Temporal Models and Their Applications

Modeling temporal dependency holds significant importance across diverse domains like finance, economics, and resource allocation. By capturing the intricate relationships between past and future observations, these models not only enhance prediction accuracy but also play a crucial role in effective risk management and optimal resource allocation. In finance, understanding temporal dependencies is essential for making informed investment decisions and quantifying market risks, while in economics, it aids in designing policies that consider the impact of historical factors on future outcomes. Over time, the HAC has gained attraction in economics and finance, particularly for its efficacy in handling clustered variables and capturing implied correlations. Its prowess in modeling Value-at-Risk across Basel regulatory phases and its role in understanding collateralized debt obligations during the 2008 financial crisis have bolstered its significance. The copula’s reputation, previously challenged by media, has been reinstated through subsequent research. Current financial trends, like high-frequency trading, have opened avenues for accurate joint distribution modeling of daily returns using HAC. These three financial applications are discussed in this chapter. While running these empirical studies, researchers have noticed that contrary to other models, in HAC not only the parameters but also the structure are changing. This observation led to another series of papers investigating exactly this issue. This chapter discusses in detail two temporal HAC models and several applications of the HAC.