###### Product Information

# Time Series Forecasting in SAP Analytics Cloud Smart Predict and Predictive Planning in Detail

Predictive features of SAP Analytics Cloud (SAC) are designed to be used by business analysts. This means that they are guided through the predictive workflows, and they don’t need to have predictive skills. The predictive outputs are shown in a convivial way to be easily interpreted and included into SAP Analytics Cloud stories or planning. You might have questions about our techniques? Is it a question of trust in the predictions proposed? The objective of this blog is to explain how Smart Predict, and consequently Predictive Planning, finds predictions. And why they are relevant!

In SAP Analytics Cloud, when you create a new Predictive Scenario, there are three choices.

Classification ranks the population relatively to an objective. It produces a score that a new event will happen. For example, who among my customers will react positively to my marketing campaign?

Regression is used to find relationship between variables describing events. For each new event, you get an estimation of the value of the target variable. For example, you predict house price by looking at similar houses.

Time Series are used to forecast the evolution of a measure in the future. For example, which quantity of products should be produced in advance?

This blog is dedicated to Time Series.

I explain the types of problems Time Series Forecasting addresses and what kind of data it is necessary to collect. Then, I’ll illustrate the technique used by Smart Predict through a specific use case.

# Which questions? Which data?

Time Series Forecasting is useful for estimating future values of a measure where you have a time dimension available to help you identify a trend. Before going into the details, let see what kind of data the time series forecasting of Smart Predict handles. Here are typical questions:

- How the revenue of my shop will evolve over the next month?
- What are the expected sells by product per regions for the next weeks?
- How the stock of my products will vary in my warehouse over the following weeks?
- How to predict the evolution of my cash flow during the next quarter?

If now the type of question is clearly defined, let’s check if the type of data you have is usable for Time Series. There are two distinct aspects:

- You must have recorded the values that your target variable had in the past and the corresponding dates. This couple (date, target value) is called the signal. It is this signal that will be analyzed by the Time Series Forecasting process of SAC Smart Predict.
- Values of other variables taken at the same dates (in the past and in the future) can be included. These explanatory variables are called “Candidate Influencers”. They are used by SAC Smart Predict to refine the analysis of the signal.

Here is some advice to correctly prepare your dataset.

Firstly, ask yourself how far into the future do I need to project? This is the horizon. It is the number of predictions you want to do in the future. This number depends directly on the size of your historical data. 5:1 is a good ratio to estimate the horizon and get predictions with relevant confidence intervals. This means that if you have 100 historical cases, you predict 20 values of your target variable in the future. Of course, the length of the horizon depends also on your use case and you can choose less than 20 values. But if you need more, it will be better to collect more historical cases.

*Fig 1: Signal and predictions on its evolution in the given horizon*

Secondly, you need to consider the scale of the predictions. If your historical data is captured every month or every week or every day or every hour or every minute or even every second, then the predictions will be produced in the same unit of time. It seems evident that if you record values every month, it is not meaningful to request predictions for the next minutes! The opposite situation may arrive: for technical reasons if data is recorded every minute by sensors, but the minute is not relevant for your use case; then you need a higher unit of time like hour.

Thirdly, you should consider the aggregation of data in the unit of time you need. For this, you must define an aggregation function. This function calculates one value for the hour from the 60 values measured for each of the 60 minutes of this hour. It can be the first value, the last value, the mid value or a calculated value (average for example or a more complex formula). An important point to keep in mind is the size of the aggregation because a large aggregation may hide information so that it could not be discovered. The consequence is to decrease the quality of the predictions. But an appropriate aggregation smooths the signal when there is a lot of noise. Now there is no secret, and you will have to test and experiment to choose the best aggregation function.

Fourthly, you should chronologically sort the historical dataset, and clean it so that each unit of time correspond to only one value of the target variable. Note that Smart Predict automatically sorts the data.

I cannot conclude this section without a word about candidate influencers I have mentioned above. They are very useful to increase the detection of the components of the signal. Very often, these variables have a meaning only in your business domain and it will be necessary to manipulate your data to get them. Here are examples of such influencers:

- Specific selling periods for a product
- Time limit discount
- Monthly closing day / Quarterly closing day
- First day of month / Last day of the month
- Rank Day of Week 1

During the analysis of at least two components of the signal (trends and cycles that will be explained below), there are constraints for candidate influencers which apply:

- The future values must be known (at least for the expected horizon).
- Candidate influencers with ordinal, continuous, and nominal types are used in the detection of trends.
- But only candidate influencers with ordinal, and continuous types are used in the detection of cycles.

