## Forecasting Sales with Times Series Modeling

Observing data over time is time series. Predicting that data in future is time series modelling. Unlike the regular prediction, this is slightly different because of the chronology in the data.

As an example say a retail outlet (call it *RetaileR*) observes the daily sale of goods from when the company was created. It has been 5 years since, and they wish to estimate the sale for the next year for two reasons

- to assess the strength of the company and its future prospects
- to optimise its inventory stock and prevent losses due to undershooting or overshooting the estimate

Understanding this data is time series analysis. Suppose, *RetaileR* forecasts sales for the next 6 months, but due to unforeseen circumstances, the prediction for the month 2 goes off by 40%, there is a huge demand but the inventory is empty, and this puts the next 4 months into disarray. This may seem innocuous but, in certain industry sectors, inventory is stacked up to 8 months in advance and so, accurate forecasts go a long way. Usually a manual estimate of 5% or higher around the trend corresponding to last season sales is quite good, which any decent tools should handle quite easily. But the forecasting models are also capable of considering more complex patterns not visually obvious. In fact its not possible for humans to fathom when more than two variables affect the outcome. That is also one of reasons why simple models are preferred, to understand the why behind forecasts.

Modelling techniques like ARIMA have been around for decades, because they are easy to understand. Time series modelling do not need any predictor variables, the past values of the outcome variable themselves act as predictor variables. Usually each time series needs a tailored set of parameters to fit the ARIMA model. With improvements in R packages, they have become even more simpler. A simple auto.arima() will fit the series with near optimal parameters.

There are a couple of ways to evaluate model performance. One way is to evaluate the AIC parameter for different models on the same training data, and the other is to compare the out of sample prediction accuracy. The caveat with AIC and AICc is that, they can only be compared within the same class of models, i.e., ETS or ARIMA, etc., comparing them across different models will lead to erroneous conclusions.

The framework of making forecasts is provided by R, the challenge is to evaluate the best model for different combinations of input (from store, category, sub-category). Each combination needs 5 different models, over different lag periods(1-12). For example, for a single Store + Category, 5 x 12 subsets are trained. So, for a chain having 5 stores, 20 categories (or 25 sub-categories) a maximum of (5 x 20(or 25) x 5 x 12 = 6000) models need to be trained (the combination of category and sub-category is ignored). Thus manual fine tuning is not quite practical.

There are many approaches to forecasting. I include ARIMA, TBATS, Thetam, STL and ETS and an ensemble of these model weighted by the performance on out-of-sample accuracy. Getting back to RetaileR, firstly an aggregate of the dataset at the monthly level for each combination (category/sub-category + chain + store) is made (this creates a list of aggregated tables in R).

Then, the models are run on each of the individual aggregated tables (say aggregated sale of Vegetables in store RetaileR-helsinki, aggregated sale of medicines in Store RetaileR-Helsinki, and so on). Each table has about 12 times 4 (years), i.e., 48 datapoints, which is quite tiny. An R function takes this time series as input and outputs a trained model and its test accuracy for different lags. This function is then repeatedly called for all the aggregated tables. Finally for every category/sub-category the 1-12 month lag forecast accuracy is averaged and compiled into an excel report. If the user so desires, just the forecast and 90% or so confidence can be got. Or, he is free to choose among the best performing models, or simply a single model for all aggregated tables. There can be more customisations, like getting the forecasts for the top 10 categories, or for the categories which contribute about 90% of the sales and so on. Imagination is the limit.

Lets supposed RetaileR has a propriety software which has been forecasting their numbers. It is quite easy to compare the forecasts obtained through R and compare it against the tools’. This can then be automatically exported as an excel file for an in-depth understanding of the comparison. On a final note, even though R comes with a lot of algorithmic punch, other tools may be superior in terms of presenting those finding. But R is still the easiest, cheapest and the best bet to test feasibility quickly.

#### Arun Balakrishnan