Predicting Stock Returns Using a Variable Order Markov Tree Model

Abstract

The weak form of the Efficient Market Hypothesis (EMH) states that the current market price fully reflects the information of past prices and rules out predictions based on price data alone. In an efficient market, consistent prediction of the next outcome of a financial time series is problematic because there are no reoccurring patterns that can be used for a reliable prediction.This research offers an alternative test of the weak form of the EMH. It uses a universal prediction algorithm based on the Variable Order Markov tree model to identify re-occurring patterns in the data, constructs explanatory models, and predicts the next time-series outcome. Based on these predictions, it rejects the EMH for certain stock markets while accepting it for other markets.The weak form of the EMH is tested for four international stock exchanges: the German DAX index; the American Dow-Jones30 index; the Austrian ATX index and the Danish KFX index. The universal prediction algorithm is used with sliding windows of 50, 75, and 100 consecutive daily returns for periods of up to 12 trading years. Statistically significant predictions are detected for 17% to 81% of the ATX, KFX and DJ30 stock series for about 3% to 30% of the trading days. A summary prediction analysis indicates that for a confidence level of 99% the more volatile German (DAX) and American (DJ30) markets are indeed efficient. The algorithm detects periods of potential market inefficiency in the ATX and KFX markets that may be exploited for obtaining excess returns.

Context Based Predictive Information

“…Stock market time series analysis is an example of a real-world application of the CBPI algorithm. In this case, the SPI condition is a reasonable assumption because of market efficiency [ 15 ]. That is, in an efficient market only a few historical patterns or contexts exist that can be used for predictions, while most of these patterns are insignificant [ 15 ].…”

“…In this case, the SPI condition is a reasonable assumption because of market efficiency [ 15 ]. That is, in an efficient market only a few historical patterns or contexts exist that can be used for predictions, while most of these patterns are insignificant [ 15 ]. The dataset comprises minute-by-minute time series of stock prices of eight large banks in the U.S. for the period of January 2008–2010, which because of the banking crisis within these years, has a potential of nonzero in between banks [ 16 ].…”

“…To overcome this challenge, we utilize the CT algorithm, a lossy compression member of the family of variable order Markov models that were originally constructed for compression of a single time series and found to be well-suited to the prediction task of discrete time series [ 9 , 15 , 26 ]. These works extend the basic Markov model by proposing an algorithm for data compression that extract important sequences (i.e., “contexts”) not necessarily of the same order, which contained significant information about the conditioned symbol.…”

“…An important consideration is the relevancy of the binning to the domain from which data are sourced. The approach taken in this paper, following other works (e.g., [ 15 , 16 , 17 ]), is that after removing the uninformative sequences, domain-relevant insights could be immediately drawn. We also note that methods that are applied directly on real valued data are limited when dealing with time series where non-linear sequential characteristics are important (as opposed to treating every time lag as a feature on its own), and in addition, they suffer from limited explainability capabilities.…”

“…Due to market efficiency, PI between time series of stock prices is expected to be small or equal to zero. In the case of a small PI, most of the past sequences are uninformative, and the SPI condition might occur (e.g., see [ 15 ] and the discussion therein). We discuss these types of scenarios in the Results Section and exemplify the CBPI algorithm’s contribution by implementing it on a simulated setup for benchmarking it relative to other methods, as well as on real stock market data of eight large banks in the U.S.…”