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Training Statistics for Neural Nets to Predict Time-Reversed Slow %K
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is the presence of redundancy between facts. Specifically, a fact derived from one bar is likely to be fairly similar to a fact derived from an immediately adjacent bar. Because of the similarity, the effective number of data points, in terms of contributing statistically independent information, will be smaller than the actual number of data points. The two corrected correlation columns represent adjustments assuming two differently reduced numbers of facts. The process of correcting correlations is analogous to that of correcting probabilities for multiple tests in optimization: As a parameter is stepped through a number of values, results are likely to be similar for nearby parameter values, meaning the effective number of tests is sotnewhat less tbau the actual number of tests.
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Training Results for Time-Reversed Slow %K Model
As evident from Table 1 l-l, the raw correlations rose monotonically with the size of the network in terms of numbers of connections. When adjusted for shrinkage, by assuming an effective sample size of 13,000, the picture changed dramatically: The nets that stood out were the small Mayer net with 6 middle layer neurons, and the smaller of the two 4-layer networks. With the more moderate shrinkage correction, the two large 4-layer networks had the highest estimated predictive ability, as indicated by the multiple correlation of their outputs with the target. On the basis of the more conservative statistics (those assuming a smaller effective sample size and, hence, more shrinkage due to curve-fitting) in Table 1 l1, two neural nets were selected for use in the entry model: the 18-6-l network (nn2.nei) and the 18-14-4-l network (nn&rer). These were considered the best bets for nets that might hold up out-of-sample. For the test of the entry model using these nets, the model implementation was run with mode set to 2. As usual, all order types (at open, on limit, on stop) were tested.
TURNING-POINT
MODELS
For these models, two additional fact sets are needed. Except for their targets, these fact sets are identical to the one constructed for the time-reversed Slow %K. The target for the first fact set is a 1, indicating a bottom turning point, if tomorrow s open is lower than the 3 preceding bars and 10 succeeding bars. If not, this target is set to 0. The target for the second fact set is a 1, indicating a top, if tomorrow s open has a price higher than the preceding 3 and succeeding 10 opens. Otherwise this target is set to 0. Assuming there are consistent patterns in the matket, the networks should be able to learn them and, therefore, predict whether tomorrow s open is going to be a top, a bottom, or neither. Unlike the fact set for the time-reversed Slow %K model, the facts in the sets for these models are generated only if tomorrow s open could possibly be a turn ing point. If, for example, tomorrow s open is higher than today s open, then
tomorrow s open cannot be considered a turning point, as defined earlier, no matter what happens thereafter. Why ask the network to make a prediction when there is no uncertainty or need Only in cases where there is an uncertainty about whether tomorrow s open is going to be a turning point is it worth asking the network to make a forecast. Therefore, facts are only generated for such cases. The processing of the inputs, the use of statistics, and all other aspects of the test methodology for the turning-point models are identical to that for the timereversed Slow %K model. Essentially, both models are identical, and so is the methodology; only the subjects of the predictions, and, consequently, the targets on which the nets are trained, differ. Lastly, since the predictions are different, the rules for generating entries based on the predictions are different between models. The outputs of the trained networks represent the probabilities, ranging from 0 to 1, of whether a bottom, a top, or neither is present. The two sets of rules for the two models for generating entries are as follows: For the tirst model, if the bottom predictor output is greater than a threshold, buy. For the second model, if the top predictor output is greater than a threshold, sell. For both models, the threshold represents a level of confidence that the nets must have that there will be a bottom or a top before an entry order is placed. // write actual in-sample facts to the fact file forccb = 1; Cb <= nix cb++l ( // ioo!&ack if (fit L&l < ISDATE~ continue; if cdt Lcb+lOl > OOS~DATE~ break; // ignore 00s data if(opnIch+l] >= Lowest(opn, 3 , Cb) I // skip these fame continue; fprintf Cfil, $6d , ++factco nt) i // fact number PrepareNe ralInputs( ar, ClS, SD); forck = 1; k c= 1s; kt+j fprintf(fil, %7.3f , varGd1; /, Standard inputs if~opn~cbill < Lowest Copn, 9. cb+lO) 1 netout I 1.0; else netout = 0.0; ,, calculate target fprintfcfil, %6.lf\Il . netout i ,, target ifC(Cb % 500) == 1) printf C = %d\n , cb) ; vZ* // progress info l // generate entry signals. stop prices and limit prices signa1=0; if~opn~cb+ll c LOWest~opn, 3 , Cbl) ( // r u n only these PrepareNe ralmputs(var. cls, &I; I/ preprocess data rmset-inputvbmet, & arIll) ; ,, feed net inputs ntlfire Cnnet) ; ,, run the net neta ~ = ntlget~output~nnet, 0); /, get mtput netout *= 100.0; // scale to percent
Since the code for the bottom predictor model is almost identical to that of the timereversed Slow %K model, only the two blocks that contain changed code are presented above. In the first block of code, the time-reversed Slow %K is not used. Instead, a series of ones or zeros is calculated that indicates the presence (1) or absence (0) of bottoms (bottom target). When writing the facts, instead of writing the time-reversed Slow %K, the bottom target is written. In the second block of code, the roles for comparing the neural output with an appropriate threshold, and generating the actual entry buy signals, are implemented. In both blocks, code is included to prevent the writing of facts, or use of predictions, when tomorrow s open could not possibly be a bottom. Similar code fragments for the top predictor model appear below.
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