Many industries collect and maintain data. You might think of the shipping industry where large SQL databases are kept to log product inventory and track the number of items shipped monthly or, perhaps weekly. Warehouses of products, such as Walmart, Best Buy, and the multitude of large malls, also contain relational databases of their product transactions. Perhaps you have a favorite restaurant down the street that tracks weekly customer volume.
How might these businesses use this data to improve their overall system?
Data Frames & Time Series
…and the Data Frame
- They pay out thousands to millions in licensing costs for commercial software.
- They don’t have the analytical ability to leverage this type of information to improve their business processes (i.e. they don’t have the software or people available to use these methods)
PendulumRock Forecasting Solution
- Our service is offered at a fraction of the cost of purchasing commercial software
- We already have the system developed
- The solution is offered by pay per forecast (per instrument)
Therefore, the company has no necessity to purchase expensive software, thus saving time and money. Ok, so you like the sound of what we have, but you are thinking you can build your own model. Well, therein lies the problem: there are MANY models that fit data patterns with various behaviors. Depending on the behavioral nature of the data in question, one model will forecast points into the future more accurately than other models. Getting an accurate model heavily depends on selecting one that correctly illuminates components inherent in the data. Taking these components into account, forecasts may be based on:
- Average of all values
- Simply the previous value
- With option to stray up or down from previous value
- Weighted average of all previous values & levels (no trend or seasonality; only level)
- With more emphasis placed on recent time periods (days, weeks, months, etc.)
- Trend, Cycle, & Seasonality
- Can be determined by smoothing techniques (moving averages, locally weighted regression)
- Trends may be constant or may follow a growth/decay rate
- Seasonality may follow constant fluctuations, changing fluctuations, or increase/decrease in magnitude with each new turn of season
- Differencing a series that is non-stationary
- Subtracting most recent observation from every observation
- Weighted moving average of error components from recent observations
- Autoregressive behavior – the dependency of future values on most recent observations
- Some combination of all of the above
It is very hard to determine the components inherent in a time series without graphical depictions, and these depictions take time to produce. Added to this, building an analysis for every model type on the same data and then comparing accuracies is extremely time-consuming and unproductive. That is why we have automated the model-building process which expediently fits any given numerical time series to 17 of the most commonly used forecasting models used in analytics. The tool then assesses the forecasting accuracy of every model (based on mean average percent error, or MAPE), and chooses the model with the least error. Naturally, this will be the model that best exemplifies the components inherent in the data (i.e. trend, seasonality, cyclicality, autocorrelation). Ok, so you understand, are tired of the discussion, and are ready to see our solution in action! Let’s walk through an example.
Airline Passenger Data
- The number of air passengers trends upward over time (i.e. there is a level trending up).
- In January and February of every year, the number of passengers is low, then there are 1-2 short peaks in the spring, followed by a large peak in July & August. From there, the number of passenger drops back down into Autumn-season lows (October & November). Hence, there is a seasonal pattern in this data, and we might expect this as more people will be travelling during the spring break & summer vacation months and working throughout the winter months.
- The magnitude of the seasonal pattern grows at an increasing rate every year.
Okay, so let’s break these patterns down individually so that we may better quantify them independent of each other. Taking a look at the figure below, we see 4 panels of plots from top to bottom:
- Original graph of number of passengers on the y-axis plotted against time on the x-axis
- Seasonal component on the y-axis plotted against time on the x-axis
- Trend component on the y-axis plotted against time on the x-axis
- Noise left over (after extracting seasonal & trend components) plotted against time
PendulumRock Demo & Analysis on Airline Passenger Data
1) Microsoft Excel Data Set (.csv format) of Forecasts
2) Microsoft Word Table of Forecasts
3) Microsoft Word Analytical Report (discussed below)
- Additive trend
- Multiplicative seasonality
The forecasts for 10 months into the future are revealed by the blue line. The shaded areas around the blue line represent 80% & 95% confidence intervals. So, you can see that the forecasts fit the pattern rather well. They are trending upward additively and show a seasonality with higher magnitude fluctuations from the previous seasons.
1) Microsoft Excel Data (.csv format) Set of Forecasts (with all instruments)
2) Microsoft Word Table of Forecasts (with all instruments)
3) Microsoft Word Analytical Report (analyses for all instruments)
But, we will discuss forecasting multiple instruments another day.
For now, just know that we are offering a free trial for any start-up or larger business. Just get in touch with us, and we will discuss what company data you would like to forecast. We respect the data integrity of all clients and will not share any data unless permitted (can be settled in a contract). If the solution helps your company save money and/or catch profit, then we will discuss payment options depending on the number of instruments you want forecasted (pay per instrument). We will also need you to fill out a questionnaire to determine the nature of your data (file format, how frequently data is recorded, etc.), the type of forecasts you want (daily, weekly, monthly, etc.), and the horizon you want (5 weeks, 4 days, 10 quarters, etc. into future).
So, contact us and let’s see how we can improve your business!
Josh Callaway, editor PendulumRock Forecasting Solution