# 程序代写代做代考 finance City University of Hong Kong Department of Economics and Finance

City University of Hong Kong Department of Economics and Finance
Course EF5213 Assignment #1 ( due February 7, 2021)
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 t1tt
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 M contracts (specified externally) being traded as
(plast)new  (plast)old (plast )old
where plast is the last traded price in the interval.
(b) Determine the EWMA model using the first half of the extracted time series in (a) as in-sample period. The parameters  should be determined by considering the notion of minimizing root-mean- square error (RMSE) defined as
RMSE√1n ∑nt1[2t (rt )2 ]2
based on the historical time series of price returns in the in-sample period. For this purpose, use the
enclosed Brent’s minimizer from netlib with your own modification.
(c) Consider the second half of the extracted time series as out-of-sample period. Develop a backtesting procedure that evaluates the confidence of the one-sigma confidence interval [  t,   t] realized by the EWMA model.