Returns the long-run variance using a Bartlett kernel with window size k.
Syntax
LRVar(X, k)
- X
- is the input data sample (a one dimensional array of cells (e.g. rows or columns)).
- K
- is the input Bartlett kernel window size. If omitted, the default value is the cubic root of the sample data size.
Remarks
- The input time series data may include missing values (e.g. #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.
- The long-run variance is computed as follows:
$$\sigma^2=\frac{1}{T}\sum_{t=k}^{T-k}\sum_{i=-k}^k w_i(x_t-\bar{x})(x_{t-i}-\bar{x}) $$
Where:
- $x_{t} \in X$ is a value from the input time series data
- $\bar{x}$ is the mean of the input time series data
- The weight ($w_i$) in Bartlett kernel is defined as follows:
$$w_i= 1- \frac{\left | i \right |}{k+1}$$
- $k$ is the input window size for the Bartlett kernel
Examples
Files Examples
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