# Use case : Optimize travel costs and expenses

We’ll follow a use case to illustrate this section, using a dataset with Smart Predict to show you how the signal is processed to propose forecasts. This use case is about the travel costs and expenses of a company that has spun out of control and negatively impacted the P&L analysis and financial performance of the company. The objective of the company is to analyze these costs and understand where they could be reduced but also to better forecast costs to avoid being over budget.

The data collected (see Fig 2) in the past are:

- The posting period of travel costs and expenses collected every month from 2013 to 2018. It will be our date variable.
- The travel costs and expenses for each posting period. This couple is our signal and the cost our target variable.
- The line of business (LOB) is also recorded because travel costs and expenses are not the same from one LOB to another.
- A series of influencers like Travel & Expense Budget, Software license sales targets per LOB per month or Number of existing headcounts and their associated budget.
- Finally, there are candidate influencers related to time, like Number of working in the month, Event during the month, Specific calendar events (summer holidays, Christmas) or specific discount per month.

*Fig 2: Dataset of the Travel costs and Expenses use case*

The graphical view of the signal for all board areas looks like Fig 3. But, members of LOB have different activities. This influences the number of voyages and consequently their costs. If travel and expenses could be distinguished and forecasted per LOB, the analysis and the previsions will be thinner from the budget point of view.

*Fig 3: Signal for dataset*

# Time Series Modeling Process

Hopefully, when a predictive scenario is created with SAC Smart Predict, there is an option (see Fig 4) which allows us to split the training dataset by the values of the selected variable.

*Fig 4: Segmentation of the dataset on the values of the LOB*

Concretely, what does this mean? In this dataset, there are nine LOB. SAC Smart Predict creates nine subsets of the dataset and generates nine forecasts. So, the predictions are specific to each LOB and are not influenced by the others.

As an example, here are the signals specific for the LOB “Cloud Services” (Fig 5) and for LOB “Sales & Marketing” (Fig 6).

*Fig 5: Signal for Cloud Services*

*Fig 6: Signal for Sales & Marketing*

Now, a little bit of theory; it’s necessary to understand how SAC Smart Predict generates the forecast for the travel costs and expenses dataset.

For each of the LOB, the signal is broken out into four components which are:

- The
**Trend**: This consist of finding out where your business is headed. In which direction it tends to go. Is it decreasing? Is it increasing? - The Periodicity patterns, which are Seasonality & Periods
**Cycles**. This means that they are reproduced regularly over time. - The
**Fluctuation**creates a model of the dependencies of the values at time “t” with previous values. - Finally, the
**Residuals**are what remains of the signal when Trends, Cycles and Fluctuations have been removed. Residuals are considered as “white noise”; this means that they are purely random effects.

At the end, SAC Smart Predict combines the models of each combination to find the best model.

This process is summarized in Fig 7.

*Fig 7: Smart Predict process to handle a time series forecasting signal*

Let see in more details each of these four steps of the time series process in SAC Smart Predict.

## Trend detection

The first step is to determine the best trend of the signal. The trend is the general orientation of the signal or its long-term evolution. The trend is presented as either linear or quadratic. To obtain the trend shown in Fig 8, SAC Smart Predict puts in competition eight trend models. Note that no choice is made at this step before the estimation of the other components of the signal.

*Fig 8: Linear trend of LOB Operations.*

These eight trend models are grouped in 2 groups of methods:

**Three stochastic methods**where there is the assumption that forecast at time “t” will depend on the past values of the signal (t-1, t-2, etc.)**Lag 1 (L1)**– the signal moved one step forward. This is the basic forecast where the predicted observation equals the latest signal observation.

Trend_{t}= Y_{t-1}**Lag 2 (L2)**– the signal moved two steps forward.

Trend_{t}= Y_{t-2}**Double Differencing**– Second order differencing. The difference between the last two observations is taken in account

Trend_{t}= Y_{t-1}+ (Y_{t-1}– Y_{t-2}) = 2Y_{t-1}– Y_{t-2}

**Five deterministic methods**where there is assumption that the forecast at time “t” is independent of any past values of the signal. The SAC Smart Predict regression algorithm is used for that but, it is based on five different inputs.**date**: A_{0}and A_{1}are estimated with Y_{t}as target variable and Time as input variable.

