ELI5: Autoregressive moving average

Explain ARMA like I’m five years old

Okay, so you know how we count numbers, like 1, 2, 3, 4, and so on? And you know how sometimes we play games where we roll a dice or draw a card and we see what number comes up? Well, the ARMA model is a way for grown-ups to guess what number might come up next, just like we do when we’re playing a game.

Let’s say we’re playing a game where we roll a dice and we want to guess what number will come up next. We might look at the numbers we’ve rolled before, like 2, 5, 3, 1, 4, and notice that we’ve rolled a 5 twice and a 4 once. So, we might guess that the next number will be 5. That’s kind of like what the ARMA model does, it looks at past numbers and uses them to make a prediction for the next number.

Another example is guessing what the weather will be like tomorrow. We might look at the weather today and yesterday and the day before that, and notice that it was sunny yesterday and today, and we might guess that it will be sunny tomorrow too. That’s like what the ARMA model does, it looks at past weather and uses it to make a prediction for tomorrow’s weather.

So, the ARMA model is like a grown-up version of guessing what number will come up next in a game or what the weather will be like tomorrow. It’s a tool that grown-ups use to make predictions about things that happen over time, like stock prices or sales.

For example, let’s say we have a series of numbers that show how much it rained every day for a week. We might notice that if it rained a lot one day, it’s more likely to rain a little bit the next day.

The ARMA model helps us figure out how much the rain on one day is related to the rain on other days, and use that information to try to predict how much it will rain in the future.

The “autoregressive” part of the model helps us understand how the rain on one day is related to the rain on the previous day.

The “moving average” part helps us understand how the rain on one day is related to the average amount of rain we’ve seen over the past few days.

By combining these two things, the ARMA model can give us a pretty good idea of how much it might rain in the future.

So, the ARMA model is a way to predict what numbers will come up next in a sequence, like the cookies sold or the dice throws. It does this by looking at past numbers and using them to make a prediction for the next number.

One way to think about it is like trying to figure out a pattern in the numbers. Imagine you have a string of numbers like 4, 6, 5, 4, 6, 5, 4, 6, 5. You might notice that the pattern is “4, 6, 5” and it repeats over and over. An ARMA model would use this pattern to predict that the next number will be 4.

Another example is weather forecasting. Imagine that we have temperature data for the last 10 days in a row, and we want to predict what the temperature will be tomorrow. The ARMA model would look at the past 10 days of temperature data and try to find patterns in the numbers, like if the temperature usually goes up or down on a certain day, or if it’s usually warmer or colder at a certain time of day. Then, the model would use these patterns to make a prediction for tomorrow’s temperature.

It’s worth noting that the ARMA model is a type of time series model, which means it’s used to predict things that happen over time, like stock prices, weather, or sales data. Time series models like ARMA are commonly used in economics, engineering and social sciences.

It’s also worth noting that the autoregressive (AR) and moving average (MA) models are the two components that make up the ARMA model. Autoregressive models focus on the relationships between a variable and the past values of the same variable. Moving average models focus on the residual errors that are left after accounting for the past values of the variable.

Overall, the ARMA model is a powerful tool that can help predict what will happen next in a sequence of numbers, by finding patterns in past data and using them to make educated guesses about the future.

How can you use an ARMA model?

Sales forecasting

Imagine you’re a store manager and you want to predict how many items you’ll sell next week. You might use an ARMA model to look at past sales data and find patterns in how many items you sell on different days of the week, or at different times of the month. For example, you might notice that you sell more items on weekends than during the week, or that you tend to sell more items at the beginning of the month than at the end of the month. Using these patterns, you can make a prediction for next week’s sales.

Stock prices

Imagine you’re an investor and you want to predict what a certain stock’s price will be next month. You might use an ARMA model to look at past stock prices and find patterns in how the stock price changes over time. For example, you might notice that the stock price tends to go up after a certain company releases positive earnings reports or that the stock price tends to go down when there’s a lot of negative news about the company. Using these patterns, you can make a prediction for next month’s stock price.

Traffic prediction

Imagine you are working on traffic management and you want to predict the number of cars that will pass through a certain road at a certain time of the day. You might use an ARMA model to look at past traffic data and find patterns in how the number of cars on the road changes over time. For example, you might notice that the number of cars on the road tends to be higher during rush hour than at other times of the day, or that the number of cars on the road tends to be higher on weekdays than on weekends. Using these patterns, you can make a prediction for the number of cars that will be on the road at a certain time of the day.

In all these examples, the ARMA model is able to make predictions by finding patterns in past data. By identifying these patterns, the model can make educated guesses about what will happen in the future. The more data the model has to work with, the more accurate its predictions will be.

In short, the ARMA model is a powerful tool that can help predict future values of a time series based on past values by finding patterns in the data. It’s commonly used in economics, engineering, and social sciences and can be used to make predictions in various fields such as finance, weather, sales, and traffic.

Other models that are similar to ARMA

The ARMA model is similar to other models that are used to make predictions about time series data, such as:

1. Autoregressive (AR) model: This model looks at past values of a time series to make predictions about future values. It assumes that future values are a function of past values.
2. Moving average (MA) model: This model looks at past errors or residuals (the difference between predicted values and actual values) to make predictions about future values. It assumes that future values are a function of past errors.
3. ARIMA (Autoregressive Integrated Moving Average) model: This model is an extension of the ARMA model that also accounts for non-stationarity (changes in the mean or variance over time) in the data.

All of these models are used to analyze and make predictions about time series data, but the ARMA model combines both the AR and MA models for better predictions.

Digging deeper into auto regressive moving averages

Here are a few sources you can use to learn more about the ARMA model:

1. “Forecasting: principles and practice” by Rob J Hyndman and George Athanasopoulos – This is a free online textbook that covers various time series forecasting methods, including the ARMA model. It provides a detailed explanation of the theory behind the model and includes examples and R code to help you understand how to apply it.
2. “Time Series Analysis and Its Applications” by Robert H. Shumway and David S. Stoffer – This is a comprehensive textbook on time series analysis that covers the ARMA model in depth. It provides a clear and detailed explanation of the theory and includes examples and R code to help you understand how to apply the model.
3. “An Introduction to Time Series Modeling” by Andreas Jakobsen – This is a free online tutorial that covers various time series modeling techniques, including the ARMA model. It provides a clear and concise explanation of the theory and includes examples to help you understand how to apply the model.
4. “Time Series Analysis and Forecasting” by Example” by Hyndsight – This is a blog by Rob J Hyndman, an expert on time series forecasting, where he covers various forecasting methods including ARMA. The blog posts are easy to follow and provide a lot of insights and tips.
5. “Time Series Analysis and Forecasting” by DataCamp – This is an online course that covers various time series forecasting methods including ARMA. The course is interactive and includes examples and exercises to help you understand how to apply the model.

These resources should provide you with a good foundation for understanding the ARMA model and how to apply it. It’s also important to practice and experiment with real data to get a better understanding of the model and its behavior.