Package com.imsl.test.example.stat

Class ARAutoUnivariateEx1

java.lang.Object

com.imsl.test.example.stat.ARAutoUnivariateEx1

public class ARAutoUnivariateEx1
extends Object

Finds the minimum AIC autoregressive model for the Wolfer sunspot data.

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. In this example, ARAutoUnivariate found the minimum AIC fit is an autoregressive model with 3 lags: $$\tilde{W_t}=\phi_1\tilde{W_{t-1}}+\phi_2 \tilde{W_{t-2}}+\phi_3\tilde{W_{t-3}} + a_t\rm{,}$$ where $$\tilde{W_t} := W_t - \mu$$ \(\mu\)is the sample mean of the time series \( \{W_t\} \). Defining the overall constant \( \theta_0 \) by \(\theta_0 := \mu(1- \sum_{i=1}^3\phi_i)\), we obtain the following equivalent representation: $$W_t=\theta_0+\phi_1W_{t-1}+\phi_2W_{t-2}+ \phi_3W_{t-3}+a_t\rm{.}$$ The example computes estimates for \(\theta_0\rm{,}\,\phi_1\rm{,}\,\phi_2\rm{,}\,\phi_3\) for each of the three parameter estimation methods available.

See Also:

• Code
• Output

Constructor Summary

Constructors

Constructor	Description
ARAutoUnivariateEx1()

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

ARAutoUnivariateEx1

public ARAutoUnivariateEx1()

Method Details

main

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

Throws:

Exception