基于两步法带宽选择的金融时间序列长记忆参数估计

金融时间序列长记忆参数的半参数估计方法以频域分析为主,带宽选择是其中必不可少的关键环节。不同的带宽可能给出差异明显的长记忆参数估计值,甚至产生矛盾的结论,进而影响时间序列平稳性的判断。本文提出一种两步法,用于金融时间序列长记忆估计的半参数方法的带宽选择,并进一步对长记忆参数进行估计:首先,为了克服半参数方法忽略短期结构的不足,通过信息准则判断ARFIMA(p,d,q)过程的短记忆结构;其次,用短记忆模型拟合差分后的序列,根据拟合效果确定选择带宽及长记忆参数估计值。数值模拟显示以长记忆参数估计值均方根误差最小为标准,两步法优于其他方法。经上证50指数已实现波动率日数据的实证检验,两步法在长记忆模型中的预测误差最小;与短记忆模型相比,两步法在中期提前预测步长上具有优势。

Estimation of Long Memory Parameters of Financial Time Series Based on Two-Step Bandwidth Selection

The semi-parametric estimation method for long memory parameters of financial time series is based on frequency domain analysis,and bandwidth selection is an essential key link.Different bandwidths may give long-distance memory parameter estimates with significant differences,and even lead to contradictory conclusions,which in turn affect the judgment of time series stationarity.This paper proposes a two-step method for bandwidth selection of semiparametric methods for financial time series long memory estimation,and further estimates long memory parameters:first,to compensate for the short-term structure neglect of the semi-parametric method,the short memory structure of the ARFIMA(p,d,q) process is judged by the information criterion;secondly,the short memory model fits the sequence after the difference,and the bandwidth and the long memory parameter estimation value are selected according to the fitting effect.Taking the minimum root mean square error of the long memory parameter estimation as the standard,the numerical simulation shows that the two-step method selects the bandwidth better than other methods.The SSE 50 Index has achieved an empirical test of the realized volatility day data:In the long memory model,the two-step method has the least prediction error;compared with the short memory model,the two-step method shows an advantage in the medium-term advance prediction step size.