论文标题
DeepVarwt：具有趋势的VAR模型的深度学习
DeepVARwT: Deep Learning for a VAR Model with Trend
论文作者
论文摘要
向量自回旋（VAR）模型已用于描述多个时间序列内部和跨多个时间序列的依赖性。这是一个固定时间序列的模型，可以扩展，以允许每个系列的确定性趋势存在。在拟合VAR模型之前，在参数或非参数上降低数据会导致后一部分的更多错误。在这项研究中，我们提出了一种称为DeepVarwt的新方法，该方法采用深度学习方法来同时对趋势和依赖性结构的最大似然估计。为此目的使用了长期的短期内存（LSTM）网络。为了确保模型的稳定性，我们使用Ansley＆Kohn（1986）的转换来实施自回归系数的因果关系。我们提供了一项模拟研究和对真实数据的应用。在仿真研究中，我们使用由真实数据产生的现实趋势函数，并将估计值与真实函数/参数值进行比较。在实际数据应用程序中，我们将该模型的预测性能与文献中的最新模型进行了比较。
The vector autoregressive (VAR) model has been used to describe the dependence within and across multiple time series. This is a model for stationary time series which can be extended to allow the presence of a deterministic trend in each series. Detrending the data either parametrically or nonparametrically before fitting the VAR model gives rise to more errors in the latter part. In this study, we propose a new approach called DeepVARwT that employs deep learning methodology for maximum likelihood estimation of the trend and the dependence structure at the same time. A Long Short-Term Memory (LSTM) network is used for this purpose. To ensure the stability of the model, we enforce the causality condition on the autoregressive coefficients using the transformation of Ansley & Kohn (1986). We provide a simulation study and an application to real data. In the simulation study, we use realistic trend functions generated from real data and compare the estimates with true function/parameter values. In the real data application, we compare the prediction performance of this model with state-of-the-art models in the literature.
