If we want to calculate an $x$-day VaR ($x$ is some time period in days) from an Exponentially Weighted Moving Average (EWMA) of vector of returns, what should the half-life in the decay factor in EWMA be?

When calculating the decay factor $\lambda$ from the half life $t_{1/2}$, we have

$$\lambda = \exp\left(\frac{\log(0.5)}{t_{1/2}}\right)$$

What should $t_{1/2}$ be given the VaR period? For example, if we set the VaR period to 10 days, should $t_{1/2}$ also be 10 days? If not, why not?


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