Trend_{t}= A_{0}+ A_{1}Time**date, date**: A^{2}, sqrt(date)_{0}, A_{1}, A_{2}and A_{3}are estimated with Y_{t}as target variable and Time, Time^{2}and Square(Time) as input variables.

Trend_{t}= A_{0}+ A_{1}Time + A_{2}Time^{2}+ A_{3}Sqrt(Time)**date, candidate influencer variables**: A_{0}, A_{1}, B_{1}, B_{2}, … are estimated with Y_{t}as target variable and Time, X_{1}, X_{2}, … as**candidate influencer**variables

Trend_{t}= A_{0}+ A_{1}Time + B_{1}X_{1}+ B_{2}X_{2}+ …**date, date**: is a combination of the two last inputs.^{2}, sqrt(date), candidate influencer variables

Trend_{t}= A_{0}+ A_{1}Time + A_{2}Time^{2}+ A_{3}Sqrt(Time) + B_{1}X_{1}+ B_{2}X_{2}+ …**candidate influencer variables**: X_{1}, X_{2}, … as candidate influencer variables

Trend_{t}= B_{1}X_{1}+ B_{2}X_{2}+ …

## Detection of Cycles

The second step consists in determining the best cycle of the signal. To obtain the cycle shown in Fig 9, SAC Smart Predict iterates to detect all possible cycles.

*Fig 9: Cycle of LOB HR*

There are two types of cycles:

**Periodicity**which describes natural events which reproduce themselves at a fixed interval of time called a period.**Seasonality**which shows the recurrence of the cyclic pattern as well as the time granularity that makes the cyclic pattern appear. Visit the online help to see the list of seasonal cycles that are tested and can be detected.

Cycles of both types are computed through an encoding of the signal. For periodicity, the encoding is based on a period length. With a period equals to 5, the encoding will be 0, 1, 2, 3 and 4 and the value will be the average signal observed on every 5^{th} step. Until 450 different periods are tested automatically for Smart Predict. The encoding for seasonality is based of calendar events.

Cycles are also evaluated on candidate influencers. For this, the encoding depends on the type of the variable.

- For nominal variables: no encoding done, thus no cycle detected.
- For ordinal and continuous variables: encoding done on the natural order

The training dataset is split into two subsets. The estimation dataset is used to detect cycles and the validation dataset is used to check accuracy of cycles. It is important to reduce the scope of cyclic search to minimize the computation time and particularly for periodicities. Thus, the maximum length of a period is by default equal to the minimum between 1/12 of the estimation dataset size and 450.

I emphasis here that it is necessary to have enough historical data to detect cycles and particularly cycles over long period or long seasonality.

At this step, all the encodings done are cycle candidates and it’s time to put them in competition to select one. To do this, SAC Smart Predict runs this iterative process:

- For each of the eight detected trends, the signal Y
_{t}is detrended to produced Y_{t}– Trend_{t} - For each candidate cycle Cycle
_{t}- Measures the link between the signal Y
_{t}– Trend_{t}and Cycle_{t} - If this improves the forecast (comparison of actual and forecasted value in the validation dataset) then analysis is repeated on Trend
_{t}+ Cycle_{t} - Else reject Cycle
_{t}

- Measures the link between the signal Y

The selection process stops when there is no significant cycle to add to the predictive model.

## Fluctuation detection

The third step consists in determining fluctuation of the signal. The fluctuation is what is left when the trend and the cycles have been extracted. To obtain the fluctuation shown in Fig 10, SAC Smart Predict creates an auto-regression that uses a window of past data to model the current residue.

*Fig 10: Fluctuation of LOB Cloud Services*

At this stage, the initial signal has been broken out and removed its trend and cycles: Signal – Trend – Cycles. An auto-regressive model is then computed on what’s left of the signal:

X_{t} = a_{0} X_{t-1 }+ a_{2} X_{t-2 }+ a_{3} X_{t-3} + … + a_{p} X_{t-p} + e …

Where p is called the order of the auto-regressive model. By default, this order is limited to 100.

