	-0.016438	-0.2162	0.41454
8	0.049795	0.6549	0.256686
9	0.084393	1.11	0.134267
10	-0.126988	-1.6703	0.048337
11	0.19853	2.6112	0.004907
12	-0.337082	-4.4336	8e-06
13	-0.163686	-2.153	0.016354
14	-0.269547	-3.5453	0.000252
15	0.05026	0.6611	0.254725
16	0.147889	1.9452	0.026687
17	-0.130994	-1.723	0.043342
18	-0.042484	-0.5588	0.288515
19	-0.008128	-0.1069	0.457495
20	0.012363	0.1626	0.43551
21	-0.005791	-0.0762	0.469688
22	-0.035621	-0.4685	0.32
23	0.021018	0.2764	0.391269
24	-0.095174	-1.2518	0.106164
25	-0.057949	-0.7622	0.223487
26	-0.058024	-0.7632	0.223196
27	0.003387	0.0445	0.48226
28	-0.126251	-1.6606	0.049305
29	0.065885	0.8666	0.193686
30	-0.112169	-1.4753	0.070968
31	-0.055442	-0.7292	0.233424
32	0.047919	0.6303	0.264675
33	-0.026251	-0.3453	0.365151
34	0.023654	0.3111	0.378042
35	0.00245	0.0322	0.487167
36	-0.019965	-0.2626	0.396587
37	-0.007379	-0.0971	0.461396
38	-0.058755	-0.7728	0.220346
39	-0.100235	-1.3184	0.094558
40	-0.032424	-0.4265	0.335148
41	0.047652	0.6268	0.265818
42	-0.048041	-0.6319	0.264149
43	-0.027721	-0.3646	0.357924
44	0.023106	0.3039	0.380782
45	-0.019743	-0.2597	0.397708
46	-0.040554	-0.5334	0.297221
47	0.073189	0.9626	0.168534
48	-0.062777	-0.8257	0.205055
49	-0.011607	-0.1527	0.43942
50	-0.022804	-0.2999	0.382291
51	-0.031876	-0.4193	0.337772
52	-0.108425	-1.4261	0.077819
53	0.027608	0.3631	0.358477
54	-0.10184	-1.3395	0.091083
55	0.027891	0.3668	0.357091
56	0.065758	0.8649	0.194143
57	-0.015837	-0.2083	0.417618
58	-0.042078	-0.5534	0.290336
59	-0.005028	-0.0661	0.473674
60	-0.03255	-0.4281	0.334545

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261078052s553syl4tp9ln3a/1jmp01261078000.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261078052s553syl4tp9ln3a/1jmp01261078000.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261078052s553syl4tp9ln3a/26c8m1261078000.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261078052s553syl4tp9ln3a/26c8m1261078000.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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