太阳黑子的多项式趋势-自回归-条件异方差模型

The Autoregressive-conditional Heteroskedasticity Model for Sunspot

用确定性趋势与残差服从条件异方差模型的自回归模型组合,作为太阳黑子相对数的数学模型.用它拟合1848—2002年太阳黑子相对数数据,取得很好的效果.首先通过逐步回归与逐步自回归,建立太阳黑子数的多项式趋势 自回归校正模型.然后通过PortmanteauQ检验和Lagrenge乘子检验证明残差存在强烈的异方差性,表明仅仅用多项式趋势 自回归校正模型是不够的.再配上一种条件异方差模型,即EGARCH模型控制其残差方差.从而建立多项式趋势+自回归+EGARCH模型.用此模型进行数据拟合回代,分析和预测,表明该模型的拟合,预测效果是好的,所分析的太阳黑子周期是恰当的.

This paper introduces a time series model whose determined trend is polynomial and errors are autocorrelated and heteroscedastic as sunspot series model. We use it to fitting 1848-2002 sunspot data. The effect is good. First we use stepwise regression and stepwise autoregression to establish polynomial trendautoregression error model. Second it is proved that there are strong heteroscedasticity in the sunspot series by Portmanteau Q test and Lagrenge test. So it shows the polynomial trend-autoregression model was insufficient. Lastly, we use polynomial trendautoregressionEGACH model to fitting sunspot data. The effect of fitting and forecast are very good, and the result that analyses the period of sunspot is appropriate.