Back to the future: an empirical investigation into the validity of stock index models over time

Abstract

The use of technical analysis to predict security price movements from past price series has been supported by a number of academic research studies. These studies are broadly based on the premise that a technical trading rule should have constant validity over time. This premise is in accord with the practitioner rational for technical analysis, which is that, in the securities markets, history tends to repeat itself due to the relative constancy of human behaviour. The primary purpose of this paper is to investigate the extent to which technical trading rules have constant validity over time by determining the extent to which rules derived entirely from a particular time period can have validity over a variety of different time periods. It is found that rules derived from the data from the early period can be predictive at a later date and, rather unexpectedly, can even exceed the predictive power of rules derived from more contemporary data. It is hypothesized that this may be due to a decreasing signal to noise ratio in the data as the volatility of the index increases over time. The findings tend to support the assertion that, with respect to share trading, ‘history repeats itself’ with the caveat that there are factors that confound modelling in later periods.

Notes

¹ In particular, moving average and trading-range breakout rules are used. Moving average rules generate buy and sells signals by comparing short-run moving averages with long-run moving averages. For example, a buy signal may be generated when the average index over the last 5 days is above the average for the last 150 days, and similarly a sell signal generated when the short run average is below the long run average. There are many variations on these rules – the length of the short and long-run averages can be changed, often the short-run average is just a single day's index. A band of, say, 1% may be introduced so that a buy signal is generated only if the short-term average is more than 1% above the long-term average, and more than 1% below for the sell signal. The trading-range breakout rule triggers a sell (buy) signal if the stock price moves below (above) a ‘support’ (resistance) level defined as the minimum (maximum) price achieved by the stock over a previous period. As for the moving average rules, it is possible to produce variants by defining the support and resistance levels over different period lengths and by introducing band widths around these levels.

² This corresponds to the longest moving average period used by Hudson et al. and therefore provides a point of comparison with that paper. The use of the 200 input neural network captures any possible technical trading rule that could be developed from the previous 200 days of data.

³ The independent validation approach uses a portion of the training data as a validation set, which does not have input to the training process but rather is used to decide when training is complete. During training the performance of the network on the validation set is monitored and training is regarded as complete when performance on the validation set is maximized.

⁴ Note that the neural network is not being used here to generate a time series model. Each day is considered as a ‘case’, which has associated with it variables corresponding to the last 200 index values for use as inputs to the network. This approach allows the random selection of the validation set from throughout the data available for model building, thus making it more representative of the time interval as a whole. The inclusion of the necessary historical data with each case also means that the network does not need to be trained on each day in sequence, nor a continuous set of days, in order to learn.

⁵ The format of these results is again in line with Hudson et al.

⁶ Sample size may be an issue in these comparisons; Hudson et al. are able to use the whole sample in their tests whereas here most of the data is used to generate the models. The samples are therefore only around 25% of the size of those used in Hudson et al. To check the effect of this a model was constructed using the period as a whole with the last 25% (quarter 4) being used as the holdout, thus providing a comparison with the fourth sub-period result in Hudson et al. using a comparable sample size. The t-values in this test exceed those in Hudson et al. as does the difference between the means on rise/steady days and that on fall days. These results suggest that technical trading rules may not be using all the available information content in the data.

⁷ To check that the results here are not peculiar to neural networks logistic regression models were also built using quarter 1 and quarter 4 training data and tested these on the quarter 4 holdout. The quarter 1 model achieves a higher t-value and the difference between the means on rise/steady days and that on fall days is also greater. In both cases the results are not so strong as with the neural models, indicating a non-linear component in the relationships being modelled.