rmaf (version 3.0.1)

qn: Optimal and Data-Driven Moving Average Lag q

Description

Determines the optimal and data-driven moving average lag $q$.

Usage

qn(x)

Arguments

x

a numeric vector or univariate time series.

Value

• qn
  the optimal moving average lag $q$.

Details

For univariate time series $x[t]$, the moving average filter is defined as $$mhat[t] = \sum x[t]/(2q+1)$$ for $q + 1 \le t \le n + q$. The optimal and data-driven moving average lag $q$ can be determined by using the rule-of-thumb estimator proposed in Section 3 of D. Qiu et al. (2013). It is determined by sample size $n$, variance $\gamma(0)$ and curvature $m''$ of the univariate series, where $m''$ is the second derivative of an unknown nonparameteric trend function $m(t)$. To obtain the preliminary estimators of variance $\gamma(0)$ and curvature $m''$, $m(t)$ can be initially fitted by a cubic polynomial model. See L. Yang and R. Tscherning (1999) for more details. For the case when $q > n$, the optimal moving average lag $q$ is set to be an integer part of $n^{4/5}/2$.

References

D. Qiu, Q. Shao, and L. Yang (2013), Efficient inference for autoregressive coeficient in the presence of trend. Journal of Multivariate Analysis 114, 40-53.

L. Yang, R. Tscherning (1999), Multivariate bandwidth selection for local linear regression. Journal of the Royal Statistical Society. Series B. Statistical Methodology 61, 793-815.

Examples

## load the global temperature data:
## first column is time and second column is temperature.
data(globtemp)
(q.n <- qn(globtemp))