Mixed-stable approach to the management of the portfolio using high-frequency financial data

Abstract

This paper considers the problem of portfolio selection using high-frequency financial time series. Such time series often exhibit the stagnation effect when the assets' returns are not changing. This effect causes a lot of unusual difficulties in the analysis and modelling of such series. In classical statistics, when the distributional law has two first moments, i.e. mean and variance, the relationship between the two random variables is described by the covariance or correlation. However, if the financial data follow the stable law, and empirical studies often support this assumption, covariance and especially correlation often cannot be calculated. In this work, alternative relation measures are applied to deal with the portfolio selection problem using the mixed-stable modelling. The modelling is applied to the high-frequency financial time series obtained from the German DAX index intra-daily data. The performance of the mixed-stable model is compared with alternative approaches. The portfolio selection problem is formulated as the optimization problem, with covariances replaced by the generalized power-correlations. The results of the portfolio selection strategy without the relationship coefficients matrix are also presented.

Mixed-Stable Models: An Application to High-Frequency Financial Data

“…As was pointed out by Cont, a parametric model to successfully reproduce specific empirical features of asset returns must have at least four parameters: a parameter describing the decay of the tails (stability index), an asymmetry parameter allowing the left and right tails to behave differently, a scale (volatility) parameter and ultimately a location parameter [22]. Our recent research on the comparison of models corroborates this opinion [15].…”

“…Examples of the use of the estimated mixed-stable parameters for the selection of the optimal asset portfolio have been provided in our preliminary comparative research [15]. This study compared stable and mixed-stable models with mixed diffusion-jump, the mixture of normals, scaled-t, logistic and normal-inverse Gaussian models and identified the mixed-stable one as the most adequate model for the data under analysis.…”

“…The paper extends the study of applying the mixed-stable models to the analysis of large sets of high-frequency financial data; see [4,14,15]. In this research, we apply the parallel computing approach (cf.…”

Comparative analysis of stock price ARIMA and LSTM forecasting methods

“…• išbandyti hibridinį (ARIMA ir neuroninių tinklų) modelį (pl. [12,17]); • atliekant eksperimentus, naudoti daugiau įvairesnių akcijų; taip pat naudoti ir išvestines finansines priemones (opcionai, uždirbimą nuo akcijos kritimo, varantai); paliesti aktualią elektros kainų sprogimo problemą ir prognozavimo galimybes; • sujungti prognozavimo metodus su portfelio optimizavimo metodais [2] (kuriant portfelį pridėti išvestines finansines priemones bei pridėti daugiau galimų investavimo priemonių, tokių kaip tarpusavio skolinimas, nekilnojamas turtas, biržos prekės); • akcijų kainas vertinti ne tik pagal jų istorinius duomenis, bet ir pagal kitus kriterijus: įmonės finansinius rezultatus, įmonės teigiamas/neigiamas naujienas, politinę bei ekonominę padėtį pasaulyje bei valstybėje, kurioje yra įmonės centrinė būstinė.…”