Intra-day transactions of stocks from competing firms in the financial markets are known to exhibit significant volatility and over-dispersion. This paper proposes some bivariate integer-valued auto-regressive models of order 1 (BINAR(1)) that are useful to analyze such financial series. These models were constructed under both time-variant and time-invariant conditions to capture features such as over-dispersion and non-stationarity in time series of counts. However, the quest for the most robust BINAR(1) models is still on. This paper considers specifically the family of BINAR(1)s with a non-diagonal cross-correlation structure and with unpaired innovation series. These assumptions relax the number of parameters to be estimated. Simulation experiments are performed to assess both the consistency of the estimators and the robust behavior of the BINAR(1)s under mis-specified innovation distribution specifications. The proposed BINAR(1)s are applied to analyze the intra-day transaction series of AstraZeneca and Ericsson. Diagnostic measures such as the root mean square errors (RMSEs) and Akaike information criteria (AICs) are also considered. The paper concludes that the BINAR(1)s with negative binomial and COM–Poisson innovations are among the most suitable models to analyze over-dispersed intra-day transaction series of stocks.

中文翻译：

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一些流行的非平稳 BINAR(1) 模型的鲁棒性比较和评估

众所周知，金融市场上竞争公司的股票日内交易表现出巨大的波动性和过度分散性。本文提出了一些 1 阶二元整数值自回归模型 (BINAR(1))，可用于分析此类金融序列。这些模型是在时变和时不变条件下构建的，以捕获计数时间序列中的过度分散和非平稳性等特征。然而，对最稳健的 BINAR(1) 模型的探索仍在继续。本文特别考虑具有非对角互相关结构和不成对创新级数的 BINAR(1) 系列。这些假设放宽了要估计的参数的数量。进行模拟实验以评估估计器的一致性和 BINAR(1) 在错误指定的创新分布规范下的鲁棒行为。所提出的 BINAR(1) 用于分析阿斯利康和爱立信的日内交易系列。还考虑了均方根误差 (RMSE) 和 Akaike 信息标准 (AIC) 等诊断措施。本文得出的结论是，具有负二项式和 COM-泊松创新的 BINAR(1) 是分析过度分散的股票日内交易系列的最合适模型之一。