Real-world time series forecasting is challenging for a whole host of reasons not limited to problem features such as having multiple input variables, the requirement to predict multiple time steps, and the need to perform the same type of prediction for multiple physical sites.<\/p>\n
The EMC Data Science Global Hackathon dataset, or the \u2018Air Quality Prediction\u2019 dataset for short, describes weather conditions at multiple sites and requires a prediction of air quality measurements over the subsequent three days.<\/p>\n
Before diving into sophisticated machine learning and deep learning methods for time series forecasting, it is important to find the limits of classical methods, such as developing autoregressive models using the AR or ARIMA method.<\/p>\n
In this tutorial, you will discover how to develop autoregressive models for multi-step time series forecasting for a multivariate air pollution time series.<\/p>\n
After completing this tutorial, you will know:<\/p>\n
- \n
- How to analyze and impute missing values for time series data.<\/li>\n
- How to develop and evaluate an autoregressive model for multi-step time series forecasting.<\/li>\n
- How to improve an autoregressive model using alternate data imputation methods.<\/li>\n<\/ul>\n
Let\u2019s get started.<\/p>\n
![\"Impact](\"https:\/\/machinelearningmastery.com\/wp-content\/uploads\/2019\/01\/Impact-of-Dataset-Size-on-Deep-Learning-Model-Skill-And-Performance-Estimates.jpg\")
<\/p>\nImpact of Dataset Size on Deep Learning Model Skill And Performance Estimates
Photo by Eneas De Troya<\/a>, some rights reserved.<\/p>\n<\/div>\nTutorial Overview<\/h2>\n
This tutorial is divided into six parts; they are:<\/p>\n
- \n
- Problem Description<\/li>\n
- Model Evaluation<\/li>\n
- Data Analysis<\/li>\n
- Develop an Autoregressive Model<\/li>\n
- Autoregressive Model with Global Impute Strategy<\/li>\n<\/ol>\n
Problem Description<\/h2>\n
The Air Quality Prediction dataset describes weather conditions at multiple sites and requires a prediction of air quality measurements over the subsequent three days.<\/p>\n
Specifically, weather observations such as temperature, pressure, wind speed, and wind direction are provided hourly for eight days for multiple sites. The objective is to predict air quality measurements for the next 3 days at multiple sites. The forecast lead times are not contiguous; instead, specific lead times must be forecast over the 72 hour forecast period. They are:<\/p>\n
+1, +2, +3, +4, +5, +10, +17, +24, +48, +72<\/pre>\n
Further, the dataset is divided into disjoint but contiguous chunks of data, with eight days of data followed by three days that require a forecast.<\/p>\n
Not all observations are available at all sites or chunks and not all output variables are available at all sites and chunks. There are large portions of missing data that must be addressed.<\/p>\n
The dataset was used as the basis for a short duration machine learning competition<\/a> (or hackathon) on the Kaggle website in 2012.<\/p>\n
Submissions for the competition were evaluated against the true observations that were withheld from participants and scored using Mean Absolute Error (MAE). Submissions required the value of -1,000,000 to be specified in those cases where a forecast was not possible due to missing data. In fact, a template of where to insert missing values was provided and required to be adopted for all submissions (what a pain).<\/p>\n
A winning entrant achieved a MAE of 0.21058 on the withheld test set (private leaderboard<\/a>) using random forest on lagged observations. A writeup of this solution is available in the post:<\/p>\n