“Prediction could be very difficult, especially if it’s in regards to the future” — Yogi Berra , NY Yankees

In this text, we’ll explore the rationale and execution of constructing a predictive time series model for annual revenue. We’ll delve into various statistical obstacles that arise, explore different model approaches to deal with these hurdles, cover the strategy of scaling the models, and touch upon the importance of monitoring them.

: Intro + Model Selection: What are we trying to resolve, what are the challenges and what models may help us solve this problem?

: Model Application: Observing the info , applying the chosen models on our data , deploying the models and scaling.

: Monitoring: Drifting, Domain shifts and model performance using Streamlit

Imagine coming to an investor and being asked what the forecast of the corporate’s revenue is for the remaining of the 12 months, and now calculate per app … after which per platform (iOS , Android , Web) … and revenue type / user group segment. Imagine that the corporate that you just work at is growing at a “non-linear” / rapid and non consistent pace. Apps are released and updated occasionally , recent and exciting features are integrated to leading apps , and up and coming viral trends end in irregular behavior on the user’s side.

Now imagine at the subsequent leadership meeting with the finance team , we want to determine whether we will afford to allocate more of our budget towards marketing, additional hiring, wellness , and resources for development. This is extremely depending on whether the forecast for the remaining of the 12 months is above or below the initial expectation. We also don’t need to find yourself with a budget deficit which can end in cuts of differing types.

Predicting & understanding our income is crucial for the functionality and future planning of an organization , because it sets structure and stability to an organization’s money flow.

So what’s Lightricks’ business model ? A user can download any of the various apps that lightricks offers resembling Facetune , Videoleap or Photoleap. While the apps contain a big selection of features available totally free, some premium features can be found only to subscribers.

A user can subscribe at any time, most frequently a monthly subscription or an annual plan.

Along with the subscription based model, Lightricks offers other services resembling individual assets (Example: AI Scenes) which pertain to a one time payment by the user , an promoting platform powered by creators and more. On this model we’ll deal with the subscription based revenues.

To completely understand the revenue flow of the corporate, there are several granularities that should be checked out. Each granularity has its own purpose financially and strategically and due to this fact all are essential.

The primary level is the day by day revenue inside a forecast window of 1 month. The second level is a weekly pooled revenue with a forecast of 1 quarter ahead. The ultimate level, and the one we’ll discuss here, is monthly revenue on a yearly forecast.

As a member of the Data Science team , I took this challenge upon myself to predict the continuing revenues on a monthly basis, looking forward 1 12 months ahead.

Lightricks, which although is already 10 years old, has many challenges by way of its time series of revenues. Some are challenges that each time series experiences (e.g. overfitting , capturing seasonal effects and adapting to trends) , and a few are more particular to fast paced growing firms.

Lets dive into a couple of of those challenges:

• : Lightricks creates fast paced and responsive products. This ends in the indisputable fact that what might need happened 4 years ago doesn’t at all times reflect and correlate to what is going on today. The corporate adapts quickly to external and internal changes. Since we’re a monthly resolution, this ends in near 12×4 = 48 observations. This can be a classic example of “small data”. How can we create robust significant predictions based on a small set of coaching? Note: as stated before, moving to a weekly or day by day resolution generates an excessive amount of noise in a yearly forecast , and will not be traditional in most models because of the cascading effect of the error.
• : Our marketing team allocates a selected budget for performance marketing per thirty days, which varies, and has a direct effect on the time series of expected recent users. (Which in fact has a direct effect on recent subscriptions and renewals, and by that an effect on recent and future revenues). We’d like to know learn how to leverage it as a feature.
• : Viral trends can occur and affect installs and revenues for a day/weekend and even every week. Sometimes they set a whole recent baseline for the revenue stream. These trends normally end in users using the apps for an abnormal period of time for brief periods, with an exponential increase momentarily , which can tamper with the worldwide trends of the time series. We would like our models to take these into consideration but not be too sensitive toward them.
• : Obviously we wish to remain so far as possible from an over-fitted model , while not generalizing the model an excessive amount of.

An example of a non linear paced growth could be the next: We will see here that for over a 12 months the revenue was quite regular and altered pace to have an exponential growth!

: These are artificial numbers to exhibit the non-linear growth pace.

Generally speaking, by way of Lightricks’ revenue time series, the granularity to predict the yearly revenue was optimal by way of minimization of error without a “macro” level.

This is hard. There are two approaches to this problem. Top->Bottom and Bottom -> Up.

Our time series aren’t continuous. As an organization, we be sure that to separate cohorts from the present budget 12 months and the previous years, which ends up in a discontinuity between the present 12 months’s revenue flow and the backlogs flow.

