International Stock Market Prediction using Artificial Neural Networks

AC 299r Independent Study

Chang Liu

Supervisor: Neil Shephard

Motivation

A body of literature in financial economics suggests that international equity markets can have cross-market momentum, where one market in a region correlates with another market in that region (or possibly in a different region) in a lagged manner. Profitable trading strategies are devised to exploit the predictability of future prices using cross market momentum. With the promising predictive power of neural networks in many successful applications including finance time series prediction, we are motivated to apply neural networks with powerful learning capacity to predict international stock market.

Previous studies primarily focus on the dynamics among selected major country indices such as the US, UK, Germany, and China, while ignoring the dynamics with other countries in the same region or across regions. In this study, we seek to investigate the price predictability of the international equity indices by looking at regional indices as well as major country indices that cover the world equity markets according to the MSCI world classification. We use large, liquid iShares Exchange-Traded-Funds (ETF) and SPDR S&P 500 ETF data downloaded from Yahoo! Finance.

Methodology

Problem Statement

It is a common issue that spurious cross-autocorrelation can be a result of thinly traded markets, asynchronous trading, or both. To minimize these impacts, we have used large, liquid iShares Exchange-Traded-Funds (ETF) trade data for international equity indices downloaded from Yahoo! Finance. Most of the international ETFs track the MSCI equity regional or country indices and trade in the US market hours. For the US market, we use SPDR S&P 500 ETF data downloaded from Yahoo! Finance. The coverage of ETFs is similar to the MSCI world equity index classification, except that we have both major country indices and the regional indices excluding countries (which usually make up a substantial percentage of the regional index capitalization), in order to better separate the effect of the two. The comprehensive coverage also represents three major market time zones: Asia Pacific, Europe, and America time zones.

Further, we break daily returns of a region or country into intraday and overnight returns that are driven by fundamentally different drivers, depending on the overlapping time zones and hence formulate the following problem:

Feature Engineering

The following momentum indicators are selected from the literature that are reported to have the more predictive power than other technical indicators. They are all based on price and volume information at or before time t:

• Exponential and Simple Moving Averages over k-period rolling window
• Past k-period volatility
• AD: number of advancing stocks at time t minus that of declining stocks
• ADV: volume of advancing stocks at time t minus that of declining stocks
• Past k-period change in price
• Past k-period log return
• Past k-period stochastic oscillator %K and stochastic oscillator %D
• Larry William’s R%
• Disparity
• Day of week

The parameter k is selected by the author within a range of 5 days for all indicators. For exponential moving averages, k = 1,2,3…,10,15,20,25.

Feature Selection

With the above technical indicators, and 3 types of (lagged intraday/overnight/daily) cross-sectional returns, plus the last available price of the target region, we have more than 60 input features with much redundant information. From practice, it adds noise that the neural network confuses with signals so that the results are not satisfactory. We use 1000 Random Forest Regressors with Mean Square Error as the criterion for selecting the top 20 optimal features in the total in-sample period (i.e. the samples that model is allowed to see in during training and validation).

Neural Network Architecture

• A 2-layer fully-connected network: 20 input units - 24 hidden units - 3 hidden units - 1 output unit
• Mean Square Loss function
• ADAM optimizer
• ReLu activation for all nodes except linear activation for output node
• L2 penalty; max norm constraints of weights; dropout layers
• Monitor training process – early stopping if validation not improving
• Normalize inputs by z-score transformation

Ensemble Forecasting Method

We break the time series into multiple rolling windows of training-validation-test sets. For each window, we train 1000 neural networks on the training set and choose the top 50% models by accuracy rates on the validation set. They form a committee and output an average prediction as the final decision. The prediction pipeline can be summarized as follows:

Evaluation Metrics

To measure how close our predictions are to the true returns, we use directional accuracy, the percentage of times of our predictions are in the same direction (i.e., positive or negative returns) as the true returns. This metric is only used to measure the validation accuracy for model selection of the ensemble neural net. As for the final prediction, we want to measure its ability to predict large values and the model performance as a trading strategy. For an incorrect prediction in terms of direction, a loss is incurred; otherwise, a profit is gained. Thus we use a new accuracy metric according to Chen et al (2017) on the test set.

