What is this page about
Our stock market forecast system consists of two major parts: an extensive database and a forecast model. The forecast model reads the database and then makes a prediction of where the market is headed. From this prediction, we forecast a trading position for the the SP500 ETF (symbol SPY). The database and forecast are updated daily at the close of trading. This document gives some details of how this all works.

Introduction - the holy grail
Wouldn't it be great to have a model that would tell you with 100 percent certainty that the market will be going in a certain direction over some specified time period? Too bad that there is no such model, but If one did exist, we would know to buy before the market goes up and sell before the market goes down. There would be virtually no risk in being in or out of the market. Profits would just keep rolling in. The quest to find such a model has been attempted by many but without success. The reasons lie in the inherent randomness of the market and something called market efficiency. What this all means is that the signal that foretells the market direction is buried deep in the noise of normal trading and the signal varies in intensity over time. For a model to be even marginally successful, two conditions must be met. First, you must resolve (find) this signal, and second, you must be able to analyze it. Resolution is achieved by accounting for the statistical fluctuations in the market variables that we measure. The analysis is possible because of the fidelity and complexity of the modeling technique. We have managed to develop a forecast model that is far from perfect but does reasonably good job meeting these two requirements.

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What do we forecast
We have developed a mathematical model that predicts the direction of the market over the next trading day. The model forecasts the SP500, but the forecast also applies to the Dow Jones industrial Average (DJIA) since they are highly correlated. We use this direction to indicate a trading position which can be either long or short the SP500 SPIDER (symbol SPY) or the Dow DIAMONDS EFT (symbol DIA), or be in cash. This trading position is used only for the purpose of computing a model return. The trading position that you use should depend on other factors including your level of acceptable risk and your financial situation. The forecast is computed after the market closes so positions can be traded in the extended hours sessions or at the open of the next trading day.

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The forecast model and the ANO
We use an advanced neural network model in combination with a genetic algorithm to calculate the SP500 forecast. The calculations are somewhat complex but can be summarized by the following three procedural steps. Step one: the genetic algorithm is used to find the optimum neural network structures and inputs. This calculation basically determines how the networks will be wired. Step two: using the information from the first step, a set of networks is initialized and then trained on about 75 percent of the market data (in-sample) in our database, which currently consists of about 7200 days of data. We use an evolutionary program to train the networks (i.e. to determine the neural network weights). You should think of training as the process of teaching the networks to predict the best trading position. Step three: after training, the networks are rigorously tested on the remaining 25 percent of market data (out-of-sample). Networks that fail the test are discarded. Networks that pass the test are included in the library that we use to calculate our forecast. The number of neural networks currently in our library varies from day to day, but normally contains more than 400.

Input to the networks are technical and fundamental market data. The table below shows the types of data that are currently used by the model:

The above data are filtered and normalized and certain functions of these data are computed. We currently compute 63 separate input variables at the close of each trading day.

The 63 inputs are applied to a neural network and after some number crunching the network outputs a value between -1.0 and +1.0, with -1.0 being a very strong down market signal and +1.0 being a very strong up market signal. A value near zero would indicate a neutral market signal. We apply the inputs to each network in our library and an average of their outputs is computed. This average network output (ANO) is used with position setpoints to determine a trading position for the Dow Diamonds (symbol DIA) or the SP500 Spiders (symbol SPY) for the next trading day. When the computed value of the ANO is above the long position setpoint, a long position is indicated. When the value of the ANO is below the short position setpoint, a short position is indicated. When the ANO falls between these two setpoints, a cash position is indicated. Because of the timing of the update, trades may be made in the extended sessions or at open of the next trading day.

When computing our performance, all trades are assumed to take place at the session close. The current trading position along with recent ANO values and the ANO setpoints are shown on our forecast page.

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Setting stops
We highly recommend that you set trailing stops when you are not in cash. This is to protect your investment from unexpected market behavior. You might also want to use a hedging strategy (like the purchase of call or put options) to further reduce risk. The trailing stop is set at some percentage below the security purchase price when a long position is entered and a percentage above the security price when a short position is entered. The percentage you should use will depend on the volatility of the security and your risk tolerance. We currently use 5 percent for the Dow DIAMONDS. The stop value is raised (to maintain the percentage) for long positions when the closing price increases and lowered for short positions when the closing price decreases; otherwise, the stop value is not changed. If the closing price of your security hits the stop price, you have been stopped out which means that you should to exit your position and go to cash for at least two days. We publish the trailing stop value on the forecast web page.

Forecast the DJIA or the NASDAQ averages
The SP500 is a good estimator of many of the other indices. It's highly correlated with the DJIA and reasonability well with the NASDAQ 100 index . The chart below illustrates their relationships.

The correlation coefficient between the DJIA and the three ETFs - DIA, SPY, and QQQ are respectively: 0.99997, 0.99468, and 0.94711.

The table below shows a list of ETFs that you may want to consider trading with this model.

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A final word
We add market data to our database daily. We also make improvements (updates) to our model. Through this development, we often see that forecast errors made in the past are corrected in the training process. As a consequence, we see a continuous improvement in our forecast accuracy and in the correlation between the DJIA and the ANO. Our forecasts will never be 100 percent accurate and this fact needs to be factored into your investment strategies. Nevertheless, the quest for the holy grail continues, even though we know that it will never be found.

Contact us should you have any questions, suggestions, or comments.

This page was updated on: January 30, 2021.

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