A topical problem of robust statistical estimation of parameters for binomial conditionally nonlinear autoregressive (BiCNAR) time series under innovation outliers is considered. This problem is solved by means of $s$-order Markov properties for observed time series and probabilistic properties of multivariate conditional frequencies of the future state under its $s$-prehistory. The new robust statistical estimator $\hat{\zeta }$ called frequencies-based estimator (FBE) is constructed for the BiCNAR parameters under innovation outliers with arbitrary discrete probability distribution having some fixed known expectation. Under mild regularity conditions the constructed FBE is shown to have the robustness properties: consistency and asymptotic normality with obtained asymptotic covariance matrix. FBE also has computational advantages: an explicit form and a fast recursive re-estimation algorithm for extension of the model. Asymptotic risk functional and its minimum are evaluated using Fisher information matrix for the considered model. Sensitivity analysis of the statistical estimator $\tilde{\zeta }$ for the BiCNAR parameters, that is constructed for the hypothetical model without outliers, is carried out for the situation with innovation outliers: $\tilde{\zeta }$ is shown to be inconsistent in this situation, its bias and the instability coefficient are evaluated and analyzed. The robust estimator $\hat{\zeta }$ has a free parameter — weight matrix $H$. The optimal weight matrix $H^{\ast }$ is found by minimization of the asymptotic risk w.r.t. $H$. Statistical estimator for $H^{\ast }$ based on the observed time series is constructed. Results of multiple computer experiments on simulated and real data illustrate the theory.

考虑了在创新异常值下二项式条件非线性自回归 (BiCNAR) 时间序列参数的稳健统计估计的热门问题。这个问题是通过以下方式解决的$秒$观察到的时间序列的阶马尔可夫特性和未来状态的多元条件频率的概率特性 $秒$-史前。新的稳健统计估计器$\widehat{\zeta }$被称为基于频率的估计器 (FBE) 是为 BiCNAR 参数在创新异常值下构建的，具有一些固定的已知期望的任意离散概率分布。在温和的正则性条件下，构建的 FBE 被证明具有鲁棒性：与获得的渐近协方差矩阵的一致性和渐近正态性。FBE 还具有计算优势：显式形式和用于模型扩展的快速递归重新估计算法。使用所考虑模型的 Fisher 信息矩阵评估渐近风险函数及其最小值。统计估计量的敏感性分析$\tilde{\zeta }$ 对于 BiCNAR 参数，即为没有异常值的假设模型构建的参数，是针对有创新异常值的情况进行的： $\tilde{\zeta }$在这种情况下显示不一致，对其偏差和不稳定系数进行评估和分析。稳健估计器$\widehat{\zeta }$ 有一个自由参数——权重矩阵 $H$. 最优权重矩阵$H^{＊}$ 通过最小化渐近风险 wrt 找到 $H$. 统计估计量$H^{＊}$根据观察到的时间序列构建。对模拟数据和真实数据的多台计算机实验结果说明了该理论。