ARIMA is a special way to predict what might happen in the future based on past information. It has three parts that work together to understand the patterns in the data. These parts are called AutoRegressive, Integrated, and Moving Average. Each part helps us learn different things about the data and make better predictions. AutoRegressive (AR) means that something is based on what came before it. It’s like a pattern or a sequence where each thing depends on the thing that came before it. It’s kind of like a chain reaction. The “I” component in the model stands for integrated. It means that the data used in the model has been adjusted to make it more predictable. This adjustment is done by taking the difference between each observation and its previous observation. The notation I(d) represents the degree of differencing, where “d” represents the number of times the data has been adjusted. Moving Average (MA) is a way to look at a set of numbers over time and see if they are changing. It helps us understand if there is a pattern or trend. The notation MA(d) tells us how many steps we need to take to see a clear pattern. The MA component is about looking at how the current observation is related to the difference between what we expect and what actually happened in the past. The notation MA(q) just means we are looking at a certain number, q, of these differences from the past.
By following these steps, we can better understand the numbers and make predictions about what might happen next: A stationarity check is like making sure that something doesn’t change too much over time. It’s like checking if a toy stays the same and doesn’t break or get damaged. We want to see if something stays consistent without big changes or surprises. Make sure that the data you are looking at stays the same over time, or change it so that it does. To figure out how to change it, you need to pick the right amount of changes to make. We need to figure out the values of “p,” “d,” and “q” by looking at patterns in the data. We use special mathematical tools to analyze these patterns, like autocorrelation and partial autocorrelation functions. This helps us find the right model for the data. After fitting the ARIMA model to the data using the chosen orders, we need to check if the model is working well. This means we want to make sure the model is accurately predicting the future values based on the patterns it learned from the data. For predicting the future, we need to make guesses based on what we know. The fitted model helps us make guesses about what might happen in the future. ARIMA models are really good at figuring out patterns in different types of data, like money, weather, and other things. They give us a way to understand how things change over time.