We survey the empirical literature on floating nominal exchange rates over the past decade. Exchange rates are difficult to forecast at short- to medium-term horizons. There is a bit of explanatory power to monetary models such as the Dornbusch "overshooting " theory, in the form of reaction to "news " and in forecasts at long-mn horizons. Nevertheless, at short horizons, a driftless random walk characterizes exchange rates better than standard models based on observable macroeconomic fundamentals. Unexplained large shocks to floating rates must then, logically, be due either to innovations in unobservable fundamentals, or to non-fundamental factors such as speculative bubbles. The observed difference in exchange rate and macroeconomic volatility under different nominal exchange rate regimes makes us skeptical of the first view. The theory and evidence on speculative bubbles, however, is not conclusive. We conclude with the hope that promising new studies of the microstructure of the foreign exchange

this paper (based on a different data set) was presented at the 1992 North American Winter Meeting of the Econometric SocietyinNew Orleans, Louisiana.

Neural networks have been shown to be a promising tool for forecasting financial time series. Several design factors significantly impact the accuracy of neural network forecasts. These factors include selection of input variables, architecture of the network, and quantity of training data. The questions of input variable selection and system architecture design have been widely researched, but the corresponding question of how much information to use in producing high-quality neural network models has not been adequately addressed. In this paper, the effects of different sizes of training sample sets on forecasting currency exchange rates are examined. It is shown that those neural networks---given an appropriate amount of historical knowledge ---can forecast future currency exchange rates with 60 percent accuracy, while those neural networks trained on a larger training set have a worse forecasting performance. In addition to higher-quality forecasts, the reduced training set sizes reduce development cost and time.

this article, we will describe (yet) another source of difficulty that arises in the analysis of time series data. The particular problem of detecting nonlinear structure --- either by comparison of the data to linear surrogate data, or by comparing linear and nonlinear predictors --- is seen to be complicated when the data exhibits long coherence times. In this section we define some terms and discuss linear modeling of time series. Section 2 describes the method of surrogate data, and compares two approaches to generating surrogate data. We find that both have difficulties trying to mimic data with long coherence time. We illustrate these problems with real and computer-generated time series in Section 3, including the time series E.dat from the the SFI competition. In the last section, we discuss what it is about the analysis or the data that is problematic.

Drawdowns (loss from the last local maximum to the next local minimum) are essential aspects of risk assessment in investment management. They o#er a more natural measure of real market risks than the variance or other cumulants of daily (or some other fixed time scale) distributions of returns. Here, we extend considerably our previous analysis by analyzing the major financial indices, the major currencies, gold, the twenty largest U.S. companies in terms of capitalisation as well as nine others chosen randomly. We find for the major financial markets that approximately 98% of the distributions of drawdowns is well-represented by an exponential (or a minor modification of it with a slightly fatter tail), while the largest to the few ten largest drawdowns are occurring with a significantly larger rate than predicted by the exponential: the largest drops thus constitute genuine outliers. This is confirmed by extensive testing on surrogate data, which unambiguously show that large stock ...

From a computation-theoretic standpoint, this paper formalizes the notion of unpredictability in the efficient market hypothesis (EMH) by a biological-based search program, i.e., genetic programming (GP). This formalization differs from the traditional notion based on probabilistic independence in its treatment of search. Compared with the traditional notion, a GP-based search provides an explicit and efficient search program upon which an objective measure for predictability can be formalized in terms of search intensity and chance of success in the search. This will be illustrated by an example of applying GP to predict chaotic time series. Then, the EMH based on this notion will be exemplied by an application to the Taiwan and U.S. stock market. A short-term sample of TAIEX and S&P 500 with the highest complexity dened by Rissanen's MDLP (Minimum Description Length Principle) is chosen and tested. It is found that, while linear models cannot predict better than the random walk, a GP-based search can beat random walk by 50%. It therefore confirms the belief that while the shortterm nonlinear regularities might still exist, the search costs of discovering them might be too high to make the exploitation of these regularities protable, hence the efficient market hypothesis is sustained.

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this paper, that observation is extended. Even when the bleaching is constrained to relatively low order (by the Akaike criterion, for instance), and even for tasks other than detecting nonlinear structure, we find that the effect of bleaching on chaotic data can be detrimental. On the other hand, bleaching

While search plays an important role in the efficient market hypothesis (EMH), the traditional formalization of the EMH, based on probabilistic independence, fails to capture it. Due to this failure, recent findings of nonlinear tests misled us into concluding that the EMH is rejected. Even though most economists are reluctant to make this conclusion, the traditional formalization leaves us no other choice. This paper reformalizes the EMH with a biologically-based search program, i.e., genetic programming (GP). The GP-based search enables us to model search in the EMH explicitly. Through this, search cost as well as search intensity can be measured objectively, and the notion of predictability and protability can then be formalized. The GP-based notion of the EMH will be exemplied by testing the EMH with a small, medium and large sample of the S&P 500 stock index.

This paper considers testing that an economic time series follows a martingale difference process. The martingale dierence hypothesis has been typically tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or in the periodograms. Tests based on these statistics are inconsistent since they just test necessary conditions of the null hypothesis. In this paper we consider tests that are consistent against all fixed alternatives and against Pitmans local alternatives. Since the asymptotic distributions of the tests statistics depend on the data generating process, the tests are implemented using a modification of the wild bootstrap procedure. The paper justifies theoretically the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments. In addition we include an application to exchange rate data.