Non‐crossing quantile double‐autoregression for the analysis of streaming time series data
针对流式到达的金融时间序列，提出一种可更新的分位数双自回归估计方法，解决存储和计算瓶颈，避免分位数曲线交叉问题，并保持条件分位数的单调性。
Many financial time series not only have varying structures at different quantile levels and exhibit the phenomenon of conditional heteroscedasticity at the same time but also arrive in the stream. Quantile double‐autoregression is very useful for time series analysis but faces challenges with model fitting of streaming data sets when estimating other quantiles in subsequent batches. This article proposes a renewable estimation method for quantile double‐autoregression analysis of streaming time series data due to its ability to break with storage barrier and computational barrier. Moreover, the proposed flexible parametric structure of the quantile function enables us to predict any interested quantile value without quantile curve crossing problem or keeping the desirable monotone property of the conditional quantile function. The proposed methods are illustrated using current data and the summary statistics of historical data. Theoretically, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. Simulation studies and an empirical example are presented to illustrate the finite sample performance of the proposed methods.