Clear Explanations of AR, MA, ARMA, and ARIMA in Times Series Analysis

Summary

This article provides clear explanations of AR, MA, ARMA, and ARIMA models used in time series analysis for forecasting future data using historical data.

Abstract

Time series analysis is a widely used method for various fields such as stock market analysis, sales forecasting, economic forecasting, astronomy, weather forecasting, and medical devices. The article focuses on four commonly used models in time series analysis: Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA), and Autoregressive Integrated Moving Average (ARIMA). The AR model represents a regression or prediction of current value based on past values, while the MA model generates current values based on errors from past forecasts. The ARMA model is a combination of AR and MA models, predicting future values based on both previous values and errors. The ARIMA model differs from ARMA by requiring differencing to make the time series stationary. ARIMA models are widely used for real-life time series analysis as most time series data are non-stationary.

Bullet points

Time series analysis is used for various fields such as stock market analysis, sales forecasting, economic forecasting, astronomy, weather forecasting, and medical devices.
The AR model represents a regression or prediction of current value based on past values.
The MA model generates current values based on errors from past forecasts.
The ARMA model is a combination of AR and MA models, predicting future values based on both previous values and errors.
The ARIMA model differs from ARMA by requiring differencing to make the time series stationary.
ARIMA models are widely used for real-life time series analysis as most time series data are non-stationary.
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Clear Explanations of AR, MA, ARMA, and ARIMA in Times Series Analysis

Time series analysis is widely used for stock market analysis, sales forecasting, economic forecasting, astronomy, sales forecasting, weather forecasting, medical devices to monitor vitals in real time, etc.

In time series analysis, the most highly used models are AR(Autoregressive), MA(Moving Average), ARMA(Autoregressive Moving Average), and ARIMA (Autoregressive Integrated Moving Average). These models are used for forecasting the future data using the available historical data.

Autoregressive Model (AR)

Autoregressive model represents a regression or prediction of current value that is generated based on the past values from that same time series. Since the current value is based on the nearby previous values, the value doesn’t change instantaneously. For example, body temperature doesn’t go up and down rapidly. It changes steadily and the measurements are close to each other.

Moving Average Model (MA)

Before we discuss moving average models, let’s not get confused with moving average smoothing (that smoothes out the times series by averaging) with moving average model.

Moving average model (MA) model generates the current values based on the ERRORS from the past forecasts instead of using the past values like AR. Past errors are analyzed to produce the current value. Perfecting a baking recipe will be like a moving average model. You will do adjustments for needed sugars or butter for today’s baking depending on the previous days’ amount to perfect the recipe.

Autoregressive Moving Average Model (ARMA)

ARMA is the combination of the AR and MA models. ARMA models cover both aspects of AR and MA. The ARMA model predicts the future values based on both the previous values and errors. Thus ARMA has better performance than AR and MA models alone.

Autoregressive Integrated Moving Average Model (ARIMA)

The difference between ARMA and ARIMA is the integration part. The integrated I stands for the number of times differencing is needed to make the times series stationary. ARIMA models are widely used for real life time series analysis since most times series data are non stationary and need differencing.