time series - Estimating correlation using EWMA

I am using an EWMA model to evaluate the correlation between yearly time series.

I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data.

Is there a value suggested for yearly data? If not, how can it be estimated?

Answer

The $\lambda$ value used in the original paper is arbitrary, but you can estimate that by assuming (in the simplest case) 2 assets and running the following model:

$\sigma^2_{12,t+1}$ $=$ $\lambda$$*$$\sigma^2_{12,t-1}$$+$$(1-\lambda)$$r_{1,t}$$*$$r_{2,t}$;

given $r_{1,t}$ and $r_{2,t}$ respectively as the returns for the asset 1 and 2 and $\sigma^2_{12,t}$ the volatility at time t.

Solving by $\lambda$ as unique unknown variable, you can find the $\lambda$ estimation.

To compute the correlation forecast, replace $\sigma^2_{12,t+1}$ in:

$\rho_{t+1}$ $=$ $\frac{\sigma^2_{12,t+1}}{\sigma_{1,t+1}* \sigma_{2,t+1}}$;

where $\rho_{t+1}$ is the forecast of the correlation 1 period ahead.

Here the reference of the original paper by JP Morgan; I suggest you to read the paper an estimate $\lambda$ again, since its value depends on the volatility of returns and it changes over time.

The authors used a 20-day returns period to estimate asset volatility and returns and the choice of such time period, again, was arbitrary.

Hope this helps.