Moving-average modelIn time series analysis, the moving-average model (MA model), also called the moving-average process, is a standard approach for modeling univariate time series. An MA model expresses the current value of a time series as a linear function of current and past random shocks (error terms) with finite lag length.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.
Autoregressive integrated moving averageIn time series analysis used in statistics and econometrics, autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models are generalizations of the autoregressive moving average (ARMA) model to non-stationary series and periodic variation, respectively. All these models are fitted to time series in order to better understand it and predict future values. The purpose of these generalizations is to fit the data as well as possible.
Stochastic processCollection of random variablesA computer-simulated realization of a Wiener or Brownian motion process on the surface of a sphere. The Wiener process is widely considered the most studied and central stochastic process in probability theory.In probability theory and related fields a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time.
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.
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.
StochasticStochasticity is the property of being well-described by a randomprobability distribution. Stochasticity and randomness are technically distinct concepts: stochasticity refers to a modeling approach, while randomness describes phenomena. These terms are often used interchangeably. In probability theory, the formal concept of a stochastic process is also referred to as a random process.
StatisticsStudy of collection and analysis of dataThe normal distribution, a very common probability density, is used extensively in inferential statistics.Scatter plots and line charts are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.Statistics (from German: Statistik, orig.Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
Recurrence relationIn mathematics, a recurrence relation is an equation according to which the n{\displaystyle n}th term of a sequence is equal to some combination of the previous terms. Often, only k{\displaystyle k} previous terms of the sequence appear in the equation, for a parameter k{\displaystyle k} that is independent of n{\displaystyle n}; this number k{\displaystyle k} is called the order of the relation.
Linear relationIn linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution.*As an Amazon Associate I earn from qualifying purchases.