Autoregressive moving-average model

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Fitting models

Partial autocorrelation functions Autocorrelation functions Akaike information criterion Bayesian information criterion Least squares

19 related topics

Mathematical formulation

Parameters White noise Independent and identically distributed Normal random variables Stationary

11 related topics

History and interpretations

Laurent series Fourier analysis Box–Jenkins Infinite impulse response Digital signal processing

5 related topics

Applications

Mean-reversion

1 related topics

Topics to explore

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Overview

Statistical
Time series
(weakly) stationary stochastic process Stationary stochastic process
Autoregression Autoregressive model
Moving average Moving-average model
Linear combination
Error terms Errors and residuals in statistics
Peter Whittle Peter Whittle (mathematician)
George E. P. Box
Gwilym Jenkins
Box–Jenkins method

Mathematical formulation

Parameters Parameter
White noise
Independent and identically distributed Independent and identically distributed random variables
Normal random variables Normal distribution
Stationary Stationary process
Augmented Dickey–Fuller test
Intrinsic mode function
Long short-term memory
Lag operator
Box George Box
Jenkins Gwilym M. Jenkins

Spectrum

Fitting models

Partial autocorrelation functions Partial autocorrelation function
Autocorrelation functions Autocorrelation function
Akaike information criterion
Bayesian information criterion
Least squares
Yule-Walker equations AR model
Mathematica
MATLAB
Julia Julia (programming language)
Scikit-learn
Pandas Pandas (software)
PyFlux PyFlux?action=edit&redlink=1
IMSL Numerical Libraries
Gretl
GNU Octave
Stata
ARIMA Autoregressive integrated moving average
SuanShu SuanShu?action=edit&redlink=1
SAS SAS (software)

History and interpretations

Applications

Mean-reversion Mean reversion (finance)

Generalizations

Vector AR Vector autoregression
Autoregressive conditional heteroskedasticity
Autoregressive fractionally integrated moving average
Tree Tree (graph theory)
Nonlinear autoregressive exogenous model

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Map overview Semantic statistics

Nodes62

Edges61

Triples13

Avg. degree1.97

Density0.032258

Components1

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Important terminology Word statistics

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Important terminology

arma model series models ar time autoregressive arima moving average analysis terms displaystyle used ma exogenous box jenkins functions values

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
OLS	instance of	and not to infer causation as in other areas of econometrics and regression methods	0.80	text
2SLS.Software implementationsIn R	instance of	and not to infer causation as in other areas of econometrics and regression methods	0.80	text
standard packagestatshas functionarima	instance of	and not to infer causation as in other areas of econometrics and regression methods	0.80	text
documented in ARIMA Modelling of Time Series	instance of	and not to infer causation as in other areas of econometrics and regression methods	0.80	text
arma	instance of	The CRAN task view on Time Series contains links to most of these.Mathematica has a complete library of time series functions including ARMA.MATLAB includes functions	0.80	text
ar	instance of	The CRAN task view on Time Series contains links to most of these.Mathematica has a complete library of time series functions including ARMA.MATLAB includes functions	0.80	text
arx to estimate autoregressive	instance of	The CRAN task view on Time Series contains links to most of these.Mathematica has a complete library of time series functions including ARMA.MATLAB includes functions	0.80	text
exogenous autoregressive	instance of	The CRAN task view on Time Series contains links to most of these.Mathematica has a complete library of time series functions including ARMA.MATLAB includes functions	0.80	text
ARMAX models	instance of	The CRAN task view on Time Series contains links to most of these.Mathematica has a complete library of time series functions including ARMA.MATLAB includes functions	0.80	text
arma.jl.Python has thestatsmodelsS package which includes many models	instance of	Julia has community-driven packages that implement fitting with an ARMA model	0.80	text
functions for time series analysis	instance of	Julia has community-driven packages that implement fitting with an ARMA model	0.80	text
including ARMA	instance of	Julia has community-driven packages that implement fitting with an ARMA model	0.80	text

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Fitting models

Mathematical formulation

History and interpretations

Applications

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Topics to explore

Overview

Mathematical formulation

Spectrum

Fitting models

History and interpretations

Applications

Generalizations

Advanced semantic analysis

Map overview Semantic statistics