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The solution to this equation can be problematic when H is poorly conditioned or nearly singular Let the singular value decomposition (see p 469) of H be H = [U1 , U2 ] 1 0 0 2 V1 V2

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Basically, his indicator follows where the big money is going by analyzing each market tick When institutions send orders to the market, they often hide them by dividing them into small orders, Willain says So instead of seeing 10,000 shares, the computer often slices it into 100-share increments I take all of the minute volume responsible for these minute price changes (Effective Volume), and separate them into two groups, large and small, Willain explains The large EV is what

where U1 RN r , 1 Rr r is nonsingular and diagonal, and V1 Rr n The parameter r is the rank of the matrix H and can be selected to exclude small singular values (ie, 2 0) Representing H as H = U1 1 V1 , show that the solution to the least squares problem can be computed as x = V1 1 U1 Y 1 (5107)

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Exercise 53 Use eqns (566) and (563) to derive eqn (568) Exercise 54 Assume that two Kalman lters provide two normally dis tributed and unbiased estimates of x Rn Denote the estimates as x1 and x2 The covariance of x1 is P1 The covariance of x2 is P2 The estimates x1 and x2 are independent random variables Construct a hypothetical set of 2n measurements: x1 x2 = I I x+ n1 n2 (5108)

where n1 N (0, P1 ) and n2 N (0, P2 ) 1 Use a method similar to that in Section 533 to show that the optimal (minimum mean squared error) combined estimate can be computed by either of the following equations: xc xc = = x1 + P 1 + P 1 1 2 x2 + P 1 + P 1 1 2

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usually tells you what the institutional players are up to I am measuring the interaction of price and volume, an interaction that occurs only when you have money moving in or out You see everyone buy at one point or retract money at some point So I m measuring all of these spikes in the market, almost like a rocket launching By statistically sorting the minute-to-minute volume that provoked a price change, he can see the large player s money flow When the price changes from one minute to the next, it is usually the result of a change of equilibrium between buyers and sellers Where there is a big spike of money, he says, a new trend often starts, especially if money is flowing in for two days or more I can see the large volume orders so that tells me if institutions are buying or selling, says Willain According to Willain, knowing what side of the market large players are on gives him an edge He analyzes the data and posts the results on his Web site It s important to see when the market changes so you can change your position, he says But once your position is changed, you keep it until the next big change, which could occur in a few weeks or months, he explains Meanwhile, you would monitor your position Willain is careful to say that his indicator does not predict what the market does, but it can give me a statistical advantage, he notes If a lot of large players are leaving the market, you can conclude the price will go down I would simply follow the money because the money is always right He says his indicator usually gives an advance warning of two days of what might happen It s a balance between the buyers and sellers But at a turning point the early sellers or early buyers will move first, observes Willain It is at that critical point, before the trend changes, that Willain tries to catch the large players buying or selling.

1 1

3 In the special case that n = 1, show that either equation reduces to xc = P2 P1 x1 + x2 P1 + P2 P 1 + P2

After price, volume is the most important piece of data Willain notes: You can trade price but you cannot trade volume Volume can give you two pieces of information: the force of the move and the change in equilibrium, which can result in a trend change

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