At the end, when trend, cycles and fluctuation are removed from the original signal, the only points which persist are the residual which are considered as noise. Fig 11 shows such residuals.

*Fig 11: Residuals of LOB Cloud Services*

## Model selection and quality of model

The fourth and last step is the selection of the best model. During the previous three steps, the initial signal Y_{t} was broken out in trends, cycles, fluctuations and residuals:

Y_{t} = Trend_{t} + Cycles_{t} + Fluctuation_{t} + Residual

The remaining signal after removing the three components represents the residues. After trying several combinations of models, the final selected model is the one whose residues are the closest possible to white noise.

Now that the components of the signal have been determined, SAC Smart Predict mix the models of each combination to find the best model. To do that it is necessary to have a quality indicator and a validation process.

The historical data is split in two parts: 75% are reserved to study the signal and generate models as seen previously. The 25% which remains constitute the validation dataset and is used to measure the quality of the candidate models so that the best could be selected. The validation process compares the actual values of the measure with the values predicted by each model. A measure called Mean Absolute Error (MAE) is computed with this formula. It is the average of the absolute difference between the predictions done by a model and the actual values.

Now in the input parameter of a forecast, you specify a horizon. This is the distance in the future where SAC Smart Predict predicts values for you. For each model, SAC Smart Predict computes several individual MAE corresponding to the requested horizon and takes their average. It is the Horizon-Wide MAE

To select the best model, SAC Smart Predict is doing a combination of these two indicators:

- The performance measured by the Horizon-Wide MAE: The predictive model with the best Horizon-Wide MAE is selected.
- The complexity of the model: In the event of a tie, with a 5% tolerance, the simplest predictive model is the winner.

Note that the MAE and Horizon-Wide MAE are internal measures and are not surfaced in SAC Smart Predict so far. The quality indicator surfaced in SAC Smart Predict is based on another metric called the Horizon Wide MAPE (Mean Absolute Percentage Error) because the MAPE in a kind of standard in the market.

To get it, the individual MAPE is computed by this formula.

It measures the accuracy of the model’s forecasts and indicates how much the forecast differ from the real signal value.

Now in the input parameter of a forecast, you specify a horizon. This is the distance in the future where SAC Smart Predict predicts values for you. For each model, SAC Smart Predict computes several individual MAPE corresponding to the requested horizon and takes their average. It is the Horizon-Wide MAPE

How to interpret the Horizon-Wide MAPE? Zero indicates a perfect model. Values above one are subject of discussion and you need to compare the model and its forecasts with your business knowledge to decide about its accuracy. You can get detailed explanations on MAPE in this blog.

# Using the forecasting model

Now that we know how SAC Smart Predict builds a forecasting model, we can run it on the travel costs and expenses dataset with these input parameters (Fig 12).

*Fig 12: Input parameters*

You’ll notice that:

- The forecasting is segmented on the 9 values of the LOB, so that 9 predictive models will be generated.
- The horizon for all the forecasts is 12 months. It is month because the granularity of the training dataset is the month.

Once the training process is complete, an overview allows to see the quality of the models per board areas as shown in Fig 13.

*Fig 13: Horizon-Wide MAPE per LOB.*

Immediately you see that quality of the forecast model for LOB Sales & Marketing is the best. This means that the predictions will be better and with a low error rate.

You get the details for this segment when you click on it as shown in Fig 14.

*Fig 14: Forecast for segment Sales & Marketing*

At the top, you recognize in green the signal for this board area. In blue, it is the 12 forecasted values with their error min and max.

A table of the forecasted values is at the bottom.

Finally, if you click on the apply button, the forecasted values are output into a dataset as shown in Fig 15.

*Fig 15: Forecasted values applied and exported into a dataset*

Up to you to include this dataset inside your BI story or your planning.

# Conclusion

It is the end of this blog, and I hope you have a better understanding of the SAC Smart Predict process to provide relevant forecasts. I hope also these explanations increase your confidence in the product.

You can continue with the blog Candidate Influencers in SAP Analytic s Cloud Smart Predict to know how to improve a time series model.

Resources to learn more about Smart Predict.

