Croston model : Forecasting Intermittent demand data (Time Series analysis)
By: Juilee Talele
Tags: Crostons Model, Time Series Analysis, Forecasting, Data Science, Econometrics

Let’s start with…

What is Forecasting ?

Forecasting is a technique that takes past data and predicts the future value for the data looking at its unique trends. For example — predicting average annual company turnover based on data from 10+ years prior. This past data is generally time based data that is nothing but “Time Series Data” and the models we build for forecasting is “Time Series Modelling”.

Time series is anything which is observed sequentially over the time at regular interval like hourly, daily, weekly, monthly, quarterly etc. Time series data is important when you are predicting something which is changing over the time using past data. In time series analysis the goal is to estimate the future value using the behaviors in the past data.

There are many statistical techniques available for time series forecast however we have found few effective ones which are listed below:

Some Techniques of Forecasting are:

Simple Moving Average (SMA)

Exponential Smoothing (SES)

Autoregressive Integration Moving Average (ARIMA)

Neural Network (NN)

Croston model

Now, let’s cut to the chase and talk more about Croston model…

Croston model is a statistical method of forecasting quantitative time series. Generally for forecasting intermittent demand.

But what is intermittent demand ?

Intermittent demand — when a product or demand experiences several periods of zero demand — is highly variable. Intermittent demand is very common in industries such as aviation, automotive, defense, manufacturing, and retail. It also typically occurs with products nearing the end of their life cycle.

Problem with intermittent demand :

Intermittent series has demand appear at random with many time periods showing no demand at all. The prominent characteristics of such series are:

The time-series contains embedded zeroes The time-series does NOT exhibit any seasonal behavior

Example of intermittent demand data,

Intermittent demand

Intermittent demand is characterized by occasional demand arrivals interspersed by time intervals during which no demand occurs. These demand patterns pose considerable difficulties in terms of forecasting and inventory control due to their compound nature as demand arrivals are coupled with demand size distribution. Thus, operational managers face a twofold forecasting problem:

(1) When the next demand will occur?

(2) Once demand is realized, what will be the respective volume?

Let’s try forecasting the intermittent data using simple exponential smoothing. Below example show simple exponential smoothing on normal data and intermittent data.

Simple Exponential Smoothing

Simple Exponential Smoothing on Intermittent data

As you can see in above two examples, consider the last observation t = 15, for normal data simple exponential smoothing predicted 35, but when we embed some zeros i.e intermittent data then the predicted value drastically fall to 18, thereby we get maximum error.

Due to the many zero values in intermittent demand time series, the usual methods of forecasting, such as exponential smoothing and ARIMA, do not give an accurate forecast. In these cases, approaches such as Croston may provide a better accuracy over traditional methods.

How does croston model solve the problem with Intermittent demand ?

Croston’s has a complex formula, however, what it output is actually very simple. The screenshot below explains what Croston’s does in a very simple way for the sake of understanding.

Above is the 12-month average vs. Croston’s vs, while below is the 5-month average vs. Croston’s.

As you can see, Croston’s removes the periods that have no demand only averaging the periods that have demand.

Working of Croston model :

Above picture shows the detail working of croston’s model.

Croston’s method is a widely used approach for intermittent demand forecasting, and is based on exponential smoothing. In particular, it involves separate simple exponential smoothing of the demand size and the time period between demands. The ratio of those estimates (sizes/intervals) may then be used as an estimate of the demand per period. Consider the following notation to explain Croston’s procedure:

The method updates the forecasts for demand size and interval only after positive demand occurs. That means, if in a period t demand is zero the method only increments the count of time periods since last positive demand. The procedure for Croston’s method is described below:

Summary :

Croston’s Method, essentially shifts the updating to only after an order occurs. n Smooths out the forecast for replenishment purposes — average usage per period n Unbiased and has lower variance than simple smoothing.

Cautions n Infrequent updating introduces a lag to responding to magnitude changes n Recommended use of smoothing for MSE of non-zero transaction periods

Conclusion:

The Croston method is a forecast strategy for products with intermittent demand. In the uni variate forecast profile, choose forecast strategy.

Croston’s can be easily emulated with exponential smoothing and any timing benefit is usually adjusted by order lot sizing, and or safety stock in supply planning. Therefore, demand history must not only be lumpy, but must also be very low in order for Croston’s to be of value. Therefore, Croston’s can be seen as a specialty forecasting method that provides value in certain limited circumstance.