This repository is the official implementation of Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting.


Recommended version of OS & Python:

To install python dependencies, virtualenv is recommended, sudo apt install python3.7-venv to install virtualenv for python3.7. All the python dependencies are verified for pip==20.1.1 and setuptools==41.2.0. Run the following commands to create a venv and install python dependencies:

python3.7 -m venv venv
source venv/bin/activate
pip install --upgrade pip
pip install -r requirements.txt



We can get the raw data through the links above. We evaluate the performance of traffic flow forecasting on PEMS03, PEMS07, PEMS08 and traffic speed forecasting on PEMS04, PEMS-BAY and METR-LA. So we use the traffic flow table of PEMS03, PEMS07, PEMS08 and the traffic speed table of PEMS04, PEMS-BAY and METR-LA as our datasets. We download the solar power data of Alabama (Eastern States) and merge the 5-minute csv files (totally 137 time series) as our Solar dataset. We delete the header and index of Electricity file downloaded from the link above as our Electricity dataset. For COVID-19 dataset, the raw data is under the folder csse_covid_19_data/csse_covid_19_time_series/ of the above github link. We use time_series_covid19_confirmed_global.csv to calculate the daily number of newly confirmed infected people from 1/22/2020 to 5/10/2020. The 25 countries we take into consideration are 'US','Canada','Mexico','Russia','UK','Italy','Germany','France','Belarus ','Brazil','Peru','Ecuador','Chile','India','Turkey','Saudi Arabia','Pakistan','Iran','Singapore','Qatar','Bangladesh','Arab','China','Japan','Korea'.

The input csv file should contain no header and its shape should be T*N, where T denotes total number of timestamps, N denotes number of nodes.

Since complex data cleansing is needed on the above datasets provided in the urls before fed into the StemGNN model, we provide a cleaned version of ECG5000 (./dataset/ECG_data.csv) for reproduction convenience. The ECG_data.csv is in shape of 5000*140, where 5000 denotes number of timestamps and 140 denotes total number of nodes. Run command python to trigger training and evaluation on ECG_data.csv.

Training and Evaluation

The training procedure and evaluation procedure are all included in the To train and evaluate on some dataset, run the following command:

python --train True --evaluate True --dataset <name of csv file> --output_dir <path to output directory> --n_route <number of nodes> --window_size <length of sliding window> --horizon <predict horizon> --norm_method z_score --train_length 7 --validate_length 2 --test_length 1

The detailed descriptions about the parameters are as following:

Parameter name Description of parameter
train whether to enable training, default True
evaluate whether to enable evaluation, default True
dataset file name of input csv
window_size length of sliding window, default 12
horizon predict horizon, default 3
train_length length of training data, default 7
validate_length length of validation data, default 2
test_length length of testing data, default 1
epoch epoch size during training
lr learning rate
multi_layer hyper parameter of STemGNN which controls the parameter number of hidden layers, default 5
device device that the code works on, 'cpu' or 'cuda:x'
validate_freq frequency of validation
batch_size batch size
norm_method method for normalization, 'z_score' or 'min_max'
early_stop whether to enable early stop, default False

Table 1 Configurations for all datasets

Dataset train evaluate node_cnt window_size horizon norm_method
METR-LA True True 207 12 3 z_score
PEMS-BAY True True 325 12 3 z_score
PEMS03 True True 358 12 3 z_score
PEMS04 True True 307 12 3 z_score
PEMS07 True True 228 12 3 z_score
PEMS08 True True 170 12 3 z_score
COVID-19 True True 25 28 28 z_score


Our model achieves the following performance on the 10 datasets:

Table 2 (predict horizon: 3 steps)

Dataset MAE RMSE MAPE(%)
METR-LA 2.56 5.06 6.46
PEMS-BAY 1.23 2.48 2.63
PEMS03 14.32 21.64 16.24
PEMS04 20.24 32.15 10.03
PEMS07 2.14 4.01 5.01
PEMS08 15.83 24.93 9.26

Table 3 (predict horizon: 28 steps)

COVID-19 662.24 1023.19 19.3