Model Selection Test for the Heavy-Tailed Distributions under Censored Samples with Application in Financial Data

Abstract

Numerous heavy-tailed distributions are used for modeling financial data and in problems related to the modeling of economics processes. These distributions have higher peaks and heavier tails than normal distributions. Moreover, in some situations, we cannot observe complete information about the data. Employing the efficient estimation method and then choosing the best model in this situation are very important. Thus, the purpose of this article is to propose a new interval for comparing the two heavy-tailed candidate models and examine its suitability in the financial data under complete and censored samples. This interval is equivalent to encapsulating the results of many hypotheses tests. A maximum likelihood estimator (MLE) is used for evaluating the parameters of the proposed heavy-tailed distribution. A real dataset representing the top 30 companies of the Tehran Stock Exchange indices is used to illustrate the derived results.

Conditional quantile correlation learning for ultrahigh dimensional varying coefficient models and its application in survival analysis

“…[36]) to determine whether the data follow heavy-tailed distribution for complete or incomplete censored cases. After the heavy tail distribution status is confirmed, we can use our proposed CQCSIS as well as CQCSIScens; otherwise, we may use the conventional correlation based screening procedures such as NSIS by [7] and CC-SIS by [10].…”

Application of Lévy processes in modelling (geodetic) time series with mixed spectra

“…This topic is currently debated in the statistical community (e.g. Panahi, 2016). Large tails should be detected in the fitting of the Lévy α-stable distribution.…”

“…Long-memory processes are modelled with a specific class of autoregressive moving average (ARMA) models called FARIMA by allowing for non-integer differentiation. A comprehensive literature on the application of FARIMA can be found in financial analysis (Granger and Joyeux, 1980;Panas, 2001) and in geodesy (Li et al, 2000;Montillet and Yu, 2015;Montillet and Bos, 2019). This model can generate long-memory processes based on different values of the fractional index d (Granger and Joyeux, 1980).…”

“…The fBm and the fractional Lévy distribution are well known in statistics (Samorodnitsky and Taqqu, 1994) and in financial analysis (Panas, 2001;Wooldridge, 2010). The fractional Lévy distribution can model the Lévy processes and, in particular, the general family of α stable Lévy processes, which can be self-similar and stationary (Samorodnitsky and Taqqu, 1994).…”

Model Selection Based on Tracking Interval under Unified Hybrid Censored Samples

“…Several articles have been published on model selection based on complete data, for example, Kundu et al (2005) compared the log-normal and generalized exponential distribution using maximized likelihood method, Dey and Kundu (2009) considered the problem of discriminating among the log-normal, Weibull and generalized exponential distributions, Cox (1961) improved the classical hypothesis testing to compare the nonnested hypothesis, Vuong (1989) tested the equivalence of the two models using the expectation of the log-likelihood ratio of the two candidate models. The results in Vuong have been extended and applied in a number of ways, including, Vuong and Wang (1993), Lien (1987), Commenges et al (2008), Sayyareh et al (2011), Commenges et al (2012) and Panahi (2016). Akaike (1973) introduced a criterion to select the best model under parsimony.…”