Autoregressive Model: Features, Process & Takeaway

Future prediction often requires a technical base. In the practical world, analysts predict future values based on past values of a commodity or trend in the market. In a statistical model, it is termed an autoregressive if it is capable of predicting future values given a series of factual data of past values.

For example, an autoregressive model might be engaged to derive a stock price in the future, based on its past performance. Analysts only use past data as input to model the behaviour.

Therefore, the prefix “auto” (the Greek meaning, “self” ) is used in the name autoregressive. AR models are also named conditional models, transition models, or Markov models.

About Autoregressive (AR) Model

In statistics, econometrics, or even image processing, the autoregressive (AR) model is considered a type of random process. Meaning, it is used to illustrate statistics of a series of definite time-varying events in nature, economics, etc.

Practically, in time-series, similarities between past and present values are observed. This implies the scope of autocorrelation within such data. For example, by knowing the stock price today, we can often make a rough forecast about its valuation tomorrow. This indicates the correlation, the aspect the autoregressive model is based on.

The Autoregressive (AR) model is one of the forecasting models built on regression methods. The multiple regression models will forecast a variable using a linear combination of predictors; whereas the autoregressive model uses a combination of past values the variable possesses. Unlike Autoregressive Distributed Lag (ADL) models, the AR models are based on serial correlations between the entities in a time series.

Therefore, Autoregression (AR) is a time series model. The autoregressive model is meant to predict future values based on the values in the past events. It uses input data from observations of previous steps, and using the regression equation predicts the value at the next time step. This model can result in accurate forecasts on a range of time series problems.

It’s commonly making use of the algorithm based on the correlations (serial correlation) derived within the values in a given time series and the values that lead and succeed them. The hypothesis that the past values affect current values makes the statistical technique useful for analyzing nature, such as weather, finance, e.g. economics, and other processes subjected to vary over time.

How to define an Autoregressive Model Python?

If we consider X to be a time-series variable, then an AR(1), commonly referred to as a simple autoregressive model, would appear something like this:

Xt = C ϕ1Xt-1 ϵt 

What is Xt-1?

To begin with, Xt-1 denotes X’s value from the prior time interval.

Let us elaborate.

If “t” stands for today and we have values for each week, then “t-1” stands for the previous week. Thus, Xt-1 shows the value that was seen one week ago.

What is ϕ1?

The coefficient  ϕ1 is a numeric constant multiplied by the lagged variable (Xt-1). It can be understood as the portion of the prior value that will continue to exist in the future. It’s important to remember that these coefficients must always range from -1 to 1.

What is ϵt?

The only portion of the equation that remains to be broken down is ϵt. The only portion of the equation that remains to be broken down is t. It is known as the residual and represents the discrepancy between our period t prediction and the actual value (ϵt = yt – t). Because if there is a pattern, it will be seen in the other incumbents of the model. These residuals are typically unpredictable differences.

Salient Features

  • Autoregressive models help predict future values based on past values.
  • Autoregressive models are used in technical analysis to forecast future trends.
  • Autoregressive models are based on the theory that the future will resemble the past.
  • Time series data are data collected on the same observational unit at multiple periods.

The prediction is subject to volatile conditions, such as rapid technological surge, or in the case of financial domain, the market conditions influenced by financial crises, etc.

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The AR Process

The process is a linear regression. It is the regression of the data within the current series of timelines versus values of past one or multiple in the same series.

In regression analysis, usually in “regular” linear regression, the outcome variable (Y) value at some point “t” in time, remains directly related to the predictor variable (X).

Here, simple linear regression and the AR models differ in the manner of Y remains dependent on X and also on the previous values for Y. Correlation analysis is a technique used to quantify the associations between two continuous variables.

The AR process is one of the stochastic processes. As per probability theory, it has degrees of uncertainty or some extent, randomness induced. The randomness implies you might predict future trends easily, well within the historical set of data. But you never be a cent percent accurate.

The process usually takes approximation and “close enough” to be relied on in most events.

AR Takeaway

Analysts in the industry often look forward to statistical techniques in forecast and prediction. The Autoregressive (AR) model related learning always helps professional analysts take Data Science and Data Analysis projects confidently. The training courses in the subject, by the providers such as upGrad, help take the journey ahead. The brand upGrad is an online higher education platform providing a vast range of industry-relevant programs ready to lead your professional success.

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Examples of the Autoregressive Model

The foundation of autoregressive models is the notion that the past impacts current values. 

For example, an investor using an autoregressive model to predict stock prices would need to assume that new buyers and merchandisers of that stock are influenced by recent request deals when deciding to offer or accept. 

Let’s take another example; suppose John is a stock market investor. He evaluates equities using past data on the performance and statistics of the company. John thinks it is wise to base investment decisions on the past performance of the stocks because it is highly correlated with future results.

He uses an autoregressive model integrated moving average with five years of pricing history. Based on the supposition that sellers and buyers track market trends and act accordingly when making investment decisions, the result provides him with a forecast for future prices.


Industry analysts often use statistics-based forecasting and prediction strategies. Professional analysts may always take on Data Science and Data Analysis projects with confidence thanks to the Autoregressive (AR) model linked learning.

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What is the Autoregressive Model?

An autoregressive model can be considered as a random process in the fields of statistics, image processing, and econometrics. It is used to represent the statistics of a chain of various time-variant events in the field of nature, economics, etc. The autoregressive model is based on the regression methods and forecasts a variable using the linear combination of predictors. These models are based on a serial correlation between the entities in a time series. It basically uses the input data collected from the observations of previous steps and predicts the next steps using the regression equations.

Name some of the alternative time series forecasting models.

The following are some of the most popular alternatives of time series forecasting models. The moving average model or the moving average process is used to model univariate time series. In this model, the output is solely dependent upon the previous and current values of a stochastic term. The autoregressive moving average model provides a description of a weakly stationary stochastic process in the form of two polynomials. The autoregressive integrated moving average model is used in econometrics and statistics for predicting future events. It has three parameters- p, d, and q that are often called the ARIMA(p,d,q) models. As the name suggests, SARIMA is an extension of ARIMA that supports univariate time series. The Vector autoregression model is used to define the relationship between multiple quantities as they vary with the time by the means of statistics.

What are the components of ARIMA?

Autoregressive Integrated Moving Average or ARIMA has three components- Autoregression (AR), Integration (I), and Moving Average (MA). Autoregression is a method that represents the statistics of a series of time-changing events in various domains including econometrics. It represents the difference between multiple observations so that the values can be replaced by the difference between their current and previous values. It shows the dependency of observation and the net error with the help of a moving average model applied to the observations with error.

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