[Paper Review] Conditional Time Series Forecasting with Convolutional Neural Networks

Anastasia Borovykh, Sander M. Bohté+1 more|arXiv (Cornell University)|Mar 14, 2017

Stock Market Forecasting Methods20 references376 citations

TL;DR

The paper adapts WaveNet-style dilated CNNs for conditional multivariate time series forecasting, showing competitive accuracy and efficiency against AR and LSTM, especially with conditioning on related series.

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.

Motivation & Objective

• Investigate whether a dilated CNN can effectively forecast financial time series with limited history.
• Assess the benefits of conditioning on multiple related time series for improved forecast quality.
• Compare CNN-based forecasting to autoregressive and LSTM benchmarks in regression-type, noisy data settings.
• Evaluate the model's ability to learn nonlinear dependencies and inter-series correlations.

Proposed method

• Adapt WaveNet-style CNN with dilated causal convolutions for time series forecasting.
• Use ReLU activations and parameterized skip connections for conditioning on multiple time series.
• Train with mean absolute error and L2 regularization; optimize weights with Adam.
• Incorporate causal padding to ensure forecasts depend only on past data.
• Apply residual connections to enable deeper architectures without degradation.
• Condition the network by adding convolved conditioning inputs via 1x1 skip pathways.

Experimental results

Research questions

• RQ1 Can a dilated CNN (WaveNet-style) learn long-range dependencies in financial time series with limited history?
• RQ2 Does conditioning on multiple related time series improve forecast accuracy over unconditional models?
• RQ3 How does CNN-based forecasting compare to autoregressive and LSTM models in terms of accuracy and training efficiency?
• RQ4 What nonlinear dependencies and cross-series relationships can be captured by the proposed conditioning mechanism?

Key findings

• Unconditional WaveNet (uWN) achieves competitive RMSE compared to a benchmark LSTM on chaotic time series.
• Conditioned WaveNet (cWN) reduces forecast error and variability, indicating effective exploitation of inter-series correlations.
• For the Lorenz system coordinates X, Y, Z, conditioning generally lowers RMSE relative to the unconditional model, with X showing notable improvement.
• The evaluated setup demonstrates the CNN can learn nonlinear dependencies and inter-series relationships without requiring long histories.
• The approach offers a time-efficient and easy-to-implement alternative to recurrent architectures for noisy, multivariate forecasting.