Discrete time series generated by mixtures III

Discrete time series generated by mixtures III

by Patricia A. Jacobs

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A scheme for obtaining a stationary sequence of discrete random variables which has p-th order Markov dependence and a specified marginal distribution is presented. This DAR(p) process, which is a particular p-th order Markov chain, has the physical and correlation structure of an autoregressive process of order p. The process and its transition matrix are determined by the specified marginal distribution and by several other parameters which, independently of the marginal distribution, determine the correlation structure. Correlational properties and initial conditions for stationarity of the process are studied. Asymptotic properties for the process are also obtained.

Discussion questions for Discrete time series generated by mixtures III

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  1. 1

    How does the introduction of the DAR(p) process challenge your initial assumptions about the boundaries between predictability and randomness in sequential data?

  2. 2

    In what ways does the structural independence between the specified marginal distribution and the correlation-determining parameters mirror the delicate balances we try to maintain in our own complex personal systems?

  3. 3

    If you had to assign a distinct personality or temperament to the transition matrix described in this text, how would it behave in a room full of other mathematical models?

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