# Advanced time series methods for sales forecasting

## What’s behind the powerful of a statistical sales forecasting tool

If you read the article Time Series Analysis for Statistical Forecasting, you know that you can view SKU past sales as unidimensional signals called time series. As you know, Time Series Analysis is a set of tools able to automatically extract seasonality, trends and cycles patterns that are necessary to understand the past behaviour and to give a reasonable future projection. In this article, we report some of the most known advanced time series methods for sales forecasting.

**ARMA** (Auto Regressive Moving Average) are well-known models for sales forecasting. As the name says, those models are characterized by a set of components listed below (suppose you have monthly sales):

- Auto Regressive: how much the current month depends on the previous months;
- Moving Average: how much the current month depends on the previous random effects.

In fact, we define ARMA models as a set of values (p,q), where:

- p represents the number of previous autoregressive components;
- q represents the number of moving average components;

But how big p and q should be?

First of all, for the estimation of the pair (p, q), we can analyze the AutoCorrelation Function and the Partial AutoCorrelation Function of the time series. Once we compute (p, q), we have to estimate the magnitude of the relationships. One possible way to do this is by solving a least squares optimization problem.

Nevertheless, ARMA models are not able to cope with all kind of time series. What about intermittent time series? When your sales contain several zeros and sometimes non-zero values, **Croston** and **TSB** (Teunter, Syntetos and Babai) methods represent suitable solutions. Basically, they divide the time series in two different ones, in order to predict **when** the next sales will be and **how much** it will be.

Although dealing with those time series is very challenging due to the high uncertainty, Croston and TSB methods give us a reasonable time series future projection.