# 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?

• What's the use of calculation correlation using yearly data? Will the data from 2008, 2009 as yearly data points help you to understand the dynamics of 2016? 2015? The world is changing ... a yearly frequency is too low in my opinion. – Ric Jul 6 '15 at 7:47
• I wish to use the EWMA for correlation between 2 time series in general, not necessarily of stock prices. I don't really know if it make sense. – Egodym Jul 6 '15 at 13:48

## 1 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.

• By doing as you said I will need an estimate of the volatility, but I get that using the EWMA model with a specic $\lambda$. Is that correct? – Egodym Jul 6 '15 at 1:13
• Not entirely @Egodym! Take a look to the paragraph 5.2.1.1, with head "Covariance and correlation estiman and forecast" at page 82 of the paper I posted in the answer. The author of the paper computed the correlation prediction with the formula I suggested above; I edited the answer in the hope to do that clearer. – Quantopik Jul 6 '15 at 7:48
• How can we implement it in STATA? – Saloni Aug 17 at 15:03
• Hi @Saloni, you should ask for that in another question, since your request is off topic here; moreover, I think such kind of question is more suitable for the crossvalidation or stackoverflow sites! – Quantopik Aug 19 at 0:22