- SAP Analytics Cloud – Learning
- Hands-On Tutorial SAP Smart Predict, Product Forecast
- Understand accuracy measure of time series forecasting models
- SAP Analytics Cloud – Smart Discovery
- SAC Planning & Smart Discovery
- SAC Planning & Smart Predict
- Getting Started with Smart Predict: Concepts of Predictive Modeling

Since the first publication of this blog, there were improvements in the Time Series Forecasting in SAC Smart Predict. Here are three links to such new features.

- Exponential Smoothing inside SAP Analytics Cloud time series forecasting scenarios
- Understand accuracy measure of time series forecasting models
- Adapting Predictive Planning to the New Normal of Planning

Finally, if you enjoyed this post, I’d be very grateful if you’d help it spread, comment and like. Thank you!

Hi Thierry, thanks for share this post.

The time series predictive forecasting feature in charts (automatic forecast: https://www.sapanalytics.cloud/resources-predictive-forecasting/) is based on the same technique than the time series forecasting made with smart predict? I mean are both made on top of the same techniques and process, and therefore deliver the same results?

Thanks!

Hi,

Thanks for reading the blog, I hope it provides you useful information. To answer to your question, yes both are using the same technques and process. Now the results may differ if the settings are not the same.

Best regards.

Hi Thierry,

Very detailed and informative blog, thanks for explaining the scenario in detail.

Please could you share the csv file which you have used in this example, so we can also replicate the scenario to understand the algorithms better.

Thanks,

Subhadeep

Hi Thierry,

thanks for your great blog!

I want to use predictive outputs from Smart Predict in a SAC planning data model.

As I could see here https://help.sap.com/doc/00f68c2e08b941f081002fd3691d86a7/2020.2/en-US/13356a1eab264511b3159f7edc2f720a.html

it´s always necessary to create a new planning model. But this process can´t be automated and doesn´t allow reusability of further data actions of the planning model.

I expect integration between Smart Predict and SAC planning models could be great new feature for the future.

As long as this is not available I have to use the integrated function to create a predictive time series forecast (manually) in a table of a story.

https://help.sap.com/doc/00f68c2e08b941f081002fd3691d86a7/2020.2/en-US/eb08d57f2d964d0b9b75234e481b1ddf.html

3 algorithms are selectable here:

- Automatic Forecast

- Linear Regression

- Triple Exponential Smoothing

Unfortunately I couldn´t find any futher information on what those algorithms are doing exactly.

Do you know where I can find this?

Kind regards,

Thomas

Hello Thomas,

Thanks for your appreciation of this blog.

Integration of Smart Predict and Planning will be very useful for planner and we think to it very seriously.

But for today you have to use the workarrond you mention.

Regarding the 3 algorithms, you will find other information here: https://help.sap.com/doc/00f68c2e08b941f081002fd3691d86a7/2020.2/en-US/8f9665dcf53f4f3f90e920995cdd5f05.html

But be careful, if the Automatic Forecast is similar to the forecast of Smart Predict, here you could only define the number of forecasts you need.

I hope this answer to you question.

Best regarDS

Thierry

Thank you very much for your clear answer!

Best regards,

Thomas

Hello Thomas, as mentioned by Thierry, we also strongly believe that bringing Smart Predict and SAC/ Planning together is a strategic topic.

As part of our product plan, we currently plan to bring this closer integration to life in 2020, allowing Smart Predict to use planning models as a data source and allowing Smart Predict to write back time series forecasts onto the planning models.

https://www.sapanalytics.cloud/product_updates/smart-predict-q2/

https://www.sapanalytics.cloud/product_updates/smart-predict-future/

We think that this planned integration will open a lot of possibilities for our customers and our partners.

Kind regards,

Antoine

Related requests on customer influence portal

https://influence.sap.com/sap/ino/#/idea/234297

https://influence.sap.com/sap/ino/#/idea/234298

Thanks for the blog!

I was doing a presentation today about Predictive in SAC. A participant asked about the statistical methods used in Smart Discovery and Predictive Scenario. I have searched on the web, and found no explicit documentation, although there is lots about, how to use it, implement, etc.

Do you know of any statistical documentation? I think it is very important to be able to inform participants about this, if they are to trust the statistical methods used. They are used to that from other statistics packages (SAS, R, SPSS and the like).

I hope you can help!

Best regards

Kenneth Wolstrup

Innologic A/S, Denmark

Hi Kenneth, thanks very much for your comment.

