Autoregressive

Autoregressive models and processes are stochastic calculations in which future values are estimated based on a weighted sum of past values.

Autoregressive models and processes operate under the premise that past values have an effect on current values, which makes the statistical technique popular for analyzing nature, economics, and other time-varying processes. Multiple regression models 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 the first order process, meaning that the current value is based on the immediately preceding value, while an AR(2) process has the current value based on the previous two values. An AR(0) process is used for white noise and has no dependence between the terms. There are also many different ways to calculate the coefficients used in these calculations, including the ordinary least squares or method of movements.

When used for forecasting, it's important to note that a one-time shock will affect the values of the calculated variables infinitely into the future.

Autoregressive concepts are used by technical analysts to forecast securities prices. For instance, trends, moving averages, and regressions take into account past prices in an effort to create forecasts of future price movement. The key difference is that many technical indicators try to capture the complex nonlinearity of financial prices to maximize profits, while autoregressive models strictly seek to minimize the mean squared error and may yield more accurate forecasts for linear underlying processes.

The upshot is that many popular technical indicators can be expressed as autoregressive forecasts, which creates an opportunity for a unified technical analysis framework. A great example is the Autoregressive Integrated Moving Average - or ARIMA - which combines elements of autoregressive, integrated, and moving average parts in creating a complete data set. This indicator can be used to take into account trends, cycles, seasonality, errors, and other non-stationary aspects of a data set when making forecasts.

One drawback to both autoregressive models and technical analysis is that past prices won't always be the best predictor of future movements, especially if the underlying fundamentals of a company have changed. As a result, traders should ensure that they use these forms of analysis in conjunction with other forms of analysis to make the right decisions. A great example would be using fundamental analysis to identify a compelling opportunity and then using technical analysis to identify entry and exit points.