Predictability of asset returns has immediate interest for investment practitioners and farreaching implications for the efficacy of asset prices in allocating capitals. Focus in this literature has been on the predictability of the level or conditional mean of asset returns (e.g., Fama 1970, 1991, Jegadeesh 1990, Lo and MacKinlay 1999, Poterba and Summers 1988). In this paper, we investigate the predictability of the direction of changes in economic variables, such as interest rates, inflation rates, exchange rates and stock prices.
The direction of changes in economic variables may be a reasonable proxy for a utility-based measure of forecasting performance. Leitch and Tanner (1991, 1995) find that the direction-of-change criterion is the best proxy among several commonly used criteria for choosing forecasts of interest rates on their ability to maximize expected trading profits. There exist important circumstances under which the direction-of-change criterion is exactly the right one for maximizing the economic welfare (e.g., profit) of the forecaster, as is nicely demonstrated in Granger and Pesaran (1999, Sections 2-4) and Leitch and Tanner (1995) from a perspective of decision-making under uncertainty. In finance, directional predictability in asset returns has important implications for market timing, which is crucial for active asset allocation management. In Merton’s (1981) classical market timing model, mutual fund managers care about the direction of excess returns, rather than their magnitude.
Most commonly used technical trading rules in financial markets are based on the prediction of the directions of financial returns. Profitable trading strategies may result if one can predict return directions. Many financial institutions evaluate forecast algorithms using the percentage of times that the algorithms predict the right-trend (see Lequarre 1993). In macroeconomists, there has been also interested in forecasting probabilities of important economic events (e.g., Diebold and Lopez 1996, Fair 1993), which, in many cases, can be formulated as the probabilities of the direction of changes in underlying economic variables.
For example, macroeconomists and investment practitioners are always interested in forecasting business cycles turning points (e.g., Wecker 1979, Boldin 1994). Central banks under pegged exchange rate systems are often interested in the direction of changes in the exchange rate. They might need to intervene to support the currency if it is expected to depreciate beyond certain threshold. Over the past few years, some central banks, including the Bank of England, have been setting the nominal interest rate according to their forecasts of the inflation rate, increasing the interest rate if their forecast of the inflation rate exceeds a politically determined threshold.
The rationale behind directional forecasts is that the patterns in economic variables may recur in the future so that the direction of changes in economic variables is predictable using historical data. The main goal of this paper is to develop a mode-free omnibus test for directional predictability and apply it to document whether the direction of stock price changes is predictable using the history of past stock price changes. Most, if not all, of the existing works in this literature are concerned with directional predictability of various models, algorithms, and investment strategies. There have been a number of popular tests for the market timing ability of these models and trading strategies (Henriksson and Merton 1981, Cumby and Modest 1987, Pesaran and Timmermann 1992). However, the directional predictability of an underlying data generating process is not the same as the predictive ability of a directional forecast model or a trading strategy. There has been no model-free test available in the literature that can check directional predictability of data, which is the key to the success of any directional forecast model or trading strategy.
Some economic and financial theory suggests that the direction of asset returns may be predictable. For example, the naive overreaction theory predicts price reversals after investors overreact to certain market events such as release of firm-specific information, which implies a negative autocorrelation in direction. More sophisticated behavioral theory (e.g., Barberis, Sheleifer and Vishny 1998, Hong and Stein 1999) predicts a short horizon underreaction and then a long horizon overreaction, implying positive autocorrelations in direction over a short horizon and negative autocorrelations in direction over a long horizon. The market contagion hypothesis, on the other hand, suggests that during a turmoil period, a large adverse price movement in one market will be more closely followed by a large adverse price movement in another market, regardless of market fundamentals. This implies a stronger positive cross-correlation in direction between two markets during the turmoil period. In the foreign exchange markets, it is often argued that the exchange rate may follow long swings it drifts upward for a considerable period of time and then switches to a long period with downward drift (e.g., Engle 1994, Engle and Hamilton 1990).
As a consequence, there will tend to be runs in one direction and then the other in the changes of the exchange rate. Such persistence pattern in the direction of changes is thus predictable. From an econometric perspective, the direction of asset returns is predictable using past returns if the conditional mean of asset returns is time-varying (i.e., when the market is not efficient). Christoffersen and Diebold (2002) show that even if the conditional mean is not predictable (i.e., the market is efficient), directional predictability can be driven solely from volatility clustering, as long as the long-run average asset return is nonzero. Breen, Glosten and Jagannathan (1989, p.1184) also point out that given a positive expected excess return, the probability of an up market is a function of both conditional mean and conditional variance. Some empirical works, based on various models and technical trading rules, appear to suggest that it is easier to forecast the direction of asset returns than the level of asset returns (e.g., Breen, Glosten and Jagannathan 1989, Engle 1994, Kuan and Liu 1995, Larsen and Wozniak 1995, Leitch and Tanner 1991, 1995, Pesaran and Timmermann 1995, 2000, Satchell 1995).
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