Abstract
In this paper we perform a statistical analysis of the returns of OMX Baltic Benchmark index. We construct symmetric α-stable, non-standardized Student’s t and normal-inverse Gaussian models of daily logarithmic returns of the index, using maximum likelihood method for the estimation of the parameters of the models. The adequacy of the modeling is evaluated with the Kolmogorov-Smirnov tests for composite hypothesis. The results of the study indicate that the normal-inverse Gaussian model outperforms alternative heavy-tailed models for long periods of time, while the non-standardized Student’s t model provides the best overall fit for the data for shorter intervals. According to the likelihood-ratio test, the four-parameter models of the log-returns of OMX Baltic Benchmark index could be reduced to the three-parameter (symmetric) models without much loss.
Highlights
Bendrovių akcijų svoris šiame indekse priklauso nuo tos bendrovės akcijų rinkos vertės ir jų skaičiaus rinkoje, t.y. į indeksą įtraukiama tik ta akcinio kapitalo dalis, kuri laisvai cirkuliuoja rinkoje [9]
According to the likelihood-ratio test, the four-parameter models of the log-returns of OMX Baltic Benchmark index could be reduced to the three-parameter (symmetric) models without much loss
Summary
Kur ν > 0 yra laisvės laipsnių skaičius, β yra asimetrijos parametras, μ yra postūmio parametras, σ > 0 yra mastelio parametras, Q = (x − μ)2σ−2 ir Kλ(x) yra antros rūšies modifikuota Beselio funkcija. Normalusis atvirkštinis Gauso (normal-inverse Gaussian, (NIG)) su tankio funkcija [5]. 1 + Q) , 1+Q kur α > 0 yra uodegos sunkumo (formos) parametras, β yra asimetrijos parametras, μ yra postūmio parametras, ir σ > 0 yra mastelio parametras. Atvejį β = 0 atitinka simetrinis normalusis atvirkštinis Gauso dėsnis (SNIG). FMSNIG (x; α, μ, σ) fSMSNIG x − μ ; α , σ kur fSMSNIG (x; α) yra standartinio MSNIG tankio funkcija. Šis metodas duoda tiksliausius įverčius, tačiau reikalauja daug kompiuterinio lauko (jei nėra taikomi lygiagretieji skaičiavimai [3, 4])
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