Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting (1905.03806v2)

Abstract: Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern datasets can have millions of correlated time-series that evolve together, i.e they are extremely high dimensional (one dimension for each individual time-series). There is a need for exploiting global patterns and coupling them with local calibration for better prediction. However, most recent deep learning approaches in the literature are one-dimensional, i.e, even though they are trained on the whole dataset, during prediction, the future forecast for a single dimension mainly depends on past values from the same dimension. In this paper, we seek to correct this deficiency and propose DeepGLO, a deep forecasting model which thinks globally and acts locally. In particular, DeepGLO is a hybrid model that combines a global matrix factorization model regularized by a temporal convolution network, along with another temporal network that can capture local properties of each time-series and associated covariates. Our model can be trained effectively on high-dimensional but diverse time series, where different time series can have vastly different scales, without a priori normalization or rescaling. Empirical results demonstrate that DeepGLO can outperform state-of-the-art approaches; for example, we see more than 25% improvement in WAPE over other methods on a public dataset that contains more than 100K-dimensional time series.

High-Dimensional Time Series Forecasting Using Deep Neural Networks

The paper "Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting" addresses the challenge of forecasting high-dimensional time series data. In modern applications such as demand forecasting and financial predictions, datasets often comprise millions of time series that are correlated and evolve together, creating a need for models that can handle such high-dimensional data effectively.

Key Contributions

The central contribution of this work is the proposal of a hybrid forecasting model that leverages both global and local features for prediction. This model combines a global matrix factorization approach, regularized by a Temporal Convolutional Network (TCN), with another network that focuses on local time series properties. The authors introduce several innovations to address existing challenges in time series forecasting:

1. Handling Diverse Scales: The authors present a scheme for initializing TCNs that allows training on datasets with widely varying scales without requiring prior normalization. This initialization helps ensure that initial predictions are the averages of input sequences, facilitating stable training.
2. Modeling Global and Local Patterns: The hybrid model integrates a global forecasting component, which captures shared temporal patterns across the dataset using a low-rank matrix factorization approach. This component is regularized by a TCN to capture nonlinear dependencies.
3. Combining Global Output with Local Features: The predictions from the global model are used as covariates for a local TCN, which then focuses on individual time series and associated covariates, allowing the model to incorporate both global dependencies and local temporal behavior.

Empirical Results

The proposed method demonstrates substantial advancements in accuracy when tested on various real-world datasets, including those with over 100,000-dimensional time series. Notably, the model achieved significant improvements in Weighted Absolute Percentage Error (WAPE), showcasing over a 25% reduction compared to state-of-the-art methods in some instances. These empirical results highlight the model's capacity to outperform traditional methods in high-dimensional settings.

Implications and Future Developments

The contributions of this paper have significant implications for practical applications, particularly in industries reliant on accurate forecasts from massive, correlated datasets. The hybrid approach could revolutionize how models are applied to tasks like retail demand forecasting, where understanding both individual and shared trends is critical.

Theoretically, this work paves the way for further developments in time series analysis by encouraging the integration of deep learning architectures with classic matrix factorization methods. The potential scalability and adaptability of the model to other applications hint at a broader future impact across different domains.

In terms of future research, exploring more complex network architectures or incorporating additional data modalities could further enhance performance. Moreover, investigating alternative regularization techniques might improve the model's robustness to highly noisy or incomplete datasets. The integration of external knowledge, such as semantic information, could also enhance prediction accuracy.

In conclusion, this paper presents a robust framework that blends global and local insights to address the challenges in high-dimensional time series forecasting, offering substantial theoretical and practical benefits. Future explorations could focus on extending the adaptability and further reducing computational requirements, broadening the scope of its applicability.