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LRVar
Returns the long run variance using a Bartlett kernel with window size k.
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.
- 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:
Where:-
is a value from the input time series data
-
is the mean of the input time series data
- The weight (
) in Bartlett kernel is defined as follows:
![\[ w_i= 1- \frac{\left | i \right |}{k+1} \]](http://cdn.spiderfinancial.com/sites/all/files/tex/5b4cdc7940ea38aecd9ec7f3593a25b394d46133.png)
-
is the input window size for the Bartlett kernel
-
Example 1:
| A | B | |
|---|---|---|
| 1 | Date | Data |
| 2 | 1/1/2008 | #N/A |
| 3 | 1/2/2008 | -1.28 |
| 4 | 1/3/2008 | 0.24 |
| 5 | 1/4/2008 | 1.28 |
| 6 | 1/5/2008 | 1.20 |
| 7 | 1/6/2008 | 1.73 |
| 8 | 1/7/2008 | -2.18 |
| 9 | 1/8/2008 | -0.23 |
| 10 | 1/9/2008 | 1.10 |
| 11 | 1/10/2008 | -1.09 |
| 12 | 1/11/2008 | -0.69 |
| 13 | 1/12/2008 | -1.69 |
| 14 | 1/13/2008 | -1.85 |
| 15 | 1/14/2008 | -0.98 |
| 16 | 1/15/2008 | -0.77 |
| 17 | 1/16/2008 | -0.30 |
| 18 | 1/17/2008 | -1.28 |
| 19 | 1/18/2008 | 0.24 |
| 20 | 1/19/2008 | 1.28 |
| 21 | 1/20/2008 | 1.20 |
| 22 | 1/21/2008 | 1.73 |
| 23 | 1/22/2008 | -2.18 |
| 24 | 1/23/2008 | -0.23 |
| 25 | 1/24/2008 | 1.10 |
| 26 | 1/25/2008 | -1.09 |
| 27 | 1/26/2008 | -0.69 |
| 28 | 1/27/2008 | -1.69 |
| 29 | 1/28/2008 | -1.85 |
| 30 | 1/29/2008 | -0.98 |
| Formula | Description (Result) | |
|---|---|---|
| =LRVar($B$2:$B$30,3) | Long-run variance (2.084) |
- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
