What is an 'Autoregressive Integrated Moving Average - ARIMA'

An autoregressive integrated moving average, or ARIMA, is a statistical analysis model that uses time series data to either better understand the data set or to predict future trends. 

BREAKING DOWN 'Autoregressive Integrated Moving Average - ARIMA'

An autoregressive integrated moving average model is a form of regression analysis that gauges the strength of one dependent variable relative to other changing variables. The model's goal is to predict future securities or financial market moves by examining the differences between values in the series instead of through actual values.

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

  • Autoregression (AR) refers to a model that shows a changing variable that regresses on its own lagged, or prior, values.
  • Integrated (I) represents the differencing of raw observations to allow for the time series to become stationary, i.e., data values are replaced by the difference between the data values and the previous values.
  • Moving average (MA) incorporates the dependency between an observation and a residual error from a moving average model applied to lagged observations.

Each component functions as a parameter with a standard notation. For ARIMA models, a standard notation would be ARIMA with p, d, and q, where integer values substitute for the parameters to indicate the type of ARIMA model used. The parameters can be defined as:

  • p: the number of lag observations in the model; also known as the lag order.
  • d: the number of times that the raw observations are differenced; also known as the degree of differencing.
  • q: the size of the moving average window; also known as the order of the moving average.

In a linear regression model, for example, the number and type of terms are included. A 0 value, which can be used as a parameter, would mean that particular component should not be used in the model. This way, the ARIMA model can be constructed to perform the function of an ARMA model, or even simple AR, I, or MA models.

Autoregressive Integrated Moving Average and Stationarity

In an autoregressive integrated moving average model, the data are differenced in order to make it stationary. A model that shows stationarity is one that shows there is constancy to the data over time. Most economic and market data show trends, so the purpose of differencing is to remove any trends or seasonal structures. 

Seasonality, or when data show regular and predictable patterns that repeat over a calendar year, could negatively affect the regression model. If a trend appears and stationarity is not evident, many of the computations throughout the process cannot be made with great efficacy.

  1. Autoregressive

    Autoregressive models and processes are stochastic calculations ...
  2. Box-Jenkins Model

    The Box-Jenkins Model is a mathematical model designed to forecast ...
  3. Regression

    A statistical measure that attempts to determine the strength ...
  4. Predictive Modeling

    Predictive modeling is the process of using known results to ...
  5. Nonlinear Regression

    Nonlinear regression is a form of regression analysis in which ...
  6. GARCHP rocess

    The generalized autoregressive conditional heteroskedasticity ...
Related Articles
  1. Investing

    Financial Models You Can Create With Excel

    The relatively modest amount of time it takes to build these models can pay for itself by leading you to better investment decisions.
  2. Insights

    The Fed Model And Stock Valuation: What It Does And Does Not Tell Us

    Learn about this popular stock market valuation model and how accurate it has been over the years.
  3. Trading

    The Linear Regression of Time and Price

    This investment strategy can help investors be successful by identifying price trends while eliminating human bias.
  4. Investing

    More Model 3 Details Emerge on Tesla Earnings Call

    Tesla said the Model 3 will have fewer "bells and whistles" but a more automated production process to enable scale.
  5. Trading

    How to Build A Forex Trading Model

    Forex trading markets work 24/7, providing ample opportunities to make profitable trades. How can you build a profitable forex trading model for yourself?
  6. Financial Advisor

    Advisor Fees: A Look At the Retainer Model

    Financial advisors may want to become familiar with new payment models sooner rather than later in order to proactively meet market demands.
  7. Investing

    What's the Gordon Growth Model?

    The Gordon growth model is used to calculate the intrinsic value of a stock today, based on the stock’s expected future dividends. It is widely used by investors and analysts to compare the predicted ...
  8. Trading

    The 7 Pitfalls of Moving Averages

    While moving averages can be a valuable tool, they are not without risk.
  1. What is the difference between linear regression and multiple regression?

    Learn the difference between linear regression and multiple regression and how multiple regression encompasses not only linear ... Read Answer >>
  2. How can I create a linear regression in Excel?

    Learn the steps involved in creating a linear regression chart in Microsoft Excel. A linear regression is a data plot that ... Read Answer >>
  3. Is there an easy way to do financial forecasting in Excel?

    Find out how to use Excel to conduct financial forecasting. Learn how to build a complex financial model, and discover functions ... Read Answer >>
  4. Why is the moving average (MA) important for traders and analysts?

    See why the statistical concept of moving averages plays a central role for traders and chartists who rely on technical analysis ... Read Answer >>
  5. What is the difference between a simple moving average and an exponential moving ...

    The only difference between simple moving average and an exponential moving average is the sensitivity each one shows to ... Read Answer >>
Trading Center