Today we are starting a new case study example series on YOU CANalytics involving forecasting and time series analysis. In this case study example, we will learn about time series analysis for a manufacturing operation. Time series analysis and modeling have many business and social applications. It is extensively used to forecast company sales, product demand, stock market trends, agricultural production etc. Before we learn more about forecasting let’s evaluate our own lives on a time scale:
Life is a Sine Wave
I learnt a valuable lesson in life when I started my doctoral research in physics & nano-technology. I always loved physics, but during my doctoral studies, I was not enjoying the aspect of spending all my time in an isolated lab performing one experiment after another. Doing laboratory research could be extremely lonely. Additionally, I always enjoyed solving more applied and practical problems which I believed was missing in my research work. After getting frustrated for some time I decided to take some career advise from a trusted physicist friend. Before you read further, I must warn you that physicists as a community are usually mathematical, and occasionally philosophical. Physicists prefer to create a simple mathematical model about a complicated situation. They slowly add complexity to this simple model to make it fit with reality. The following is the key point I discovered during that conversation with my friend.
A simple model for life is a sine wave – where we go through ups and downs of moods and circumstances. Like a sine wave, we don’t spend much of our time either on the peaks or the troughs but most of our time is spent climbing up or sliding down. Now keeping these moods and circumstances cycle in mind, a perfect choice of career is where one could enjoy both climbs and slides – as the up and down cycle is inevitable in life.
Keeping the above in mind I prepared a list of keywords that I associated with a job that I can truly love to absorb the up and down cycle of life. The following is my list of keywords:
|Working with people on smart solutions||Scientific investigation||Learning every day|
|Seeing the fruits of my efforts reasonably fast||Producing quantifiable business benefits||Knowledge sharing|
This prompted me to change my career from laboratory research to data science and business consulting. I am lucky that my career in data science and business analytics for over a decade has allowed me to check mark all these keywords.
|Your work is going to fill a large part of your life, and the only way to be truly satisfied is to do what you believe is great work. And the only way to do great work is to love what you do. If you haven’t found it yet, keep looking. Don’t settle. As with all matters of the heart, you’ll know when you find it. And, like any great relationship, it just gets better and better as the year’s roll on. So keep looking until you find it. Don’t settle. – Steve Jobs|
Interference of Other waves
Now in the true tradition of physics, let me add some complexity to the simple sine wave model for life. We live in a society and interact with many people. Everyone around us has a different shape to their lives’ sine waves. The interference of different regular and predictable sine waves can produce patterns that are highly irregular and could at times be close to randomness.
This is what is displayed in the adjacent chart where the product of four harmonic sine waves is an irregular shape at the bottom. Eventually, our actual lives’ function looks more like an irregular pattern produced through the interference of several sine waves.
|On some level the above is the fundamental principle behind Fourier series and Fourier transforms; most engineering and physics students will get a cold chill of fear at the mention of Fourier series. However, the basic idea is simple that the linear combination of sine and cosine functions (similar to our lives’ sine waves) can produce any complicated patterns including the irregular function we observed and much more complicated Fractals. I find it absolutely wonderful that a combination of harmonic motions can produce absolutely irregular patterns!|
Time Series Analysis – Decomposition
Now, let me try to create a connection between what we discussed above with time series analysis and forecasting. The fundamental idea for time series analysis is to decompose the original time series (sales, stock market trends, etc.) into several independent components. Typically, business time series are divided into the following four components:
- Trend – overall direction of the series i.e. upwards, downwards etc.
- Seasonality – monthly or quarterly patterns
- Cycle – long-term business cycles
- Irregular remainder – random noise left after extraction of all the components
Interference of these components produces the final series.
Now the question is: why bother decomposing the original / actual time series into components? The answer: It is much easier to forecast the individual regular patterns produced through decomposition of time series than the actual series. This is similar to reproduction and forecasting the individual sine waves (A, B, C, and D) instead of the final irregular pattern produced through the product of these four sine waves.
Time Series Analysis – Manufacturing Case Study Example
PowerHorse, a tractor and farm equipment manufacturing company, was established a few years after World War II. The company has shown a consistent growth in its revenue from tractor sales since its inception. However, over the years the company has struggled to keep it’s inventory and production cost down because of variability in sales and tractor demand. The management at PowerHorse is under enormous pressure from the shareholders and board to reduce the production cost. Additionally, they are also interested in understanding the impact of their marketing and farmer connect efforts towards overall sales. In the same effort, they have hired you as a data science and predictive analytics consultant.
You will start your investigation of this problem in the next part of this series using the concept discussed in this article. Eventually, you will develop an ARIMA model to forecast sale / demand for next year. Additionally, you will also investigate the impact of marketing program on sales by using an exogenous variable ARIMA model.
Sign (Sine) off Note
Whether you like it or not, life inevitably goes through up and down cycle. A perfect career or relationship doesn’t make the variability disappear from our lives but makes us appreciate the swings of life. They keep us going in the tough times. They make us realise that variability is beautiful!