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The code is comprised of two functions: the usual function that implements the trading model (Model), and a procedure to prepare the neural network inputs (PrepareNeuralInputs). The procedure that prepares the inputs requires the index of the current bar (cb) and a series of closing prices (cls) on which to operate. The PrepareNeurallnputs function, given the index to the currant bar and a series of closing prices, calculates all inputs for a given fact that are required for the neural network. In the list, pbars, the numbers after the tirst zero (which is ignored), are the lookbacks, relative to the current bar, which are used to calculate the price differences discussed earlier. The first block of code, after the declarations, initializes a price adjustment factor table. The table IS tmualized on the first pass through the function and contains the square-roots of the number of bars between each pair of prices from which a difference is computed. The next block of code calculates the adjusted price differences, as well as the sum of the squares of these differences, i.e.,
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the squared amplitude or length of the resultant vector. The final block of code in this function normalizes the vector of price differences to unit length. The general code that implements the model follows our standard practice. After a block of declarations, a number of parameters are copied to local variables for convenient reference. The 50-bar average true range, which is used for the standard exit, and the time-reversed lo-bar Slow %K, used as a target, are then computed. One of the parameters (mode) sets the mode in which the code will run. A mode of 1 runs the code to prepare a fact file: The file is opened, the header (consisting of the number of inputs, 18, and the number of targets, 1) is written, and the fact count is initialized to zero. This process only occurs for the first market in the portfolio. The tile remains open during all further processing until it is closed after the last tradable in the portfolio has been processed. After the header, facts are written to the tile. All data before the in-sample date and after the out-of-sample date are ignored. Only the in-sample data are used. Each fact written to the file consists of a fact number, the 18 input variables (obtained using PrepareNeuralInpufs), and the target (which is the time-reversed Slow %K). Progress inforntation is displayed for the user as the fact file is prepared. If mode is set to 2, a neural network that has been trained using the fact tile discussed above is used to generate entries into trades, The first block of code opens and loads the desired neural network before beginning to process the first commodity. Then the standard loop begins. It steps through bars to simulate actual trading. After executing the usual code to update the simulator, calculate the number of contracts to trade, avoid limit-locked days, etc., the block of code is reached that generates the entry signals, stop prices, and limit prices. The PrepareNeuralInpufs function is called to generate the inputs corresponding to the current bar, these inputs are fed to the net, the network is told to run itself, the output from the net is retrieved, and the entry signal is generated. The rules used to generate the entry signal are as follows. If the output from the network is greater than a threshold (thresh), a sell signal is issued; the net is predicting a high value for the time-reversed Slow %K, meaning that the current closing price might be near the high of its near-future range. If the output from the network (the prediction of the time-reversed Slow %K) is below 100 minus thresh, a buy signal is issued. As an example, if thresh were set to 80, any predicted,time-reversed Slow %K greater than 80 would result in the posting of a sell signal, and any predicted timereversed Slow %K less than 20 would result in the issuing of a buy signal. Finally, there are the two blocks of code used to issue the actual entry orders and to implement the standardized exits. These blocks of code are identical to those that have appeared and been discussed in previous chapters. Test Methodology for the Reverse Slow %K Model The model is executed with the mode parameter set to 1 to generate a fact set. The fact set is loaded into N-TRAIN, a neural network development kit (Scientific
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Consultant Services, 516-696-3333). appropriately scaled for neural processing, and shuffled, as required when developing a neural network. A series of networks are then trained, beginning with a small network and working up to a fairly large network. Most of the networks are simple, 3-layer nets. Two 4.layer networks are also trained. All nets are trained to maximum convergence and then polished to remove any small biases or offsets. The process of polishing is achieved by reducing the learning rate to a very small number and then continuing to train the net for about 50 runs. Table 1 l-l contains information regarding all networks that were trained for this model, along with the associated correlations and other statistics. In the table, Nei Name = the file name to which the net was saved; Net Size = the number of layers and the number of neurons in each layer; Connecrions = the number of connections in the net optimized by the training process (similar to the number of regression coeff%zients in a multiple regression in terms of their impact on curvefitting and shrinkage); and Correlarion = the multiple correlation of the network output with the target (this is not a squared multiple correlation but an actual correlation). Corrected for Shrinkage covers two columns: The left one represents the correlation corrected for shrinkage under the assumption of an effective sample size of 40,000 data points or facts in the training set. The right column represents the correlation corrected for shrinkage under the assumption of 13,000 data points or facts in the training set. The last line of the table contains the number of facts or data points (Actual N) and the number of data points assumed for each of the shrinkage corrections (Assumed). The number of data points specified to the shrinkage adjustment equation is smaller than the actual number of facts or data points in the training set. The reason
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