This can be a huge challenge and makes the whole task much harder to forecast. One technique to bypass the problem is by a better granularity. If we will predict the overall revenue per a time series, and in parallel predict the time series of the proportions that the overall revenue splits into the various revenue types, we may not have to predict the actual time series of every revenue type and may skip the non-continuous time series. One assumption here is that the proportions have a certain pattern that we will detect. This method is excellent when jumping from EOY to the beginning of the subsequent 12 months. (Dec -> Jan)

Below is an indication of the breakdown in a top-bottom approach using the proportions to “decompose” the overall revenue to revenue types.

Lets have a look at the primary graph. Here we will see an indication of total revenue time series until a given date and the predictions going forward. On this case we’re leveraging the info from 2023 until mid 2025 to predict until the tip of the 12 months.

Next, let’s have a look at an example of proportions of three revenue types , where the sum of the three proportions sum as much as 1 , and which represent the proportion from the overall revenue that comes from that revenue type. Here too we predict the continuing proportions per revenue type.

Last, we apply a multiplication between the anticipated revenue of the overall revenue and the anticipated proportions to estimate the revenue time series per revenue type.

This manner, we don’t need to really predict the continuing time series per revenue type, but only the actual proportions.

One other approach is each user individually. One problem is that if we have a look at the granularity of a user, we may aggregate errors which sum as much as a bigger error. One other issue is lack of information for brand spanking new users. Ideally, predicting LTV based on the user behavior would have solved the issue, though we’d need to do that on users that haven’t installed the app yet. This ends in predicting what number of users will install the app every month and rolling the prediction from there. That is an approach that will likely be examined, nevertheless, takes more time to check in a world of fast delivery.

After assessing the errors per each method, we decided that diving a bit deeper than the very best level is perfect — constructing a model per app + platform + revenue type. The tradeoff between non continuous time series and tailor made modeling is worth it.

One thing price noting here is that we now have a small set of information which could be pretty chaotic, especially when forecasting long run series (as much as 12 months ahead). This ends in many limitations throughout the modeling process, resembling degrees of freedom, lack of depth for seasonal effects in some cases etc.

We treat every combination of app-revenue type in a different way, because the behavior is different. The apps differ by the users, prices, etc .Due to this fact we want to treat every time series and revenue flow in a different way. Several varieties of models were tested , specifically time series and regression based models. Essentially the most robust model by way of adaptation to alter (historically through cross validation tests) was the SARIMAX.

• SARIMAX — Seasonal ARIMA with Exogenous Variables,.

ARIMA, which stands for Auto Regressive Integrated Moving Average, is a widely used forecasting method for univariate time series data. ARIMA models take note of three features:

• AR (Autoregression): This component refers back to the use of past values within the regression equation for the series Y. The autoregressive aspect of the model is specified by p within the ARIMA model. As an example, if p is 1, meaning the present value relies on the immediately preceding value. If p is 2, the present value relies on the 2 preceding values, and so forth.
• I (Integrated): The integrated component represents the differencing of raw observations to permit for the time series to grow to be stationary. Time series are stationary in the event that they wouldn’t have trend or seasonal effects and the spread over time is constant. Differencing involves subtracting the previous statement from the present statement. The order of differencing is represented by d within the ARIMA model.
• MA (Moving Average): The moving average component represents the dependency between an statement and a residual error from a moving average model applied to lagged observations. The order of the moving average component is denoted by q.

ARIMA decomposes time series into trends + seasonalities + residuals and makes it easier to treat and model noise that could be characterised as a trend or a seasonal effect.

Once we’re capable of break the time series down, we will model the residuals (lower block) much easier.

Along with these core fundamentals of the model, SARIMAX embeds 2 additional elements.

• “S” refers back to the incorporation of seasonal patterns within the model. Seasonality is a characteristic of many time series data where patterns or fluctuations repeat at regular intervals. The seasonal component in SARIMAX captures these recurring patterns and helps improve the accuracy of forecasting by considering the influence of past observations throughout the same seasonal cycle.
• “X” refers to exogenous variables. Exogenous variables are external aspects that may influence the time series being analyzed. These variables aren’t a part of the time series itself but are regarded as additional inputs to the model. By incorporating exogenous variables, SARIMAX allows for the modeling of the impact of those external aspects on the time series.

Due to this fact excluding the exogenous variables because of complexity , we will represent the SARIMAX as below:

Other models price noting are:

• Prophet ( Meta ) — Time series forecasting modeling whose benefits are mostly lay under the methods of handling seasonality and outliers, in addition to its very user friendly and interpretable outputs. This model performed just in addition to ARIMA in our case.
• Neural Prophet — NeuralProphet, an upgrade to Meta’s Prophet model, incorporates elements of neural networks into the time series forecasting model — specifically throughout the covariates of the model, offering potentially more powerful and versatile forecasting capabilities than traditional ARIMA. The model doesn’t fit here because it requires a bit more data to perform in a sturdy manner. The models are inclined to overfit on sets smaller than 100 observations ( rule of thumb)

Until here we now have explained the issue, approaches and model strategy. In the subsequent blog post we’ll dive into the applying of the model, features and deployment.

Stay tuned for Part 2!