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Conventional measures of the risk of a financial asset make use of the unobserved (conditional) variance or standard deviation of its return. In this paper, we treat the observed absolute return as a measure of risk and explore its forecastability. Two simple models are considered. One is a new AR‐like model which is applied to the absolute return. The other is an ARCH‐like model called Asymmetric Power ARCH. The forecastability is evaluated with the average log‐likelihood of absolute return, instead of that of return itself. While the absolute return is interpreted as ‘volatility’, some quantities of its entire distribution, such as the 95th quantiles, can be interpreted as ‘volatility of volatility’. We apply both models to three stock indices, namely the Hang Seng Index, the Nikkei 225 Index and the Standard and Poors 500 Index. The new model by and large outperforms the ARCH‐like model in both in‐sample goodness of fit and post‐sample forecastability. It performs exceptionally well in the post‐sample period after the outbreak of the Asian financial crisis. Copyright © 2000 John Wiley & Sons, Ltd.

We examine whether economic growth is generated endogenously or exogenously, and estimute the externality effects due t o private and public capitul respectively. Applying a multivariate stochastic cointegrution method to US dutu. we find that the evidence is utlfrrvourublr t o the endogenous growth model with public infrustructure. The estimuted elusticity of output with respect to public capital is 0. I I , smaller tliun epicul vulues obtuined in single-eyuution regression studies. On the other hund. i f the share .f capitd income is tuken to be otie-third, then the spillover effect due t o privote capitul is positive but mu! be us low as 0.10.( 2 ) Only the first two cointegrating vectors are reported, and the vectors are normalized so that PI = 1.(3) Critical values for the hypotheses about cointegnting rank can be found in Table V of Johansen (1994). For example, the critical value of the Trace Test Statistic at 5% significance level is 42.35 for r = 0, 25.43 for r I and 12.49 for r S 2, and the critical value of the Maximum Eigenvalue Test Statistic at 5% significance level is 25.44 for r = 0, 19.16 for r S I and 12.49 for r S 2.run from 1927 to 1989.(4) The test statistic for H,: p, + pz + p3 = 0 and p4 ,= 0 is Chi-square distributed with 2 degrees of freedom.

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