## What is an Autoregressive Integrated Moving Average (ARIMA)?

Autoregressive Integrated Moving Average (ARIMA) is a statistical analysis model that uses time series data to better understand a dataset or predict future trends.

A statistical model is autoregressive if it predicts future values based on past values. For example, an ARIMA model might predict the future price of a stock based on past performance, or a company’s earnings based on past periods.

key takeaways

- Autoregressive Integrated Moving Average (ARIMA) models predict future values based on past values.
- ARIMA uses lagging moving averages to smooth time series data.
- They are widely used in technical analysis to predict future security prices.
- Autoregressive models implicitly assume that the future is similar to the past.
- As such, they may prove to be inaccurate under certain market conditions, such as financial crises or times of rapid technological change.

## Understanding the Autoregressive Integrated Moving Average (ARIMA)

An autoregressive composite moving average model is a form of regression analysis used to measure the strength of one dependent variable relative to other variable variables. The goal of this model is to predict future security or financial market movements by examining the differences between values in a series rather than by actual values.

An ARIMA model can be understood by outlining each of its components as follows:

*Autoregressive (AR)*: refers to a model that shows a changing variable that regresses on its own lag or previous value.*Comprehensive (1):*Represents the difference in the original observations so that the time series is stationary (that is, the data values are replaced by the difference between the data value and the previous value).*Moving Average (MA)*:

## ARIMA parameters

Every component in ARIMA is used as a parameter with standard notation. For ARIMA models, the standard notation is ARIMA with p, d, and q, where integer values replace the parameters to indicate the type of ARIMA model used. Parameters can be defined as:

*p*: Number of lagged observations in the model; also known as lag order.*d*: The number of times the original observations differ; also known as the degree of dissimilarity.- q: The size of the moving average window; also known as the order of moving averages.

For example, in a linear regression model, include the number and type of terms. A value of 0 that can be used as a parameter means that a particular component should not be used in the model. In this way, an ARIMA model can be built to perform the functions of an ARMA model, or even a simple AR, I or MA model.

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Because ARIMA models are complex and work best on very large datasets, computer algorithms and machine learning techniques are used to compute them.

Because ARIMA models are complex and work best on very large datasets, computer algorithms and machine learning techniques are used to compute them.

## Autoregressive Integrated Moving Average (ARIMA) and Stationarity

In an autoregressive ensemble moving average model, the data is varied to make it stationary. A model that shows stationarity is one that shows constancy of the data over time. Most economic and market data show trends, so the purpose of the difference is to remove any trend or seasonal structure.

Seasonality, or when data shows regular and predictable patterns that repeat over a calendar year, can negatively impact regression models. If there is a trend and the stationarity is not obvious, many computations throughout the process cannot be performed efficiently.

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A one-time shock will affect subsequent values of the ARIMA model indefinitely. So the legacy of the financial crisis still exists in today’s autoregressive models.

A one-time shock will affect subsequent values of the ARIMA model indefinitely. So the legacy of the financial crisis still exists in today’s autoregressive models.

## special attention items

ARIMA models are based on the assumption that past values have some residual effect on current or future values. For example, an investor using an ARIMA model to predict the price of a stock assumes that new buyers and sellers of that stock are influenced by recent market transactions when deciding how many securities to offer or accept.

While this assumption holds in many cases, this is not always the case. For example, in the years leading up to the 2008 financial crisis, most investors were unaware of the risks posed by large portfolios of mortgage-backed securities (MBS) held by many financial firms.

During that time, investors using autoregressive models to predict the performance of U.S. financial stocks had good reason to predict a continued steady or upward trend in the sector’s stock prices. However, once the public knew that many financial institutions were at risk of imminent failure, investors suddenly became less concerned with the recent prices of these stocks and more concerned with their potential exposure. As a result, the market quickly revalued financial stocks to much lower levels, a move that would completely confuse the autoregressive model.

## Frequently Asked Questions

### What is ARIMA used for?

ARIMA is a method of forecasting or predicting future outcomes based on historical time series. It is based on the statistical concept of serial correlation, where past data points influence future data points.

### What is the difference between an autoregressive model and a moving average model?

ARIMA combines autoregressive features with moving average features. For example, an AR(1) autoregressive process is a process in which the current value is based on the previous value, while an AR(2) process is a process in which the current value is based on the previous two values. A moving average is a calculation used to analyze data points that removes the effects of outliers by creating a series of averages of different subsets of the complete data set. As a result of this combination of techniques, ARIMA models can take into account trends, cycles, seasonality, and other non-static types of data when making forecasts.

### How does ARIMA forecast work?

ARIMA forecasting is achieved by interpolating time series data for variables of interest. Statistical software will identify the appropriate number of lags or variances to apply to the data and check for stationarity. It will then output results that are often interpreted similarly to multiple linear regression models.