Conditional Time Series Forecasting with Convolutional Neural Networks

TL;DR

Financial time series are noisy and often short, making robust forecasting challenging. The paper adapts a WaveNet-inspired CNN with dilated, causal convolutions and a novel conditioning scheme to forecast multivariate series efficiently. It demonstrates that the approach learns non-linear dependencies and inter-series dynamics, often outperforming autoregressive models and LSTMs while requiring less historical data. The method is validated on artificial chaotic data and real financial data (stocks, volatility, rates, and FX), showing strong robustness and practical potential for regime-aware forecasting. Overall, conditional WaveNet offers a fast, interpretable, and competitive alternative for multivariate financial forecasting.

Abstract

We present a method for conditional time series forecasting based on an adaptation of the recent deep convolutional WaveNet architecture. The proposed network contains stacks of dilated convolutions that allow it to access a broad range of history when forecasting, a ReLU activation function and conditioning is performed by applying multiple convolutional filters in parallel to separate time series which allows for the fast processing of data and the exploitation of the correlation structure between the multivariate time series. We test and analyze the performance of the convolutional network both unconditionally as well as conditionally for financial time series forecasting using the S&P500, the volatility index, the CBOE interest rate and several exchange rates and extensively compare it to the performance of the well-known autoregressive model and a long-short term memory network. We show that a convolutional network is well-suited for regression-type problems and is able to effectively learn dependencies in and between the series without the need for long historical time series, is a time-efficient and easy to implement alternative to recurrent-type networks and tends to outperform linear and recurrent models.

Figures (7)

• Figure 2.1: A feedforward neural network with three layers (L) vs. a convolutional neural network with two layers and filter size $1\times 2$, so that the receptive field of each node consists of two input neurons from the previous layer and weights are shared across the layers, indicated by the identical colors (R).
• Figure 2.2: A dilated convolutional neural network with three layers.
• Figure 2.3: The network structure. In the first layer (L) the input and condition (with the zero padding) are convolved, passed through the non-linearity and summed with the parametrized skip connections. The result from this first layer is the input in the subsequent dilated convolution layer with a residual connection from the input to the output of the convolution. This is repeated for the other layers, until we obtain the output from layer $L$ (M). This output is passed through a 1$\times$1 convolution, resulting in the final output: the forecasted time series (R).
• Figure 3.1: The $X$-coordinate of the Lorenz map (green), the unconditional one-step ahead forecast (red) (TL), the conditional forecast (blue) (TR), the convergence behaviour of unconditional and conditional forecast for different learning rates (LL) and the histogram of the errors for the one-step-ahead forecast on the test set (LR).
• Figure 3.2: The training sample $t\in [0,1000]$ and a fully out-of-sample forecast for time steps $t\in[1000, 1500]$ for the $X$-coordinate (L) and the $Y$-coordinate (R)

Theorems & Definitions (2)

• Remark 1: Relation to the Bayesian framework
• Remark 2: Ability to learn non-linear dependencies