November 4

# Sales Forecasting Using Monte Carlo and Trend

One way of categorising forecasting methods is if they are deterministic or probabilistic. Each of these methods has their own merits. Each method also has some disadvantages which the other deals with quite well.

This post looks at using some of the advantages of both forecasting methods to create a hybrid between the two.

We will discuss an overview of both approaches as well as the advantages and disadvantages of both. This will be used as a basis of creating a hybrid approach.

### Deterministic Models

In a previous post we looked at trying out different forecasting models on your data. The idea was to try a wide range of models in order to select and use the ones that have the best fit for the previous sales pattern.

These fall under the category of deterministic modelling. The outputs of the model are “determined” by inputs and nothing else. In this type of modelling, a set of inputs will always result in the same set of outputs.

Some of the advantages of this approach:

1. Old and robust method of statistical analysis with a range of models to choose from, each with a well understood set of advantages and disadvantages.
2. Can go from the very simple to very complex models quickly with the same dataset and select the ones that best fit your data.
3. Some models can give you a higher level understanding of your data like trend, seasonality.
4. It is a simple approach that is easily explained to the end user.

Each model gives a very specific view of what its prediction is going to be. But in reality, the forecast is usually within a range of values. You can use multiple models to determine a range but each one will have its own specific outcome.

### Probabilistic Models

Probabilistic models incorporate randomness into their predictions. The same inputs into a model won’t necessarily produce the same detailed outputs.

Monte Carlo simulation is one type of probabilistic modelling. It puts historical data into a distribution and uses it to run simulations of the future. These simulations form the basis of statistical analysis which can then be used to estimate likelihoods of events.

Probabilistic modelling was covered in a previous post that went through a Monte Carlo forecasting exercise.

1. It deals with a range of possible outcomes along with how likely each of these outcomes are. So this type of modelling is a better representation of how reality works.
2. Better for risk management because it shows you the likelihood of something happening that can be planned for.
3. It is an established statistical technique that has been used for a long time.

1. They are more complex than the deterministic models to build, and need more work to create.
2. Although the concept is easy to explain, building enough simulations for the model to be useful is not straightforward. It can be done on a spreadsheet, but is a cumbersome process as It is data and computation intensive.

### A Combination

the problem with Monte Carlo simulations in this context is that each of the simulations is a random outcome pulled from a distribution.

This is OK for completely random events, but activities like sales forecasting sometimes follow predictable patterns.

In the report “Simulations of 1,000 Random Events”, even though there seems to be a trend in last years sales, the don’t follow a pattern.

Combining deterministic and probabilistic forecasting can make use of the advantages in both methods of forecasting. You can run simulations but they can also follow a pattern.

The reports run a Monte Carlo simulation based on a simple trend of last years sales.

Although this is a good way of making predictions more accurate, the method does have some shortcomings.

1. The hybrid method has more steps than both deterministic and probabilistic forecasting on their own.
2. An even more complicated explanation to end users as it has more steps and more data to deal with.

In the report “Monte Carlo Simulation of Trended Sales” the simulations follow a clear pattern of a trend. The simulated sales also follow a nice normal distribution. The distribution shows no skew even though the simulations have been influenced by a trend.

Tags

Python, SalesForecasting