# Autoregressive

### What does autoregressive mean?

A statistical model is autoregressive if it predicts future values ​​based on past values. For example, an autoregressive model could seek to predict future prices of a stock based on its past performance.

### Key points to remember

• Autoregressive models predict future values ​​based on past values.
• They are widely used in technical analysis to predict future prices of securities.
• Autoregressive models implicitly assume that the future will look like the past. As a result, they may prove to be inaccurate under certain market conditions, such as financial crises or periods of rapid technological change.

### Understanding autoregressive models

Autoregressive models assume that past values ​​have an effect on current values, making statistical technique popular for analyzing nature, economics and other time-varying processes. Multiple regression models predict a variable using a linear combination of predictors, while autoregressive models use a combination of past values ​​of the variable.

An AR (1) autoregressive process is a process in which the current value is based on the immediately preceding value, while an AR (2) process is a process in which the current value is based on the two previous values. An AR (0) process is used for white noise and has no dependency between terms. In addition to these variations, there are also many different ways to calculate the coefficients used in these calculations, such as the method of least squares.

These concepts and techniques are used by technical analysts to forecast securities prices. However, since autoregressive models base their predictions only on past information, they implicitly assume that the fundamental forces that influenced past prices will not change over time. This can lead to surprising and inaccurate forecasts if the underlying forces in question actually change, as if an industry is undergoing rapid and unprecedented technological transformation.

However, traders continue to refine the use of autoregressive models for forecasting purposes. An excellent example is the Autoregressive Integrated Moving Average (ARIMA), a sophisticated autoregressive model that can take into account trends, cycles, seasonality, errors and other types of non-static data when forecasting.

### Analytical approaches

Although autoregressive models are associated with technical analysis, they can also be combined with other investment approaches. For example, investors can use fundamental analysis to identify an attractive opportunity and then use technical analysis to identify entry and exit points.

### Real example of an autoregressive model

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

While this assumption holds true in most circumstances, 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 the large portfolios of mortgage-backed securities held by many financial companies. At that time, an investor using an autoregressive model to predict the performance of US financial stocks would have had good reason to predict a steady or rising share price trend in this sector.

However, once it became public that many financial institutions were in danger of an impending collapse, investors suddenly became less concerned about recent stock prices and much more concerned about their underlying risk exposure. As a result, the market quickly revalued financial stocks to a much lower level, a decision that would have completely confused an autoregressive model.

It is important to note that, in an autoregressive model, a point shock will affect the values ​​of the variables calculated infinitely in the future. Consequently, the legacy of the financial crisis continues in today’s autoregressive models.