# Time Convolution

The temporal convolution is responsible for capturing temporal patterns in a sequence.

### Dilated Temporal Convolution

Unit8 has a nice blog about temporal convolution and dilated temporal convolution^{1}. In this

### Inception

A good convolutional network should capture both short-term and long-term patterns in the time series data. However,

- single large kernel is good for long-term pattern but not good at short-term pattern,
- single small kernel is good for short-term pattern but not good at long-term pattern.

The **inception** strategy employs multiple dilated temporal convolution and the outputs are concatenated. By applying multiple such layers, we can extract patterns longer than any of the single dilated temporal convolutions^{2}.

$$ \operatorname{concat}( z\star f_2, z\star f_3, z\star f_6, z\star f_7). $$

### Dilated Inception Layer

See Fig 5 in the paper^{2}.

Lässig2021 Lässig F. Temporal Convolutional Networks and Forecasting. In: Unit8 [Internet]. 6 Jul 2021 [cited 28 Nov 2022]. Available: https://unit8.com/resources/temporal-convolutional-networks-and-forecasting/ ↩︎

Wu2020 Wu Z, Pan S, Long G, Jiang J, Chang X, Zhang C. Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. arXiv [cs.LG]. 2020. Available: http://arxiv.org/abs/2005.11650 ↩︎ ↩︎

- Wu2020 Wu Z, Pan S, Long G, Jiang J, Chang X, Zhang C. Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. arXiv [cs.LG]. 2020. Available: http://arxiv.org/abs/2005.11650
- Lässig2021 Lässig F. Temporal Convolutional Networks and Forecasting. In: Unit8 [Internet]. 6 Jul 2021 [cited 28 Nov 2022]. Available: https://unit8.com/resources/temporal-convolutional-networks-and-forecasting/

L Ma (2022). 'Time Convolution', Datumorphism, 11 April. Available at: https://datumorphism.leima.is/cards/forecasting/time-convolution/.