In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962--1985) and for all subperiod for a variety of aggregate returns indexes and size-sorted portofolios. Although the rejections are due largely to the behavior of small stocks, they cannot be attributed completely to the effects of infrequent trading or timevarying volatilities. Moreover, the rejection of the random walk for weekly returns does not support a mean-reverting model of asset prices.

After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expected under a normal distribution. There are a number of possible explanations. A popular one is that the stock market is governed by chaotic dynamics. What exactly is chaos and how is it related to nonlinear dynamics? How does one detect chaos? Is there chaos in financial markets? Are there other explanations of the movements of financial prices other than chaos? The purpose of this paper is to explore these issues. -1Chaos has captured the fancy of many macroeconomists and financial economists. The attractiveness of chaotic dynamics is its ability to generate large movements which appear to be random, with greater frequency than linear models. As a result, there has been an explosion of pa...

this paper is to derive an ecient fully-adaptive procedure for estimating

System identification is the art and science of building mathematical models of dynamic systems from observed input-output data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous necessity for successful applications. System identification is a very large topic, with different techniques that depend on the character of the models to be estimated: linear, nonlinear, hybrid, nonparametric etc. At the same time, the area can be characterized by a small number of leading principles, e.g. to look for sustainable descriptions by proper decisions in the triangle of model complexity, information contents in the data, and effective validation. The area has many facets and there are many approaches and methods. A tutorial or a survey in a few pages is not quite possible. Instead, this presentation aims at giving an overview of the “science ” side, i.e. basic principles and results and at pointing to open problem areas in the practical, “art”, side of how to approach and solve a real problem. 1.

This paper investigates the empirical characteristics of investor risk aversion over equity return states by estimating a time-varying pricing kernel, which we call the empirical pricing kernel (EPK). We estimate the EPK on a monthly basis from 1991 to 1995, using S&P 500 index option data and a stochastic volatility model for the S&P 500 return process. We find that the EPK exhibits countercyclical risk aversion over S&P 500 return states. We also find that hedging performance is significantly improved when we use hedge ratios based the EPK rather than a time-invariant pricing kernel.

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We apply the local linear regression technique for estimation of functional-coefficient regression models for time series data. The models include threshold autoregressive models (Tong 1990) and functional-coefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better post-sample forecasting performance. We have also proposed a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross-validatory estimation for the expected forecasting errors. The proposed methodology is data-analytic and is of appreciable flexibility to analyze complex and multivariate nonlinear structures without suffering from the "curse of dimensionality". The asymptotic properties of the proposed estimators are investigated under the ff-mixing condition. Both simulated and real data examples are used for illustration. Key Words: ff-mixing; Asymptotic normali...

We study the inflation uncertainty reported by individual forecasters in the Survey of Professional Forecasters 1969-2001. Three popular measures of uncertainty built from survey data are analyzed in the context of models for forecasting and asset pricing, and improved estimation methods are suggested. Popular time series models are evaluated for their ability to reproduce survey measures of uncertainty. The results show that disagreement is a better proxy of inflation uncertainty than what previous literature has indicated, and that forecasters underestimate inflation uncertainty. We obtain similar results for output growth uncertainty.

This paper uses the Specific-to-General methodological approach that is widely used in science, in which problems with existing theories are resolved as the need arises, to illustrate a number of important developments in the modelling of univariate and multivariate financial volatility. Twenty frequently arising issues in analysing timevarying univariate and multivariate conditional volatility and stochastic volatility are discussed. In view of some of these difficulties, including the number of parameters to be estimated, and the computational complexities associated with multivariate conditional volatility models and both univariate and multivariate stochastic volatility models, automated inference is argued to be unhelpful to modelling in empirical financial econometrics. Some suggestions for future research are also presented. *The author wishes to acknowledge helpful discussions with Manabu Asai, Massimiliano

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