dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma

Class ARMAModel

java.lang.Object

dev.nm.stat.timeseries.linear.univariate.arima.ARIMAXModel

dev.nm.stat.timeseries.linear.univariate.arima.ARIMAModel

dev.nm.stat.timeseries.linear.univariate.stationaryprocess.arma.ARMAModel

Direct Known Subclasses:

ARModel, MAModel

public class ARMAModel
extends ARIMAModel

A univariate ARMA model, \(X_{t}\), takes this form. \[ X_t = \mu + \sum_{i=1}^p \phi_i X_{t-i} + \sum_{i=1}^q \theta_j \epsilon_{t-j} + \epsilon_t \]

Parameter and observation conventions

The constant argument is the intercept in \(X_t=c+\sum_i\phi_i X_{t-i}+\varepsilon_t+\sum_j\theta_j\varepsilon_{t-j}\), not the unconditional mean. For a stationary AR model the latter is \(c/(1-\sum_i\phi_i)\). AR and MA arrays contain coefficients from lag one onwards: do not prepend a leading one. The argument named sigma is the innovation variance, not its standard deviation.

Supply finite coefficients for a causal/stationary specification and finite, chronologically ordered observations at a consistent interval. Constructing a model is not a model-selection, missing-data-cleaning, or stationarity-validation step. Use ARMAForecast with a supplied model, or ConditionalSumOfSquares when parameters must be estimated.

See Also:

Wikipedia: Autoregressive moving average model

Constructor Summary

Constructors

Constructor and Description
ARMAModel(ARMAModel that) Copy constructor.
ARMAModel(double[] AR, double[] MA) Construct a univariate ARMA model with unit variance and zero-intercept (mu).
ARMAModel(double[] AR, double[] MA, double sigma) Construct a univariate ARMA model with zero-intercept (mu).
ARMAModel(double mu, double[] AR, double[] MA) Construct a univariate ARMA model with unit variance.
ARMAModel(double mu, double[] AR, double[] MA, double sigma) Construct a univariate ARMA model.

Method Summary

Modifier and Type	Method and Description
double	conditionalMean(double[] arLags, double[] maLags) Compute the univariate ARMA conditional mean, given all the lags.
ARMAModel	getDemeanedModel() Get the demeaned version of the time series model. \[ Y_t = (X_t - \mu) = \sum_{i=1}^p \phi_i (X_{t-i} - \mu) + \sum_{i=1}^q \theta_j \epsilon_{t-j} + \epsilon_t \] μ is the unconditional mean.
double	unconditionalMean() Compute the multivariate ARMA unconditional mean.

Methods inherited from class dev.nm.stat.timeseries.linear.univariate.arima.ARIMAModel

getARMA

Methods inherited from class dev.nm.stat.timeseries.linear.univariate.arima.ARIMAXModel

AR, d, getARMAX, MA, maxPQ, mu, p, phi, phiPolynomial, psi, q, sigma, theta, thetaPolynomial, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

ARMAModel

public ARMAModel(double mu,
                 double[] AR,
                 double[] MA,
                 double sigma)

Construct a univariate ARMA model.

Parameters:

mu - the intercept (constant) term

AR - the AR coefficients (excluding the initial 1); null if no AR coefficients

MA - the MA coefficients (excluding the initial 1); null if no MA coefficients

sigma - the white noise variance

ARMAModel

public ARMAModel(double mu,
                 double[] AR,
                 double[] MA)

Construct a univariate ARMA model with unit variance.

Parameters:

mu - the intercept (constant) term

AR - the AR coefficients (excluding the initial 1); null if no AR coefficients

MA - the MA coefficients (excluding the initial 1); null if no MA coefficients

ARMAModel

public ARMAModel(double[] AR,
                 double[] MA,
                 double sigma)

Construct a univariate ARMA model with zero-intercept (mu).

Parameters:

AR - the AR coefficients (excluding the initial 1); null if no AR coefficients

MA - the MA coefficients (excluding the initial 1); null if no MA coefficients

sigma - the white noise variance

ARMAModel

public ARMAModel(double[] AR,
                 double[] MA)

Construct a univariate ARMA model with unit variance and zero-intercept (mu).

Parameters:

AR - the AR coefficients (excluding the initial 1); null if no AR coefficients

MA - the MA coefficients (excluding the initial 1); null if no MA coefficients

ARMAModel

public ARMAModel(ARMAModel that)

Copy constructor.

Parameters:

that - a univariate ARMA model

Method Detail

conditionalMean

public double conditionalMean(double[] arLags,
                              double[] maLags)

Compute the univariate ARMA conditional mean, given all the lags.

Parameters:

arLags - the AR lags

maLags - the MA lags

Returns:

the conditional mean

unconditionalMean

public double unconditionalMean()

Compute the multivariate ARMA unconditional mean.

Returns:

the unconditional mean

getDemeanedModel

public ARMAModel getDemeanedModel()

Get the demeaned version of the time series model. \[ Y_t = (X_t - \mu) = \sum_{i=1}^p \phi_i (X_{t-i} - \mu) + \sum_{i=1}^q \theta_j \epsilon_{t-j} + \epsilon_t \] μ is the unconditional mean.

Returns:

the demeaned time series