In a recent Night Talk on Bloomberg interview (via MR) Robert Engle said:
Methinks the problem with ARCH models is that you know what to expect (like when choosing between a 5-day or 10-day moving average). A.) Is your volatility forecast just based on the last couple of days, it will be highly erratic. It will do fine when there are successive days of either only large moves or only small moves (volatility clustering) but deliver many wrong signals in case big moves are more or less evenly dispersed between average and small moves. B.) When your volatility forecast is based on too much data it will be slow to react to sharp increases or decreases in daily volatility but on the other hand don't deliver a wrong signal in case there is only a short-lived correction or inaction.
I ran an ARCH(5) regression and an ARCH(10) regression on the last 10 years of S&P 500 returns. According to standard information criteria, the optimal lag-length is actually 5. But information criteria didn't change significantly when changing the lag-length and I can imagine that they depend more on the data window. The plots cover the last 200 trading days. The estimated (daily) standard deviation from the ARCH models was multiplied by sqrt(265) to annualize it:
Anybody with practical experience around?
R: A Language and Environment for Statistical Computing, R Development Core Team, R Foundation for Statistical Computing, Vienna, Austria.
PS: You actually won't believe the coefficients for the ARCH(5) model (cross checked with a different package):
"[The ARCH model] is the key ingredient for short-run risk forecasting for financial markets. <> We know some things about financial markets, which is if they are really volatile today, they are likely to be pretty risky tomorrow. And that kind of information allows you to update every day of what the risk is of a particular position."For Non-Quants: Imagine you have an estimate of the daily volatility. Could be the squared daily return or a volatility measure based on intraday-data or ... Now for calculating tomorrow's risk, you could just take an n-day average of your daily volatility. Something a little bit more sophisticated would be a weighted average where you'd put more weight on recent data points (today, yesterday) and less weight on past data points. With an ARCH model, you actually estimate those weights, i.e. "optimize" them by looking at past data.
Methinks the problem with ARCH models is that you know what to expect (like when choosing between a 5-day or 10-day moving average). A.) Is your volatility forecast just based on the last couple of days, it will be highly erratic. It will do fine when there are successive days of either only large moves or only small moves (volatility clustering) but deliver many wrong signals in case big moves are more or less evenly dispersed between average and small moves. B.) When your volatility forecast is based on too much data it will be slow to react to sharp increases or decreases in daily volatility but on the other hand don't deliver a wrong signal in case there is only a short-lived correction or inaction.
I ran an ARCH(5) regression and an ARCH(10) regression on the last 10 years of S&P 500 returns. According to standard information criteria, the optimal lag-length is actually 5. But information criteria didn't change significantly when changing the lag-length and I can imagine that they depend more on the data window. The plots cover the last 200 trading days. The estimated (daily) standard deviation from the ARCH models was multiplied by sqrt(265) to annualize it:
Anybody with practical experience around?
R: A Language and Environment for Statistical Computing, R Development Core Team, R Foundation for Statistical Computing, Vienna, Austria.
PS: You actually won't believe the coefficients for the ARCH(5) model (cross checked with a different package):
Mahalanobis - am 2009-02-09 12:29 - Rubrik: Finance
