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WS10 - PACF Y d = 1/ D=0 / lambda = 1

*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: Wed, 09 Dec 2009 07:56:44 -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/09/t126037067718hal35mec6agzk.htm/, Retrieved Wed, 09 Dec 2009 15:58:00 +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/2009/Dec/09/t126037067718hal35mec6agzk.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 «

286.1 307 358.1 341.8 378.8 375.2 295.6 362.7 409.6 336.8 389.1 389.3 355.9 542 648.4 452 582.4 506.5 555.5 530.4 609.4 543.9 616.2 634.6 541.7 549.8 627.6 797.4 689.8 1576.6 1572.1 1626.4 1972.4 1509.6 1584.9 1880 1324 1777.7 2172.4 1780.3 2134.9 1838.4 1557 1755.2 1702 1577.5 1485.9 2179.1 1740.9 1724.5 2328.1 1774.1 2224.2 1536.3 1521.2 2051.8 2483.1 1929.8 1808.6 2584.9 1997.9 1639.9 2379.1 1715 2750.9 1865.4 1647.4 2180.4 2593 2057.2 2635.8 2315.4 1863.6 2038 2235.8 2222.1 2636.9 2076.8 1935.5 2086.3 2470.9 1854.6 2041.3 2170.8 1905.5 2130.2 2791.2 2539.7 2661.3 1764.9 2176.9 2458.5 2179 2242.5 2089.6 2661.6 2112 2367.3 2543 2603.9 3146.7 1789.2 2114.8 2236.3 2288.1 2173.2 1877.7 2807.4 2357.4 2107.7 2856.8 2510.8 2875 2229.7 2055.1 2545.4 2775.1 2252.2 2091.7 2433

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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.459901	-5.0169	1e-06
2	-0.111142	-1.2124	0.113877
3	0.16483	1.7981	0.03735
4	-0.132484	-1.4452	0.075511
5	0.125577	1.3699	0.086651
6	-0.078923	-0.8609	0.195499
7	-0.050233	-0.548	0.292368
8	0.050562	0.5516	0.291139
9	0.116906	1.2753	0.102345
10	-0.101359	-1.1057	0.135545
11	-0.277068	-3.0225	0.001535
12	0.556078	6.0661	0
13	-0.248838	-2.7145	0.003812
14	-0.116128	-1.2668	0.10385
15	0.081348	0.8874	0.188325
16	-0.052978	-0.5779	0.282205
17	0.065315	0.7125	0.238773
18	0.040947	0.4467	0.327959
19	-0.102861	-1.1221	0.132044
20	0.043323	0.4726	0.318682
21	0.115358	1.2584	0.105354
22	-0.134982	-1.4725	0.071765
23	-0.158674	-1.7309	0.043028
24	0.367447	4.0084	5.4e-05
25	-0.177839	-1.94	0.027373
26	-0.08677	-0.9465	0.172893
27	0.14282	1.558	0.060946
28	-0.109748	-1.1972	0.116802
29	0.028226	0.3079	0.379346
30	0.107242	1.1699	0.122195
31	-0.103589	-1.13	0.130369
32	0.015111	0.1648	0.434674
33	0.089732	0.9789	0.164817
34	-0.187429	-2.0446	0.021549
35	-0.012399	-0.1353	0.446319
36	0.282918	3.0863	0.001261
37	-0.210577	-2.2971	0.01168
38	0.016302	0.1778	0.42958
39	0.031122	0.3395	0.367416
40	0.001816	0.0198	0.492114
41	0.05557	0.6062	0.27277
42	-0.108382	-1.1823	0.11972
43	0.075718	0.826	0.205232
44	-0.064821	-0.7071	0.240439
45	0.078291	0.8541	0.197394
46	-0.049727	-0.5425	0.294258
47	-0.153314	-1.6725	0.048531
48	0.341174	3.7218	0.000152
49	-0.216144	-2.3578	0.010006
50	-0.014463	-0.1578	0.43745
51	0.056314	0.6143	0.270091
52	-0.038428	-0.4192	0.337912
53	0.066051	0.7205	0.236306
54	-0.080067	-0.8734	0.192095
55	0.013339	0.1455	0.442278
56	0.01012	0.1104	0.456139
57	0.092129	1.005	0.158465
58	-0.083833	-0.9145	0.181149
59	-0.093834	-1.0236	0.154049
60	0.189845	2.071	0.020262

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.459901	-5.0169	1e-06
2	-0.409201	-4.4639	9e-06
3	-0.145314	-1.5852	0.057789
4	-0.215739	-2.3534	0.01012
5	-0.006166	-0.0673	0.47324
6	-0.07324	-0.7989	0.212956
7	-0.113489	-1.238	0.109073
8	-0.134363	-1.4657	0.07268
9	0.113182	1.2347	0.109694
10	0.062322	0.6799	0.248959
11	-0.403098	-4.3973	1.2e-05
12	0.287417	3.1354	0.001081
13	0.166483	1.8161	0.035935
14	0.005377	0.0587	0.476663
15	-0.170593	-1.861	0.032609
16	0.019868	0.2167	0.414393
17	-0.142314	-1.5525	0.061604
18	0.025016	0.2729	0.392706
19	0.082312	0.8979	0.185522
20	0.057679	0.6292	0.265211
21	-0.013104	-0.143	0.443286
22	-0.041276	-0.4503	0.326668
23	-0.063696	-0.6948	0.244253
24	0.039921	0.4355	0.331999
25	0.013053	0.1424	0.443504
26	-0.074666	-0.8145	0.208491
27	0.124149	1.3543	0.089102
28	0.019484	0.2125	0.416024
29	-0.102392	-1.117	0.133129
30	-0.023576	-0.2572	0.398739
31	0.166028	1.8112	0.03632
32	0.021665	0.2363	0.406789
33	0.002705	0.0295	0.488256
34	-0.121504	-1.3255	0.09378
35	-0.047902	-0.5225	0.301131
36	0.031112	0.3394	0.367457
37	-0.0226	-0.2465	0.402844
38	0.085992	0.9381	0.175055
39	-0.122032	-1.3312	0.092832
40	0.072839	0.7946	0.21422
41	0.210217	2.2932	0.011796
42	-0.102891	-1.1224	0.131973
43	-0.016028	-0.1748	0.430749
44	-0.051241	-0.559	0.288617
45	-0.048294	-0.5268	0.299648
46	0.149713	1.6332	0.052538
47	-0.059021	-0.6438	0.26046
48	-0.047532	-0.5185	0.302533
49	-0.093462	-1.0195	0.155006
50	0.002669	0.0291	0.488409
51	-0.024715	-0.2696	0.393963
52	0.009789	0.1068	0.457569
53	-0.080997	-0.8836	0.189354
54	-0.008505	-0.0928	0.463118
55	-0.050009	-0.5455	0.293205
56	0.01412	0.154	0.438924
57	0.045543	0.4968	0.310119
58	-0.035537	-0.3877	0.34948
59	0.088159	0.9617	0.169074
60	-0.097821	-1.0671	0.144042

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t126037067718hal35mec6agzk/1xc8l1260370602.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t126037067718hal35mec6agzk/1xc8l1260370602.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t126037067718hal35mec6agzk/2uv7o1260370602.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t126037067718hal35mec6agzk/2uv7o1260370602.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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