City University of Hong Kong Department of Economics and Finance
Course EF5213 Assignment #1 ( due February 11, 2018)
1. In the Exponentially weighted moving average model (EWMA), future variance is a weighted average of its immediate past estimation and the most recent observation of squared residual of price return. It follows an iteration equation given by
2 (1)(r )2 2 t1tt
with weight factor 1 0. The parameter can be estimated based on the historical mean of a given time series {r1, … , rn} as (1/n)(r1 … rn).
(a) Given, in file hsiapr_1tick.csv, intraday tick data for Hang Seng Index Futures of April 2015 as {timestamp, traded price, number of contracts}
use VBA to develop a procedure that captures the time series of price returns for every tradeVol number of contracts being traded as
(plast)new (plast)old (plast)old
where plast is the last traded price in the interval.
(b) Determine the EWMA model for the extracted time series in (a). The parameters should be
determined by considering the notion of minimizing root-mean-square error (RMSE) defined as RMSE√1n ∑nt1[2t (rt )2 ]2
based on the historical time series of price returns { r1 , r2 , … , rn }. For this purpose, use the enclosed Brent’s minimizer from netlib with your own modification.
(40 points)