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

ARMA model fitting and forecasting from an ordered observation history.

See: Description

Interface Summary

Interface	Description
ARMAFit	This interface represents a fitting method for estimating \(\phi , \theta , \mu , \sigma ^{2}\) in an ARMA model.

Class Summary

Class	Description
ARMAForecast	Forecasts an ARMA time series using the innovative algorithm.
ARMAForecastMultiStep	Computes the h-step ahead prediction of a causal ARMA model, by the innovative algorithm.
ARMAForecastOneStep	Computes the one-step ahead prediction of a causal ARMA model, by the innovative algorithm.
ARMAModel	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.
ARMAXModel	The ARMAX model (ARIMA model with eXogenous inputs) is a generalization of the ARMA model by incorporating exogenous variables.
ARModel	This class represents an AR model.
AutoCorrelation	Compute the Auto-Correlation Function (ACF) for an AutoRegressive Moving Average (ARMA) model, assuming that \(EX_{t} = 0\).
AutoCovariance	Computes the Auto-CoVariance Function (ACVF) for an AutoRegressive Moving Average (ARMA) model by recursion.
ConditionalSumOfSquares	The method Conditional Sum of Squares (CSS) fits an ARIMA model by minimizing the conditional sum of squares.
LinearRepresentation	The linear representation of an Autoregressive Moving Average (ARMA) model is a (truncated) infinite sum of AR terms.
MAModel	This class represents a univariate MA model.

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

ARMA model fitting and forecasting from an ordered observation history.

Choose a workflow

• Parameters already known: construct ARMAModel, then ARMAForecast.
• Estimate parameters: fit ConditionalSumOfSquares, inspect its model, then forecast from the same observation history.
• Differenced levels: fit with the chosen differencing order, then use ARIMAForecast with the fitted ARIMA model and the original levels.

Prepare data and interpret parameters

Observations must be finite, ordered oldest to newest and sampled on one consistent time grid. Missing periods are a data-modeling decision; dropping rows silently changes the meaning of one lag. These APIs do not resample timestamps, impute missing values or choose the sampling interval.

Coefficient arrays start at lag one, whereas NMDEV observation/vector indices start at one and Java arrays/lists start at zero. A model intercept is not its unconditional mean; for a stationary AR model the mean is \(c/(1-\sum_i\phi_i)\). The sigma constructor argument is innovation variance.

Evaluate a forecast honestly

Choose orders and fit parameters using training observations only. Compare predictions with a chronologically held-out period. Forecast horizon advances on each next call; actual new observations require a new forecaster. Inspect stationarity/invertibility, residual dependence and finite estimates separately from whether the optimizer returned an object.

Consult ARMAForecastMultiStep's current non-unit error-scaling limitation before turning its reported error variances into prediction intervals. The runnable known-model example deliberately uses unit innovation variance.