As a Chief Financial Officer, I am always challenged with balancing short and long-term decisions. Understanding the short-term outlook enables me to properly accelerate or hold back long-term investments without compromising near-term results. Too many executives guesstimate the short-term trend based on gut feel or experience, particularly when there is a very simple time-series method – appropriately called Trend Analysis – to give us a statistical view of the short-term. Here’s how Minitab can help you make confident short-term forecasts in minutes (or less!).
Trend Analysis: Your Short-Term Go-To Method for Forecasting
To be clear, there are many powerful statistical methods that can be used to forecast. Trend Analysis is favored in the short-term due to its simplicity and the ability to set up and run a model quickly. Other methods like ARIMA or other machine learning methods are quite powerful but may take longer to set up or run.
See the Trend and to Identify it Before Forecasting
As simple as Trend Analysis is, like most statistical methods, it requires some thought. In this case, the shape or slope of the trend is going to be critical to your analysis. Plotting out your data should give you a visual cue as to which Trend Analysis model to use. However, at times, shapes can look similar, so having a deeper understanding of the typical scenarios described by these models will help you decide. If you’re still not confident, you can run each model on your data set, and measure the fit of the model using accuracy measures like MAPE, MAD and MSD. Measuring the fit of every model may be diligent, but it can also be time consuming.
To visualize your trend, use Minitab Statistical Software and go to our popular Graph Builder and select time series plot or go to the Stat Menu/Time Series/Time Series Plot and graph your data. Once you have your graph, your model should likely resemble one of the most common model types: Linear, Quadratic, Exponential Growth and S-Curve/Pearl-Reed Logistic.
Below are sample time series plots of the types of trends that are associated with the different model types.
Understanding Linear Models: Linear models are straight lines (for those of you mathematically inclined, they are represented by the equation of Y = a + bX). In practical terms, linear models represent trends with constant or fixed rates. In manufacturing, this could be a simple rate of production (i.e. how much a machine produces per hour), energy consumption rate or costs (assuming there’s no cost savings at scale). In terms of forecasting sales, the linear model is used when there is an expected similar growth rate.
Quadratic Models: A Smile or a Frown?
Unlike linear models, quadratic models reflect a rate of change that is not constant. Quadratic models can reflect an accelerating or decelerating trend, and as a result can be confused with an exponential model (which is exactly why it’s so important to understand your data too!). A common quadratic manufacturing example might be modeling output as a function of labor. At some point adding too many workers or increasing their hours leads to diminishing returns. Another common example is modeling price and profits. While increasing prices increase profits, over time, a higher price could stymie demand, thereby hurting demand and slowing down incremental profit growth.
Exponential Growth: Whether you’re up, up and away or experiencing exponential decay, this model means that the rate of change is not only accelerating or decelerating (like quadratic models), but that the rate is changing faster than quadratic models. This type of model can be used across varying disciplines. In finance, it may be used to model out compounding interest, whereas in science it could model out the spread of a pandemic or a spread of bacteria in an experiment. Exponential growth may also be seen in a new product or drug launch, as adoption accelerates with awareness and acceptance.
Deciphering quadratic from exponential growth is probably the trickiest, which is why understanding the situation around the data is so critical. As I said earlier, when in doubt, compare the quadratic and exponential models by measuring the fit using accuracy measures like MAPE, MAD and MSD.
S-Curve/Pearl-Reed Logistic: The S-curve, often referred to as the Pearl-Reed logistic curve, was first formalized in 1920 by Raymond Pearl and Lowell J. Reed, two American biologists. They introduced this logistic function to describe population growth under constraints like limited resources. Basically, as resources become scarcer, population growth slows and levels off. Outside of biology, the S-curve is typically associated with adoption of products or technology. It can also represent training (once trained, skills level off) or even customer loyalty. Overall, it reflects a scenario that has room to grow, but ultimately will hit saturation and for forecasting purposes, is typically used when the forecaster recognizes that saturation is beginning to occur.
Now You’re Ready to Forecast! A Quick Minitab Tutorial
Once you’ve identified the model type, forecasting is a cinch. Using the same data that you used to plot your trend go to Stat/Time Series/Trend Analysis. A dialogue box will come up that will ask what Variable you want to forecast
Once you select your variable, simply select your model type and check generate forecasts. In this example, I want to generate 5 more data points, so I typed “5” in the number of forecasts.
Read Your Results…
Your results will now provide you with an equation for your forecast, accuracy measures, forecasted data points and a graph. Voila! Forecast mission achieved.
Fitted Trend Equation
|
Yt = (10^4) / (10.0320 + 4601.91×(0.663545^t)) |
Accuracy Measures
|
MAPE |
1.9285 |
|
MAD |
2.5353 |
|
MSD |
11.4483 |
Forecasts
|
Period |
Forecast |
|
31 |
995.441 |
|
32 |
995.902 |
|
33 |
996.209 |
|
34 |
996.412 |
|
35 |
996.547 |
…And Let Minitab AI Give You the Confidence to Explain Them
Many of us who are responsible for forecasting aren’t necessarily statistics whizzes. While you’ve now mastered the art of short-term forecasting, providing additional context around it will give you more confidence in your predictions. Using Minitab AI to generate a natural language summary, you can quickly understand all the great information Minitab provides. In our example, the AI generated content explains that the data set is large enough to make an accurate prediction and that the model produced is reliable.
Minitab AI
Summary of Statistical Analysis
Purpose
The analysis aims to evaluate the trend of S_Curve_Values over a specified time period using an S-Curve Trend Model. It provides insights into the future behavior of the data based on the fitted trend equation.
Key Findings
- Fitted Trend Equation: The model predicts S_Curve_Values using the equation ( Yt = \frac{10^4}{10.0320 + 4601.91 \times (0.663545^t)} ), indicating a decreasing trend as time progresses.
- Forecasted Values: The forecasts for the next five periods (31 to 35) show values gradually increasing from 995.441 to 996.547, suggesting a stabilization in the S_Curve_Values.
- Accuracy Measures: The model demonstrates good accuracy with a Mean Absolute Percentage Error (MAPE) of 1.9285, Mean Absolute Deviation (MAD) of 2.5353, and Mean Squared Deviation (MSD) of 11.4483, indicating reliable predictions.
- Data Completeness: The analysis utilized a complete dataset with no missing values (NMissing = 0), ensuring the robustness of the trend analysis.
- Length of Data: The analysis is based on a dataset of 30 time periods, providing a solid foundation for the trend evaluation.
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