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Probability space of regression models and its applications to financial time series

机译：回归模型的概率空间及其在金融时间序列中的应用

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摘要

We introduce a notion of a probability space of regression models and discuss its applications to financial time series. The probability space of regression models ℒ = ( ℳ , ℘ ) consists of a set of regression models ℳ and a probability measure ℘ , which is based on the model “quality”, i.e. its ability to “fit” into historical data and to forecast the future values of the target variable. The set of regression models ℳ is assembled by selecting various combinations of input variables with different lags, transformations, etc., and varying historical data sets that are used for model building and validation. It is assumed that the model set ℳ is “complete” in the sense that it exhausts all the “meaningful” regression models that are possible to be built given available historical data and independent variables. Each model M from the set ℳ yields a scenario y ⁢ ( t ; m ) for the target variable y , and thus the probability space of regression models ℒ = ( ℳ , ℘ ) allows one to build a probability distribution for Y ⁢ ( t ) for each projection time t . We demonstrate how those distributions can be used to estimate risk capital reserves required by the regulators for large U.S. banks for credit and operational risks under the macroeconomic scenarios provided by the Federal Reserve Bank (FRB) for the Comprehensive Capital Analysis and Review (CCAR) stress testing.
机译：我们介绍了回归模型的概率空间的概念，并讨论了其在金融时间序列中的应用。回归模型ℒ的概率空间=（ℳ，℘）由一组回归模型ℳ和概率测度consists组成，其基于模型“质量”，即其“适应”历史数据和预测的能力目标变量的未来值。通过选择具有不同滞后，变换等的输入变量的各种组合以及用于模型构建和验证的各种历史数据集，来组装回归模型集合。假设模型集ℳ是“完整的”，就意味着它会耗尽所有“有意义”的回归模型，这些模型在给定可用的历史数据和自变量的情况下有可能建立。集合中的每个模型M都产生了目标变量y的情形y⁢（t; m），因此回归模型ℒ=（ℳ，℘）的概率空间使人们可以建立Y⁢（t ）每个投影时间t。我们将展示这些分布如何用于估算联邦储备银行（FRB）为综合资本分析和评估（CCAR）压力而提供的宏观经济情景下，监管机构对美国大型银行的信贷和操作风险所需的风险资本准备金。测试。

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