Autoregressive model, the Glossary
In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc.[1]
Table of Contents
56 relations: Autocorrelation, Autocovariance, Autoregressive integrated moving average, Autoregressive moving-average model, Brownian noise, Cauchy distribution, Central limit theorem, Characteristic equation (calculus), Colors of noise, Confidence interval, Differential equation, Fourier transform, Gaussian process, Geometric progression, Gilbert Walker (physicist), GNU Octave, Impulse response, Infinite impulse response, Initial condition, Kronecker delta, Lag operator, Large language model, Levinson recursion, Linear least squares, Linear predictive coding, Linear recurrence with constant coefficients, Low-pass filter, Mark Thoma, MATLAB, Maximum entropy spectral estimation, Maximum likelihood estimation, Method of moments (statistics), Moving-average model, Multivariate statistics, Ordinary least squares, Ornstein–Uhlenbeck process, Philosophical Transactions of the Royal Society, Polynomial, Polynomial long division, Predictive analytics, Proceedings of the Royal Society, PyMC, Python (programming language), R (programming language), Resonance, Spectral density, Stationary process, Stochastic, Time constant, Transfer function, ... Expand index (6 more) »
- Autocorrelation
Autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Autoregressive model and Autocorrelation are signal processing.
See Autoregressive model and Autocorrelation
Autocovariance
In 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. Autoregressive model and autocovariance are Autocorrelation.
See Autoregressive model and Autocovariance
Autoregressive integrated moving average
In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model.
See Autoregressive model and Autoregressive integrated moving average
Autoregressive moving-average model
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). Autoregressive model and autoregressive moving-average model are Autocorrelation.
See Autoregressive model and Autoregressive moving-average model
Brownian noise
In science, Brownian noise, also known as Brown noise or red noise, is the type of signal noise produced by Brownian motion, hence its alternative name of random walk noise.
See Autoregressive model and Brownian noise
Cauchy distribution
The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.
See Autoregressive model and Cauchy distribution
Central limit theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution.
See Autoregressive model and Central limit theorem
Characteristic equation (calculus)
In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree upon which depends the solution of a given th-order differential equation or difference equation.
See Autoregressive model and Characteristic equation (calculus)
Colors of noise
In audio engineering, electronics, physics, and many other fields, the color of noise or noise spectrum refers to the power spectrum of a noise signal (a signal produced by a stochastic process).
See Autoregressive model and Colors of noise
Confidence interval
Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated.
See Autoregressive model and Confidence interval
Differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
See Autoregressive model and Differential equation
Fourier transform
In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function.
See Autoregressive model and Fourier transform
Gaussian process
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution.
See Autoregressive model and Gaussian process
Geometric progression
A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
See Autoregressive model and Geometric progression
Gilbert Walker (physicist)
Sir Gilbert Thomas Walker (14 June 1868 – 4 November 1958) was an English physicist and statistician of the 20th century.
See Autoregressive model and Gilbert Walker (physicist)
GNU Octave
GNU Octave is a scientific programming language for scientific computing and numerical computation.
See Autoregressive model and GNU Octave
Impulse response
In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse.
See Autoregressive model and Impulse response
Infinite impulse response
Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response h(t) that does not become exactly zero past a certain point but continues indefinitely.
See Autoregressive model and Infinite impulse response
Initial condition
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t.
See Autoregressive model and Initial condition
Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
See Autoregressive model and Kronecker delta
Lag operator
In time series analysis, the lag operator (L) or backshift operator (B) operates on an element of a time series to produce the previous element.
See Autoregressive model and Lag operator
Large language model
A large language model (LLM) is a computational model notable for its ability to achieve general-purpose language generation and other natural language processing tasks such as classification.
See Autoregressive model and Large language model
Levinson recursion
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix.
See Autoregressive model and Levinson recursion
Linear least squares
Linear least squares (LLS) is the least squares approximation of linear functions to data.
See Autoregressive model and Linear least squares
Linear predictive coding
Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model.
See Autoregressive model and Linear predictive coding
Linear recurrence with constant coefficients
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
See Autoregressive model and Linear recurrence with constant coefficients
Low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. Autoregressive model and low-pass filter are signal processing.
