Autoregressive modelRepresentation of a type of random processIn statistics, an autoregressive (AR) model is a modelled representation of a type of random process. It can be used to describe time-varying processes from many natural and artificial sources. The model specifies output variables that are dependent linearly on their own previous values on a stochastic basis.
Stationary processClass of stochastic processIn mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical properties, such as mean and variance, do not change over time. More formally, the joint probability distribution of the process remains the same when shifted in time. This implies that the process is statistically consistent across different time periods.
Autoregressive moving-average modelIn the statistical analysis of time series, an autoregressive–moving-average (ARMA) model is used to represent a (weakly) stationary stochastic process by combining two components: autoregression (AR) and moving average (MA). These models are widely used for analyzing the structure of a series and for forecasting future values.
Linear regressionIn statistics, linear regression is a model that estimates the relationship between a scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable) related via a linear combination. A linear model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression.
Time seriesIn mathematics, a time series is a sequence of data points indexed, listed, or graphed in chronological order. Most commonly, a time series consists of observations recorded at successive equally spaced points in time. Thus, it represents a form of discrete-time data. A time series may describe measurements collected over seconds, days, years, or even centuries.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations.
Order of integrationIn statistics, the order of integration, denoted I(d), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series (i.e., a time series whose mean and autocovariance remain constant over time). The order of integration is a key concept in time series analysis, particularly when dealing with non-stationary data that exhibits trends or other forms of non-stationarity.
AutocovarianceIn probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question.
EconometricsEconometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference." An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships."
StatisticsStatistics (from German: Statistik, orig. "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.*As an Amazon Associate I earn from qualifying purchases.