Package com.imsl.test.example.stat

Class ARMAMaxLikelihoodEx1

java.lang.Object

com.imsl.test.example.stat.ARMAMaxLikelihoodEx1

public class ARMAMaxLikelihoodEx1
extends Object

Fits an \(\text{ARMA}(2,1)\) to the Wolfer sunspot data using the method of maximum likelihood.

Consider the Wolfer Sunspot Data (Anderson 1971, p. 660) consisting of the number of sunspots observed each year from 1749 through 1924. The data set for this example consists of the number of sunspots observed from 1770 through 1869. The \(ARMA(2, 1)\) model can be expressed as

$$z_t = \theta _0 + \phi _1 z_{t - 1} + \phi _2 z_{t - 2} - \theta _1 A_{t - 1} + A_t$$

where the errors \(A_t\) are independently normally distributed with mean zero and variance \(\sigma _A^2\).

The maximum likelihood estimates

$${\rm{\hat \theta }}_{\rm{0}} {\rm{,\hat \phi }}_{\rm{1}} {\rm{,\hat \phi }}_{\rm{2}} {\rm{, and \, \hat \theta }}_{\rm{1}}$$

from ARMAMaxLikelihood are compared to the same estimates using the method of moments and least squares from the ARMA class. For each method, the coefficients and forecasts for the last ten years, 1860-1869, are compared. The method of moments and maximum likelihood estimates produced similar results, but the least squares estimates were very different from the other two.

See Also:

• Code
• Output

Constructor Summary

Constructors

Constructor	Description
ARMAMaxLikelihoodEx1()

Method Summary

Modifier and Type	Method	Description
static void	main(String[] args)

Methods inherited from class java.lang.Object

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

Constructor Details

ARMAMaxLikelihoodEx1

public ARMAMaxLikelihoodEx1()

Method Details

main

public static void main(String[] args)
                 throws Exception

Throws:

Exception