See Autoregressive model and Low-pass filter
Mark Thoma
Mark Allen Thoma (born December 15, 1956) is a macroeconomist and econometrician and a professor of economics at the Department of Economics of the University of Oregon.
See Autoregressive model and Mark Thoma
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.
See Autoregressive model and MATLAB
Maximum entropy spectral estimation
Maximum entropy spectral estimation is a method of spectral density estimation.
See Autoregressive model and Maximum entropy spectral estimation
Maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.
See Autoregressive model and Maximum likelihood estimation
Method of moments (statistics)
In statistics, the method of moments is a method of estimation of population parameters.
See Autoregressive model and Method of moments (statistics)
Moving-average model
In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series.
See Autoregressive model and Moving-average model
Multivariate statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables.
See Autoregressive model and Multivariate statistics
Ordinary least squares
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.
See Autoregressive model and Ordinary least squares
Ornstein–Uhlenbeck process
In mathematics, the Ornstein–Uhlenbeck process is a stochastic process with applications in financial mathematics and the physical sciences.
See Autoregressive model and Ornstein–Uhlenbeck process
Philosophical Transactions of the Royal Society
Philosophical Transactions of the Royal Society is a scientific journal published by the Royal Society.
See Autoregressive model and Philosophical Transactions of the Royal Society
Polynomial
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.
See Autoregressive model and Polynomial
Polynomial long division
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division.
See Autoregressive model and Polynomial long division
Predictive analytics
Predictive analytics is a form of business analytics applying machine learning to generate a predictive model for certain business applications.
See Autoregressive model and Predictive analytics
Proceedings of the Royal Society
Proceedings of the Royal Society is the main research journal of the Royal Society.
See Autoregressive model and Proceedings of the Royal Society
PyMC
PyMC (formerly known as PyMC3) is a probabilistic programming language written in Python.
See Autoregressive model and PyMC
Python (programming language)
Python is a high-level, general-purpose programming language.
See Autoregressive model and Python (programming language)
R (programming language)
R is a programming language for statistical computing and data visualization.
See Autoregressive model and R (programming language)
Resonance
In physics, resonance refers to a wide class of phenomena that arise as a result of matching temporal or spatial periods of oscillatory objects.
See Autoregressive model and Resonance
Spectral density
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. Autoregressive model and Spectral density are signal processing.
See Autoregressive model and Spectral density
Stationary process
In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Autoregressive model and stationary process are signal processing.
See Autoregressive model and Stationary process
Stochastic
Stochastic refers to the property of being well-described by a random probability distribution.
See Autoregressive model and Stochastic
Time constant
In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.
See Autoregressive model and Time constant
Transfer function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input.
See Autoregressive model and Transfer function
Udny Yule
George Udny Yule, CBE, FRS (18 February 1871 – 26 June 1951), usually known as Udny Yule, was a British statistician, particularly known for the Yule distribution and proposing the preferential attachment model for random graphs.
See Autoregressive model and Udny Yule
Unit circle
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1.
See Autoregressive model and Unit circle
Variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.
See Autoregressive model and Variance
White noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.
See Autoregressive model and White noise
Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z-domain or z-plane) representation.
See Autoregressive model and Z-transform
Zeros and poles
In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable.
See Autoregressive model and Zeros and poles
See also
Autocorrelation
- Autocorrelation
- Autocorrelation technique
- Autocovariance
- Autoregressive conditional heteroskedasticity
- Autoregressive fractionally integrated moving average
- Autoregressive model
- Autoregressive moving-average model
- Cochrane–Orcutt estimation
- Correlogram
- Detrended fluctuation analysis
- Durbin–Watson statistic
- Fractional Brownian motion
- Hildreth–Lu estimation
- Hurst exponent
- Lag windowing
- Long-range dependence
- Long-tail traffic
- Partial correlation
- Portmanteau test
- Rescaled range
- Self-similar process
References
[1] https://en.wikipedia.org/wiki/Autoregressive_model
Also known as AR model, AR noise, AR process, AR(1), Auto-regression, Auto-regressive process, Autoregression, Autoregressive, Autoregressive Modeling, Autoregressive forecasting, Autoregressive models, Autoregressive process, Burg algorithm, Burg method, Stochastic difference equation, Stochastic term, Yule-Walker equations.
, Udny Yule, Unit circle, Variance, White noise, Z-transform, Zeros and poles.