A bivariate first-order autoregressive time series model in exponential variables (Bear 1)

Article Abstract:

A non-complex time series model for bivariate exponential variables having a first-order autoregressive structure is developed called the BEAR (1) model. The New Exponential Autoregressive model (NEAR 2) is adapted to create the linear random coefficient difference equation model. This process is Markovian in the bivariate sense and has correlation development that is similar to that of the Gaussian AR(1) bivariate time series model. Research results indicate that the model shows a full range of cross-correlations and positive correlations. Research results also indicate that the marginal processes have correlation structure of ARMA (2,1) models.

Mathematical models, Time-series analysis, Time series analysis

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The parameter iteration method in dynamic programming

Article Abstract:

A practical method called the Parameter Iteration Method is developed for obtaining approximate solutions for problems involving systems with many components. Such multi-component systems would normally lead to impractical dynamic programming problems with too many state variables. An iteration method is used to overcome the computational difficulties and provide successive approximations of the value functions using recursive estimation and simulation. A problem of optimal replacement policy in a multi-item Markovian system is used as an example.

Dynamic programming, Recursive functions

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An autoregressive process for beta random variables

Article Abstract:

Autoregressive processes involving stationary first-order autregression with beta marginal distribution are modeled and investigated. The models differ in that one has positive autocorrelation functions, whereas the other has alternating sign autocorrelation; both models exhibit linear and additive processes and both have beta random variables. The applications of these models to simulation techniques are discussed, as are the bivariate beta distributions of two consecutive observations and bivariate uniform processes.

Variables (Mathematics), Random variables

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