We introduce new methods of filtering and forecasting for the causal–noncausal convolution model. This model represents the dynamics of stationary processes with local explosions, such as spikes and bubbles, which characterize the time series of commodity prices, cryptocurrency exchange rates, and other financial and macroeconomic variables. The convolution model is a structural mixture of independent latent causal and noncausal component series. We propose an algorithm that recovers the latent components by evaluating the filtering density of one component, conditional on the observed past, present, and future values of the time series. Forecasts of the observed time series are obtained as a combination of filtered causal and noncausal component forecasts. The new filtering and forecasting methods are illustrated in a simulation study and compared with the results obtained from the mixed causal–noncausal autoregressive MAR model in application to WTI crude oil prices.

中文翻译：

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基于卷积的过滤和预测：在 WTI 原油价格中的应用

我们为因果-非因果卷积模型引入了新的过滤和预测方法。该模型表示具有局部爆炸的平稳过程的动态，例如尖峰和泡沫，它们表征商品价格、加密货币汇率以及其他金融和宏观经济变量的时间序列。卷积模型是独立潜在因果和非因果成分系列的结构混合。我们提出了一种算法，通过评估一个组件的过滤密度来恢复潜在组件，条件是观察到的时间序列的过去、现在和未来值。观察到的时间序列的预测是作为过滤的因果和非因果成分预测的组合获得的。