This nice blog from Thierry is a first in a series covering the "behind the scenes" aspects of Smart Features. We do have plans to do more of them in the future and cover all our major Smart Features.

Kind regards,

Antoine

Thierry BRUNET Priti Mulchandani Robert McGrath Richard Mooney

Classification blog: https://blogs.sap.com/2020/06/19/classification-in-sap-analytics-cloud-in-detail/

Regression blog: https://blogs.sap.com/2020/08/13/regression-in-sap-analytics-cloud-in-detail/

"Immediately you see that quality of the forecast model for LOB Operations is the best."

Is this a typo? The line of business with the lowest Horizon-Wide MAPE is Sales & Marketing.

Thanks!

Best,

Ethan

Typo indeed - thanks for the catch. Best, Antoine

Thanks for very informative blog.

I have few question regarding long term prediction. I have yearly sales data and want to forecast next years sales. I have few questions while interpreting output:

How to determine the influnce of a variable ? How it is calculated in automated?

Second question, how automated takes time as input. Why its taking square root time?

Hello Saba,

Thanks for your appreciation of this blog.

Regarding your question about the influencers, I redirect you to blog Candidate Influencers in SAP Analytics Cloud Smart Predict.

Can you precise your second question? The time is used to sort data point of the time series in the chronological order. It also gives the granularity of the data points: I mean in hours or days or months.

Best regards

Thierry

In the article above under Five deterministic methods - i am unable to understand how its taking ( date, date

^{2}, sqrt(date).For example in my case, I have yearly sales data 01.01.1993 to 01.01.2019 with many influencing factor but model selected by automated is Polynomial in year.

How this year date is calculated or estimated? How date figure is normalized and weighted?

How Can I view formula of trends with constant that is formed?

It is deterministic methods that are in competition to find the best trend. You don't have to change your data. This process is completely automated. Don't forget that we are in the context of a SAC user. You don't have access to the formula. The information provided about the components of the time series is shown in the Forecast and Signal Analysis panes of Smart Predict.

Best regards

Thierry

To complete on Thierry's previous comment, those deterministic trends would appear simply in the product as linear trend or quadratic trend.

Best

Antoine

Hi Thierry,

Thanks for the blog.

Could you please share the csv file used in the blog.

Thanks,

K Srinivas.

Hi Srinivas

File name is T&E Cost Prediction Extra - LOB.csv and it is available here: https://github.com/antoinechabert/predictive.

Best regards

Thierry

Hi Thierry,

Thanks for the file.

Regards,

K Srinivas.

Hi, thanks for this wounderful blog,

It worked on a sample dataset of Ozone Depletion, but when i give a huge finacial data I often get error, when i changed the data, I get warnings. At times cant understand what data should be given to a predictive model.

Error

Warning

It would be great if you can help me on how to choose a data set for Time Series

Hi,

This means there is still problems in your dataset. Preparing dataset is an important step because it directly impact the quality of the predictive model. What I can only suggest is to check that the conditions mentioned in the error message are fully satisfied and check also the date format. You can refer to the restriction section of the online help.

Best regards

Thierry

thanks Thierry

Hello Thierry BRUNET,

thank you very much for this great blog! I am trying to leverage the time series forecasting in SAC using the Smart Predict feature for a couple of months already and I found one important thing missing. When I calculate the model using a dataset I am able to save both the predictions and the confidence intervals back to the dataset and then use it in a Story. Unfortunately the same is not currently possible for planning models which is a pity. Do you have any information when it will be possible to save the confidence intervals into the planning model?

Thank you very much!

Adam Nekola

Hello Adam,

Thanks for your appreciation of this blog and I'm happy if it was useful for you.

The answer to your question is difficult because we do not own the planning model which contains only values. There is no space for confidence interval. This is why it is not written back into the planning model.

If such a feature is useful, can you email me your business case and why it is so important.

Best regards

Thierry

Hi Adam Nekola nice to meet you. Please note SAC customers & partners can raise such enhancement requests via https://influence.sap.com/sap/ino/#/campaign/884.

When checking at the moment we do not have such a request, while of course it would be meaningful.

Best regards Antoine

Hello Antoine CHABERT , nice to meet you too. I created the request. Thank you for the info.

Kind regards,

Adam Nekola

Thank you, appreciated!

Best

Antoine