Stock price prediction is a challenging task due to its complexity and the dynamics associated with stock prices. In this paper, we propose a deep-learning based end-to-end framework with a novel architecture, for multi-step ahead stock closing price forecasts. The architecture exploits an encoder-decoder framework with variants of convolutions and recurrent neurons, in order to perform representation learning for the past behavior of the stock as well as associated exogenous factors. We incorporate an attention mechanism to capture the long term dependencies between inputs and outputs, and deploy Monte Carlo dropout layers in the architecture design to provide a stochastic setting for uncertainty estimation. We validate our model on two real datasets for AMZN and AAPL stocks.

This paper considers the problem of assessing the reliability of a software system that can be decomposed into a finite number of modules. It uses a Markovian model for the transfer of control between modules in order to develop the system reliability expression in terms of the module reliabilities. An operational test procedure is considered in which only the individual modules are tested and the system is considered acceptable if, and only if, no failures are observed. The minimum number of tests required of each module is determined such that the probability of accepting a system whose reliability falls below a specified value R/sub 0/ is less than a specified small fraction /spl beta/. This sample size determination problem is formulated as a two-stage mathematical program and an algorithm is developed for solving this problem. Two examples from the literature are considered to demonstrate the procedure.

Acceptance testing is analyzed for a series system of n components, each having an unknown, different, constant failure rate. Components are tested individually, and tests are terminated when a preassigned number of failures is observed for each component. The total time-on-test for each component is noted, and a statistic is constructed using observed test times and the number of failures of the components; the statistic is based on the maximum likelihood estimation of system reliability. This statistic is then used in specifying a decision rule for accepting or rejecting the entire system. The design of the test plan is stated as an optimization problem which minimizes test costs while ensuring that specified consumer and producer risks on system reliability are not exceeded. Numerical examples are provided, and implications of the test plan are discussed.