![\"Sugercane](\"https:\/\/i0.wp.com\/ucanalytics.com\/blogs\/wp-content\/uploads\/2015\/05\/Sugercane-Juice.jpg\")
<\/a>Sugar Cane Juice and ARIMA – by Roopam<\/p><\/div>\n
For the last couple of articles, we are working on a manufacturing case study to forecast tractor sales for a company called PowerHorse. You can\u00a0find the previous articles on the links Part 1<\/a><\/strong> and Part 2<\/a><\/strong>.\u00a0In this part, we will start with ARIMA modeling for forecasting. ARIMA is an abbreviation for \u00a0A<\/strong>uto-R<\/strong>egressive\u00a0I<\/strong>ntegrated M<\/strong>oving A<\/strong>verage<\/em>. However, before we learn more about ARIMA let’s create a link between…<\/p>\n May and June are the peak summer months in India. Indian summers are extremely hot and draining.\u00a0Summers are followed by monsoon rains. It’s no wonder that during summers everyone in India has the habit of looking up towards the sky in the hope to see\u00a0clouds as an indicator of the arrival of monsoons. While waiting for the monsoons, Indians have a few drinks that keep them hydrated. Sugar cane juice, or ganne-ka-ras<\/em>, is by far my favorite drink to beat the heat. The process of making sugar cane juice is fascinating and has similarities with ARIMA modeling.<\/p>\n Sugar cane juice is prepared by crushing\u00a0a long piece of\u00a0sugar cane through the juicer with two large cylindrical rollers as shown in the adjacent picture.\u00a0However, it is difficult to extract all the juice from a tough sugar cane in one go hence the process is repeated multiple times. In the first go, a fresh sugar cane is passed through the juicer and then the residual of the sugar cane that still contains juice is again passed through the juicer many times till there is no more juice left in the residual. This is precisely how ARIMA models work<\/p>\n . Consider your time series data as a sugar cane and ARIMA models as sugar cane juicers. The idea with ARIMA models is that the final residual should look like white noise otherwise, there is juice or information available in the data to extract.<\/p>\n We will come back to white noise (juice-less residual) in the latter sections of this article. However, before that let’s explore more about ARIMA modeling.<\/p>\n ARIMA\u00a0is a combination of 3 parts i.e. AR (AutoRegressive<\/em>), I (Integrated<\/em>), and MA (Moving Average<\/em>). A convenient notation for ARIMA model is ARIMA(p,d,q). Here p,d, and q are the levels for each of the AR, I, and MA parts. Each of these three parts is an effort to make the final residuals display a white noise pattern (or no pattern at all).\u00a0In each step of ARIMA modeling, time series data is passed through these 3 parts like a sugar cane through a sugar cane juicer to produce juice-less residual.\u00a0The sequence\u00a0of three passes for ARIMA analysis is as follows:<\/p>\n Integrated<\/em> (I)<\/strong> – subtract time series with its lagged series to extract trends from the data<\/p>\n In this pass of ARIMA juicer, we extract trend(s) from the original time series data. Differencing is one of the most commonly used mechanisms for extraction of trends. Here, the\u00a0original series is subtracted\u00a0from it’s lagged series e.g.\u00a0November’s sales values are subtracted from October’s values to produce trend-less residual series. The formulae for different orders of differencing are as follow:<\/p>\nARIMA and Sugar Cane Juice<\/span><\/h2>\n
<\/p>\nARIMA Modeling<\/span><\/h2>\n
1st Pass of ARIMA to Extract Juice \/ Information<\/span><\/span><\/h5>\n