Existenta unor corelații liniare în seria rentabilităților utilizând rezultatele din testul Ljung-Box (statistica Q)

Problema 1. Se considera datele din problema 3, proiectul 1. Se cere:

a) Studiati existenta unor corelatii (dependente) liniare in seria rentabilitatilor utilizand rezultatele din problema 3 proiectul 1, precum si testul Ljung-Box (statistica Q)

1)

Date: 01/24/10 Time: 17:36

Sample: 1 300

Included observations: 288

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

.|. | .|. | 1 -0.033 -0.033 0.3132 0.576

.|. | .|. | 2 0.045 0.044 0.9070 0.635

*|. | .|. | 3 -0.060 -0.057 1.9446 0.584

.|. | .|. | 4 -0.044 -0.049 2.5062 0.644

.|. | .|. | 5 0.005 0.007 2.5132 0.775

*|. | *|. | 6 -0.173 -0.174 11.424 0.076

.|. | .|. | 7 -0.029 -0.047 11.667 0.112

*|. | *|. | 8 -0.087 -0.080 13.904 0.084

.|* | .|. | 9 0.087 0.064 16.167 0.063

.|. | .|. | 10 0.017 0.008 16.253 0.093

.|. | .|. | 11 0.045 0.030 16.871 0.112

.|. | .|. | 12 0.018 -0.008 16.968 0.151

*|. | *|. | 13 -0.065 -0.076 18.269 0.148

.|* | .|* | 14 0.107 0.082 21.767 0.084

.|. | .|. | 15 -0.032 0.001 22.084 0.106

.|* | .|* | 16 0.141 0.140 28.220 0.030

.|. | .|. | 17 0.014 0.060 28.283 0.042

.|. | .|* | 18 0.064 0.074 29.562 0.042

.|. | .|. | 19 -0.039 -0.043 30.039 0.051

*|. | .|. | 20 -0.073 -0.048 31.687 0.047

.|. | .|. | 21 0.046 0.050 32.350 0.054

*|. | .|. | 22 -0.096 -0.025 35.227 0.037

.|. | .|* | 23 0.064 0.071 36.536 0.036

*|. | .|. | 24 -0.092 -0.042 39.213 0.026

.|. | .|. | 25 0.061 0.025 40.402 0.027

.|. | .|. | 26 0.007 -0.024 40.415 0.036

.|* | .|* | 27 0.102 0.098 43.732 0.022

.|. | .|. | 28 0.052 0.027 44.608 0.024

.|. | .|. | 29 -0.046 -0.001 45.305 0.027

.|. | .|. | 30 0.045 0.013 45.970 0.031

.|. | .|* | 31 0.028 0.076 46.225 0.039

.|. | *|. | 32 -0.052 -0.107 47.111 0.041

.|. | .|. | 33 -0.048 -0.020 47.876 0.045

.|. | .|. | 34 -0.032 -0.014 48.208 0.054

.|. | .|. | 35 0.036 0.038 48.642 0.062

.|. | .|. | 36 0.009 0.033 48.667 0.077

Prelucrari ale autorului in Eviews 5.1.

Toti coeficientii de autocorelatie respectiv de autocorelatie partiala sunt nesemnificativi.

Pentru k=12 avem Qcalculat=16.968 iar probabilitatea corespunzatoare P=0.151 >5%=0.05 rezulta primii 15 coeficienti de autocorelatie sunt nesemnificativi (un difera semnificativ de zero). Rezulta nu exista corelatii (dependente) liniare in seria rentabilitatilor.

b)*Estimati un model de tip GARCH, daca varianta nu este constanta. Elaborati previziuni

Dependent Variable: RLTEL

Method: ML - ARCH (Marquardt) - Normal distribution

Date: 01/24/10 Time: 17:50

Sample (adjusted): 2 289

Included observations: 288 after adjustments

Convergence achieved after 12 iterations

Coefficient Std. Error z-Statistic Prob.

Variance Equation

C 6.53E-05 2.59E-05 2.521292 0.0117

ARCH(1) 0.200546 0.048861 4.104427 0.0000

GARCH(1) 0.737211 0.053771 13.71014 0.0000

R-squared -0.001955 Mean dependent var -0.001562

Adjusted R-squared -0.008986 S.D. dependent var 0.035382

S.E. of regression 0.035541 Akaike info criterion -4.189805

Sum squared resid 0.359997 Schwarz criterion -4.151649

Log likelihood 606.3319 Durbin-Watson stat 2.043791

Prelucrari ale autorului in Eviews 5.1.

Coeficientii sunt semnificativi.

c)**Studiati existenta unor corelatii neliniare, in seria rentabilitatilor, utilizand testul BDS. Daca exista corelatii liniare filtrati aceasta componenta, prin estimarea unui model ARMA adecvat si testati existenta unor corelatii neliniare in seria filtrata (reziduurile din modelul ARMA). Concluzii privind eficienta informationala prin prisma acestui titlu.

BDS Test for RLTEL

Date: 01/24/10 Time: 18:42

Sample: 1 300

Included observations: 300

Dimension BDS Statistic Std. Error z-Statistic Prob.

2 0.003228 0.002618 1.232735 0.2177

3 0.004945 0.001812 2.728849 0.0064

4 0.002724 0.000942 2.891049 0.0038

5 0.000862 0.000429 2.007678 0.0447

6 0.000291 0.000181 1.607431 0.1080

Raw epsilon 0.015414

Pairs within epsilon 25024.00 V-Statistic 0.301698

Triples within epsilon 2704106. V-Statistic 0.113200

Dimension C(m,n) c(m,n) C(1,n-(m-1)) c(1,n-(m-1)) c(1,n-(m-1))^k

2 3808.000 0.092785 12282.00 0.299262 0.089558

3 1298.000 0.031849 12212.00 0.299644 0.026904

4 433.0000 0.010699 12094.00 0.298839 0.007975

5 133.0000 0.003310 12073.00 0.300428 0.002447

6 41.00000 0.001027 11990.00 0.300479 0.000736