Autoregressive refers to a variable that depends on previous values of itself, and autoregression is a form of regression analysis used to determine if a variable is autoregressive. Autoregressive variables are found in various fields and can be analyzed using predictive analytics methods. Autoregressive moving average (ARMA) models combine autoregressive and moving average models and are used to model and test time series. They are commonly used in time series forecasting and other forms of predictive analytics.
“Autoregressive” is a statistical term used when working with time series data that refers to a variable quantity or value of interest that is correlated with or depends on previous values of that same variable. The related term “autoregression” is a form of regression analysis that uses time series data as input to discover whether a variable of interest is truly autoregressive, that is, it depends on previous values of itself. A variable of interest that turns out to be autoregressive suggests, but does not itself prove, that a cause-and-effect relationship exists between current and past values. Therefore, time series of known or suspected autoregressive amounts or values are often analyzed using predictive analytics methods to forecast future values of such variables.
Variables of interest that exhibit some significant degree of autoregression appear in a variety of places as a result of human and natural processes. Stock market prices, exchange rates, digital signals, and the number of people in a population, for example, are all considered to be autoregressive, at least to some degree. Furthermore, there are a variety of forms of autoregression analysis, each considered better or worse adapted and therefore applied to particular types of autoregressive data sets. Among such applications, autoregression is being used in healthcare to improve the resolution and interpretation of ultrasound diagnostic tests; in telecommunications to improve the transmission, reception and processing of digital signals; in economics to forecast macroeconomic and business performance; and in financial services to calculate personal credit scores, detect fraud, and calculate insurance risk profiles and premiums.
Autoregressive moving average (ARMA) models combine autoregressive and moving average models, averages whose constituent elements change as time passes. Also known as Box-Jenkins models, named for George Box and Gwilym Jenkins, the statisticians who improved their original formulations and popularized their use, are generally used to model and test time series that are functions of external or external shocks. and their own past performance. ARMA models are “fit” to actual observations over time of some known or suspected autoregressive variable or variables of interest to better understand the processes that generate them. Unlike strictly autoregressive models, they are considered a means of establishing causality: the existence of a cause-and-effect relationship between the independent and dependent variable(s). Therefore, they are commonly used in time series forecasting and other forms of predictive analytics.
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