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.
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ARAutoUnivariateEx1() |
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