ARMA

java.lang.Object
- smile.timeseries.ARMA

All Implemented Interfaces:

java.io.Serializable
```
public class ARMA
extends java.lang.Object
implements java.io.Serializable
```
Autoregressive moving-average model. 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).
Given a time series of data, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The AR part involves regressing the variable on its own lagged values. The MA part involves modeling the error term as a linear combination of error terms occurring contemporaneously and at various times in the past. The model is usually referred to as the ARMA(p,q) model where p is the order of the AR part and q is the order of the MA part.

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor and Description

ARMA(double[] x, double[] ar, double[] ma, double b, double[] fittedValues, double[] residuals)
Constructor.

Constructors
Constructor and Description
`ARMA(double[] x, double[] ar, double[] ma, double b, double[] fittedValues, double[] residuals)` Constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`adjustedRSquared()` Returns adjusted R² statistic.
`double[]`	`ar()` Returns the linear coefficients of AR(p).
`int`	`df()` Returns the degree-of-freedom of residual standard error.
`static ARMA`	`fit(double[] x, int p, int q)` Fits an ARMA model with Hannan-Rissanen algorithm.
`double[]`	`fittedValues()` Returns the fitted values.
`double`	`forecast()` Returns 1-step ahead forecast.
`double[]`	`forecast(int l)` Returns l-step ahead forecast.
`double`	`intercept()` Returns the intercept.
`double[]`	`ma()` Returns the linear coefficients of MA(q).
`double`	`mean()` Returns the mean of time series.
`int`	`p()` Returns the order of AR.
`int`	`q()` Returns the order of MA.
`double[]`	`residuals()` Returns the residuals, that is response minus fitted values.
`double`	`RSquared()` Returns R² statistic.
`double`	`RSS()` Returns the residual sum of squares.
`java.lang.String`	`toString()`
`double[][]`	`ttest()` Returns the t-test of the coefficients (including intercept).
`double`	`variance()` Returns the residual variance.
`double[]`	`x()` Returns the time series.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - ARMA
```
public ARMA(double[] x,
            double[] ar,
            double[] ma,
            double b,
            double[] fittedValues,
            double[] residuals)
```
    Constructor.
    
    Parameters:
    
    x - the time series
    
    ar - the estimated weight parameters of AR(p).
    
    ma - the estimated weight parameters of MA(q).
    
    b - the intercept.
- Method Detail
  - x
```
public double[] x()
```
    Returns the time series.
  - mean
```
public double mean()
```
    Returns the mean of time series.
  - p
```
public int p()
```
    Returns the order of AR.
  - q
```
public int q()
```
    Returns the order of MA.
  - ttest
```
public double[][] ttest()
```
    Returns the t-test of the coefficients (including intercept). The first column is the coefficients, the second column is the standard error of coefficients, the third column is the t-score of the hypothesis test if the coefficient is zero, the fourth column is the p-values of test. The last row is of intercept.
  - ar
```
public double[] ar()
```
    Returns the linear coefficients of AR(p).
  - ma
```
public double[] ma()
```
    Returns the linear coefficients of MA(q).
  - intercept
```
public double intercept()
```
    Returns the intercept.
  - residuals
```
public double[] residuals()
```
    Returns the residuals, that is response minus fitted values.
  - fittedValues
```
public double[] fittedValues()
```
    Returns the fitted values.
  - RSS
```
public double RSS()
```
    Returns the residual sum of squares.
  - variance
```
public double variance()
```
    Returns the residual variance.
  - df
```
public int df()
```
    Returns the degree-of-freedom of residual standard error.
  - RSquared
```
public double RSquared()
```
    Returns R² statistic. In regression, the R² coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R² of 1.0 indicates that the regression line perfectly fits the data.
    In the case of ordinary least-squares regression, R² increases as we increase the number of variables in the model (R² will not decrease). This illustrates a drawback to one possible use of R², where one might try to include more variables in the model until "there is no more improvement". This leads to the alternative approach of looking at the adjusted R².
  - adjustedRSquared
```
public double adjustedRSquared()
```
    Returns adjusted R² statistic. The adjusted R² has almost same explanation as R² but it penalizes the statistic as extra variables are included in the model.
  - fit
```
public static ARMA fit(double[] x,
                       int p,
                       int q)
```
    Fits an ARMA model with Hannan-Rissanen algorithm.
    
    Parameters:
    
    x - the time series.
    
    p - the order of AR.
    
    q - the order of MA.
  - forecast
```
public double forecast()
```
    Returns 1-step ahead forecast.
  - forecast
```
public double[] forecast(int l)
```
    Returns l-step ahead forecast.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class ARMA

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

ARMA

Method Detail

x

mean

p

q

ttest

ar

ma

intercept

residuals

fittedValues

RSS

variance

df

RSquared

adjustedRSquared

fit

forecast

forecast

toString