# What Are Autoregressive Models? How They Work and Example

![Autoregressive Models: A statistical model that forecasts future values based on past values.](https://www.investopedia.com/thmb/jLd5uqLxAG-Jj_BsQMy7y6-iRSU=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/autoregressive.asp-final-17e7a70746c3409c901f6c72101b9438.png)

*— Investopedia / Zoe Hansen*

> **Definition**
>
> Autoregressive models are statistical models that use past data to predict future values, such as by forecasting stock prices based on historical prices.

## What Are Autoregressive Models?

Autoregressive models are statistical models used for time series analysis, where current values are predicted based on a linear combination of past values. These models assume that past behavior influences future outcomes, making them useful for forecasting trends and patterns in data over time.

### Key Takeaways

*   Autoregressive models predict future values based on past values.
*   They are widely used in technical analysis to forecast future security prices.
*   Autoregressive models implicitly assume that the future will resemble past observations.
*   Therefore, they can prove inaccurate under certain market conditions, such as financial crises or periods of rapid technological change.

## Understanding Autoregressive Models

Autoregressive models operate under the premise that past values have an effect on current values. This makes the statistical technique popular for analyzing nature, economics, and other processes that vary over time. [Multiple regression models](https://www.investopedia.com/terms/m/mlr.asp) forecast a variable using a linear combination of predictors, whereas autoregressive models use a combination of past values of the variable.

An AR(1) autoregressive process is one in which the current value is based on the immediately preceding value, while an AR(2) process is one in which the current value is based on the previous two values. An AR(0) process is used for [white noise](https://www.investopedia.com/articles/trading/07/stationary.asp) and has no dependence between the terms. In addition to these variations, there are also many different ways to calculate the coefficients used in these calculations, such as the [least squares method](https://www.investopedia.com/terms/l/least-squares-method.asp).

These concepts are used in technical analysis to forecast security prices. However, since autoregressive models base their predictions only on past information, they implicitly assume that the fundamental forces that influenced the past prices will not change over time. This can lead to inaccurate predictions if the underlying forces actually are changing, such as if an industry is undergoing technological transformation.

Nevertheless, traders continue to refine the use of autoregressive models for forecasting purposes. One example is the [Autoregressive Integrated Moving Average](https://www.investopedia.com/terms/a/autoregressive-integrated-moving-average-arima.asp) (ARIMA), a sophisticated autoregressive model that factors in trends, cycles, seasonality, errors, and other non-static data when making forecasts.

> **Important**
>
> Although autoregressive models are associated with technical analysis, they can also be combined with other approaches to investing. For example, investors can use fundamental analysis to identify a compelling opportunity and then use technical analysis to identify entry and exit points.

## Example of an Autoregressive Model

Autoregressive models are based on the assumption that past values affect current values. For example, an investor using an autoregressive model to forecast stock prices would assume that new buyers and sellers of that stock are influenced by recent market transactions when deciding how much to offer or accept for the security.

Although this assumption will hold under most circumstances, this is not always the case. For example, in the years before the [2008 Financial Crisis](https://www.investopedia.com/articles/economics/09/financial-crisis-review.asp), most investors were not aware of the risks posed by [mortgage-backed securities](https://www.investopedia.com/terms/m/mbs.asp). During those times, an investor using an autoregressive model to predict the performance of U.S. financial stocks would have had good reason to predict an ongoing trend of stable or rising stock prices in that sector. 

However, once it became public knowledge that many financial institutions were at risk of imminent collapse, investors suddenly became less concerned with these stocks' recent prices and far more concerned with their underlying risk exposure. Therefore, the market rapidly revalued financial stocks to a much lower level, a move which would have utterly confounded an autoregressive model.

It is important to note that, in an autoregressive model, a one-time shock will affect the values of the calculated variables infinitely into the future. Therefore, the legacy of the financial crisis lives on in today’s autoregressive models.

## Explain Like I'm Five

An autoregressive model is a statistical model that uses past observations to forecast future data. An example might be a stock trader looking at historical price data, or a climate scientist predicting the temperature based on last summer's observations.

Autoregressive models can be very accurate in stable systems, but they lose their predictive power when there is a rapid shift in fundamental variables. For example, an autoregressive model of a company's stock price might become less accurate if the company's technology becomes obsolete. Or, a weather model might show greater errors during periods of rapid climate change.  

## Why Are Autoregressive Models Popular in Financial Markets?

Autoregressive models are popular with technical analysts because they can predict future asset prices without requiring deep research into company fundamentals. Although they are not perfect, analysts can use these models to inform investment and trading decisions.

## What Assumptions Do Autoregressive Models Make About Data?

Autoregressive models assume that future values will follow past patterns in historical data, making them effective under stable conditions. However, their predictive ability falls in times of rapid fundamental change, when current values stop following historical patterns.

## Can Autoregressive Models Be Inaccurate?

Yes, autoregressive models can be inaccurate, in particular during periods of significant market volatility or rapid changes. During major technological changes or paradigm shifts, new data may stop following the patterns in historical observations.

## The Bottom Line

Autoregressive models aim to predict future values based on past data, making them essential in technical analysis for forecasting security prices. By assuming that future patterns will mirror past trends, they provide valuable insights for market predictions.

However, their accuracy can be limited during volatile conditions like financial crises or rapid technological changes, where historical patterns may not hold.