Description Usage Arguments Details Value Author(s) References Examples
Determines the optimal and data-driven moving average lag q.
1 | qn(x)
|
x |
a numeric vector or univariate time series. |
For univariate time series x[t], the moving average filter is defined as
mhat[t] = ∑ x[t]/(2q+1)
for q + 1 ≤ t ≤ 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 γ(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 γ(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.
qn |
the optimal moving average lag q. |
Debin Qiu
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.
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