EWXCF - Exponential-Weighted Correlation

1. The time series is homogeneous or equally spaced.
2. The two time series must have identical size and time order.
3. The correlation is defined as:
   $$\rho^{(xy)}_t=\frac{\sigma_t^{(xy)}}{{_x\sigma_t}\times{_y\sigma_t}} $$
   $$\sigma_t^{(xy)} = \lambda\sigma_{t-1}^{(xy)}+(1-\lambda)x_{t-1}y_{t-1}$$
   $$_x\sigma_t^2=\lambda\times{_x\sigma_{t-1}^2}+(1-\lambda)x_{t-1}^2 $$
   $$_y\sigma_t^2=\lambda\times{_y\sigma_{t-1}^2}+(1-\lambda)y_{t-1}^2 $$
   Where:
   
   • $\rho^{(xy)}_t$ is the sample correlation between X and Y at time t.
   • $\sigma_t^{(xy)}$ is the sample exponential-weighted covariance between X and Y at time t.
   • $_x\sigma_t$ is the sample exponential-weighted volatility for the time series X at time t.
   • $_y\sigma_t$ is the sample exponential-weighted volatility for the time series Y at time t.
   • $\lambda$ is the smoothing factor used in the exponential-weighted volatility and covariance calculations.
4. If the input data sets do not have a zero mean, the EWXCF Excel function removes the mean from each sample data on your behalf.
5. The EWXCF uses the EWMA volatility and EWCOV representations which do not assume a long-run average volatility (or covariance), and thus, for any forecast horizon beyond one-step, the EWXCF returns a constant value.

Files Examples

Related Links

• Wikipedia - Correlation
• Wikipedia - Cross-Correlation

References

• Hull, John C.; Options, Futures and Other Derivatives Financial Times/ Prentice Hall (2003),pp 385-387, ISBN 1-405-886145
• 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