To evaluate the risk-reward ratio for our trading models, Sharpe ratio is commonly used a standard and calculate Sharpe ratio based on the adjusted returns for our models accordingly:

Experimental Results

We test our models from 2015-09-08 to 2017-04-07 over 400 market days for Asia ex Japan which fewer data, and from 2015-02-05 to 2017-04-07 over 800 market days for all other regions. Results are shown as follows. For comparison, a baseline is calculated as the fraction of positive returns in the test set, which does not vary with the proportion of transaction.

We can make several observations:

• For overnight returns, on average, all the models perform slightly better than the baseline, except for Asia ex Japan. For intraday returns, on average, the models perform on par with the baselines. This suggests that there is predictive information in the features of overnight returns across all regions. One reason might be that the trading outside the exchange hours does not happen as often as within them, so that the market does not react as timely as information arrives. In addition, in a less efficient after-hour market, the bid-ask spreads are probably higher in trading; therefore, to access the execution feasibility of the trading strategy, it would be helpful to compute the break-even trading costs based on our model returns to compare with real-world trading costs.

• A prediction accuracy higher than the baseline is not always equivalent to a good Sharpe ratio or feasible strategy; nor does a feasible strategy require a high prediction accuracy. For example, our ensemble neural net has below baseline accuracy in predicting overnight returns in Asia ex Japan. Yet, its Sharpe ratio is significantly above 1.0 and outperforms the benchmark models. This suggests a small proportion of good predictions that turn out to earn large returns can outweigh a large proportion of bad predictions with smaller losses. On the other hand, the benchmark models with higher-than-baseline accuracy, for example in predicting Canada overnight returns, can have zero or even negative Sharpe ratios. Therefore, it is important to observe consistency in both accuracy and Sharpe ratio curves to confirm performance stability of a model.

• In terms of Sharpe ratio, our ensemble neural net outperforms the benchmarks in predicting intraday returns in China and overnight returns in Asia ex Japan. In all other cases, its performance is on average at par or even worse than the benchmark models. The sub-par performance highlights one potential issue with the neural net that the ensemble after model averaging can still have variation that cause performance instability, because the neural nets with powerful learning capacity can mistake noises as true patterns in the data. However, given the large set of neural network hyper-parameters (precise architecture, learning rate, convergence criteria, regularization, etc), we have minimal amount of fine-tuning the algorithm, striking a balance between an overly-tuned model and simplicity. It is certainly possible to select optimal parameters using other machine learning algorithms such as particle swarm optimization and genetic algorithm. Another explanation for the performance instability is that we have given very similar input features for all experiments; however, returns of different types and regions may have different dynamics and require specialized features.

Concluding Remarks

In this study, we propose to predict the intraday and overnight returns of international equity indices that cover most of the world equity markets. To minimize spurious correlations due to low liquid or asynchronous trading, we use large, liquid Exchange-Traded-Funds trade data that closely track MSCI regional indexes or the S&P 500. We aim to predict the next intraday or overnight returns of an ETF based on the last available price and volume information. We computed the technical indicators of the price and volume information and selected the most important features as inputs. Then we train an ensemble of neural networks and benchmark it with Lasso and Ridge, in terms of adjusted accuracy rates and Sharpe ratio. The results show that in all regions except for Asia ex Japan, all the models outperform the baseline in predicting overnight returns in terms of directional accuracy, which suggests predictability of cross-market momentum. However, quantifying to what extent the result can be attributed to thin markets for overnight returns is outside the scope of this study.

In addition, our ensemble of 2-layer models is on average on par with the regularized linear models as benchmarks. This highlight some issues regarding application of neural networks to financial time series: 1) much of the nuisance the neural net learns (better than a simple linear model) in financial time series can be just noise, which is random or inherently unpredictable. 2) to fine-tuning an ensemble to beat linear methods, the computational cost and risks of over-fitting are high; and 3) to improve the overall performance, no matter what method to use, one could focus on engineering the appropriate features in addition to tuning the model.

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