MTHetGNN

Multivariate time series forecasting using heterogeneous graph neural networks.

This repository is the official implementation of MTHetGNN: A heterogeneous graph embedding framework for multivariate time series forecasting.

Requirements

• python 3.7.7
• Pytorch 1.4.0

To install requirements:

pip install -r requirements.txt

Overview

Dataset

We conduct experiments on three benchmark datasets for multivariate time series forecasting tasks, this table shows dataset statistics

Dataset	T	D	L
Exchange_rate	7588	8	1 day
Solar	52560	137	10 minutes
Traffic	17544	862	1 hour

where T is the length of time series, D is the number of variables, L is the sample rate. Download the dataset and put them under data folder

Preprocessing

We split the raw data into train set, validation set and test set, in the ratio of 6:2:2.

In each set, consecutive time series with certain length of window size are sampled as a slice, which forms a forecasting unit. The slice window moves over the entire time series in the pace of 1 step each time

Adjacency matrix

We use three adjacency matrix to model explicit relations among time series in both static and dynamic way. Casual inference matrix and correlation relation matrix can be calculated in following steps.

We use R to measure static casual inference between time series. To get the Casual inference matrix, run this code under data folder:

Rscript rte.R

and place the result files under TE folder.

We also implement a python version of Casual inference measurement, run this code:

python Teoriginal.py

We use pandas toolkit to get static correlations among time series. To get the Correlation matrix, run this code under data folder:

python corr.py

and place the result files under TE folder.

Training

To train the model(s) in the paper, run this code:

python train.py --model MTHetNet --num_adjs 3 --channel_size 12 --hid1 40 --hid2 10

Evaluation

To evaluate the model in the paper, run this code:

python eval.py --model_file model.pt --data data/exchange_rate.txt --horizon 5

Pre-trained Models

You can download pre-trained models here:

• MTHetGNN pre-trained model trained on different datasets.

and place the pre-trained model under model folder. Note that this model should be loaded directly with Pytorch, or passed to eval.py.

On a 1070Ti, it took 2.6 seconds per epoch on Exchange_rate dataset, in the default setting of hyper parameters.

Results

We train MTHetGNN for 100 epochs for each train option, and use the model that has the best performance on validation set for test.

We use three conventional evaluation metrics to evaluate the performance of MTHetGNN model: Mean Absolute Error(MAE), Relative Absolute Error(RAE) and Empirical Correlation Coefficient(CORR), the following table shows the results:

Model name	Dataset	horizon	MAE	RAE	CORR
		3	0.0173	0.0132	0.9824
MTHetGNN	exchange_rate	6	0.0238	0.0190	0.9746
		12	0.0327	0.0266	0.9604
		24	0.0430	0.0361	0.9415
		3	0.1668	0.0788	0.9872
MTHetGNN	solar	6	0.2175	0.1111	0.9772
		12	0.2872	0.1514	0.9583
		24	0.3862	0.2217	0.9210
		3	0.4142	0.2349	0.8975
MTHetGNN	traffic	6	0.4303	0.2490	0.8887
		12	0.4376	0.2592	0.8828
		24	0.4500	0.2661	0.8776

Examples with parameters to run different datasets are in runExchangeRate.sh, runSolar.sh and runTraffic.sh, in which specific hyperparameters for each training options are listed.