From: Bob Wheeler Subject: Re: Fitting vs. Forecasting? Date: Mon, 11 Jan 1999 20:12:17 -0500 Newsgroups: sci.math.num-analysis Keywords: martingales To nameless: It depends on the nature of the stochastic process. If you are attempting to predict stock market values, then lots of luck, since many theoreticians assume these to be martingales, or at best submartingales. Quite a bit of practical data supports the assumption. A martingale, by the way, is a process such that the expectation of the next observation is the value of the current observation. You cannot predict such a process, although you can find ways to lay bets that may pay off. -- Bob Wheeler --- (Reply to: bwheeler@echip.com) ECHIP, Inc. ??@world.std.com wrote: > > This might be a dumb question, but here goes : > > I've got a time series of 930 observations, daily returns specifically. > > I've fitted an ARIMA model to the 1st 500 observations; using Q and > t statistics, I belive this is a good fit. > > But when I forecast the next 430 observations, the Theil and rms > don't indicate an optimum model. > > I believe, based on my experiences above, that it *is* possible to > have a model that precisely fits data, but doens't forecast well. > > Is this true? > > PS - I told it it might be a dumb question! ============================================================================== From: "G. A. Edgar" Subject: Re: probability of winning by choosing bets... Date: Fri, 14 May 1999 09:21:14 -0400 Newsgroups: sci.math In article <7hgeev$q3p$1@nntp3.atl.mindspring.net>, Spiffy wrote: > Hi > > I was talking to my friend and we ended up talking about betting. If I were > to go into a casino with $1000 and played a coin flipping game (50% > winning/losing), would I be more likely to win money because of the fact > that I can chose what I want to bet and when to stop? > This is what we call in probability theory a "martingale". It is a fair game (your expected winnings are zero on each play). You choose when to stop. This is known as a "stopping time" or "optional time"...you are NOT allowed to use the outcome of a toss to decide whether to stop before that toss... In your example, you have to stop once you have lost $1000, so this process is bounded. There is a theorem that shows, under such conditions, that your expected winnings (regardless of how you choose your stopping time) are zero. -- Gerald A. Edgar edgar@math.ohio-state.edu Department of Mathematics telephone: 614-292-0395 (Office) The Ohio State University 614-292-4975 (Math. Dept.) Columbus, OH 43210 614-292-1479 (Dept. Fax)