This
paper expounds the nitty-gritty of stock returns transitory, periodical
behavior of its markets’ demands and cyclical-like tenure-changing of number of the
stocks sold. Mingling of autoregressive random processes via Poisson and
Extreme-Value-Distributions (Fréchet, Gumbel, and Weibull) error terms were
designed, generalized and imitated to capture stylized traits of k-serial tenures (ability to handle cycles),
Markov transitional mixing weights, switching of mingling autoregressive
processes and full range shape changing predictive
distributions (multimodalities) that are usually caused by large fluctuations
(outliers) and long-memory in stock returns. The Poisson and
Extreme-Value-Distributions Mingled Autoregressive (PMA and EVDs) models were
applied to a monthly number of stocks sold in Nigeria from 1960 to 2020. It was
deduced that fitted Gumbel-MAR (2:1, 1) outstripped other linear models as well
as bestfitted among the Poisson and Extreme-Value-Distributions Mingled autoregressive models subjected to the discrete
monthly stocks sold series.
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