Demand Forecasting using multivariate time Series forecasting

Question

I have a multivariate time series data which has fields Order_date, store_id, region, product_ID, Unit_sold, discount, holiday(yes/no) etc. Number of unique products is 50. I need to perform demand forecasting of each product. I want to apply SARIMAX model on this dataset.

Do i need to build individual forecast model for each of the products seperately or there is some workaround to deal with forecasting of multiple products together?

Another aspect: How should i check for the stationarity of multivariate time series. I came across adf test which works for univariate data and Johansen's test which can work upto 12 independent variabes. Is Johansen's test the best way of checking stationarity of multivariate time series.

I am a beginner in time series. Please guide me through the steps.

Answer 1

Let's approach this with an example. Suppose you sell sweaters, IKEA furniture, and ice cream. Logically, sweaters will sell best just before and during winter, IKEA furniture sells best during weekends, but is fairly even throughout the year, and ice cream sells best in summer, but mostly when it's hot. If you fit a time series model to all these at once, even though the products might all show trends with the same periodicities, their impacts will be completely opposite!

Of course more people buy ice cream, sweaters, and furniture during weekends, but the impact of it being a weekend will be much larger for the last one than for others. And sweaters and ice cream probably both show yearly trends, but in opposite directions.

I'd advise you to build a model for one product, then look into automating the process, and for the rest of the products, just review the results of the automation process.

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Although some of us have mathematical backgrounds, asking about which (statistical) tests is the best is bound to get subjective, complex answers, since that really depends on the situation. Supposing that you're working for a business - in my experience it's often sufficient to get a good enough answer instead of a perfect one. Yang and Shahabi use Johansen's test, for example, and talk about stationarizing non-stationary multivariate time series if they fail it.

In the end, the main way you'll find out whether an approach worked is through trial and error. If you use Johansen's test, the series passes it, but you see in the results that the predictions get worse over time, then the time series apparently wasn't stationary. If you want a more mathematically correct answer, or if you're not working in a business environment, I'd pose the second question at CrossValidated, which has similar queries.