Many current approaches to shrinkage within the time-varying parameter framework assume that each state is equipped with only one innovation variance for all time points. Sparsity is then induced by shrinking this variance towards zero. We argue that this is not sufficient if the states display large jumps or structural changes, something which is often the case in time series analysis. To remedy this, we propose the dynamic triple gamma prior, a stochastic process that has a well-known triple gamma marginal form, while still allowing for autocorrelation. Crucially, the triple gamma has many interesting limiting and special cases (including the horseshoe shrinkage prior) which can also be chosen as the marginal distribution. Not only is the marginal form well understood, we further derive many interesting properties of the dynamic triple gamma, which showcase its dynamic shrinkage characteristics. We develop an efficient Markov chain Monte Carlo algorithm to sample from the posterior and demonstrate the performance through sparse covariance modeling and forecasting of the returns of the components of the EURO STOXX 50 index.

翻译：在时变参数框架内的许多当前收缩方法假设每个状态在所有时间点仅配备一个创新方差，并通过将该方差向零收缩来诱导稀疏性。我们认为，当状态呈现大幅跳跃或结构性变化（这在时间序列分析中经常出现）时，这一方法并不充分。为弥补这一不足，我们提出动态三重伽马先验——一种已知具有三重伽马边缘形式且允许自相关的随机过程。关键的是，三重伽马拥有许多有趣的极限情形和特例（包括马蹄形收缩先验），这些均可作为边缘分布的选择。该边缘形式不仅易于理解，我们还进一步推导出动态三重伽马的诸多有趣性质，揭示了其动态收缩特征。我们开发了一种高效的马尔可夫链蒙特卡洛算法从后验分布中抽样，并通过欧元斯托克50指数成分股收益的稀疏协方差建模与预测展示了其性能。