The instability of wealth effect on consumption over the business cycles is widely recognized in recent empirical studies. We develop a consumption and investment problem for an investor with direct preference for wealth under regime switches in assets return processes. Furthermore, the model is extended to allow the investor's borrowing rate to be higher than her risk-free rate. An utility-maximizing policy is derived such that optimal consumption-wealth ratio depends not only on both current and future regimes, but also on the transition across different regimes. Numerical simulation demonstrates that low frequent changes in regimes produce in-stability of consumption-wealth ratio, while high frequent regime-changes produce stable consumption-wealth ratio. These features are enhanced by investor's wealth accumulation motive and tighter credit spread between borrowing rate and risk-free rate, both of which can be applied to explain the instability of consumption-wealth ratio observed in the U.S.
Negative correlation between the previous day's stock return and today's volatility is widely observed in many stock markets. This relationship is known as the leverage effect in the literature and has been regarded as an indisputable stylized fact among researchers. Recently, however, some studies found that the leverage effect in the EGARCH model might be non-linear and the impact of the past return on the present volatility could be better approximated by a higher-order Hermite polynomial. In our study, we attempt to extend this non-linear leverage approach to the stochastic volatility model, instead of the EGARCH model. Since it is difficult to estimate a stochastic volatility model with a higher-order Hermite polynomial leverage even in the Bayesian MCMC approach, we apply particle learning for Bayesian estimation of this non-linear time series model.
For stock index returns in the major markets, we found some supportive evidence for the existence of the non-linear leverage effect in the stochastic volatility model.
This paper evaluates density forecasts using micro data from the ESP forecast (ESPF), a monthly survey of Japanese professional forecasters. The ESPF has collected individual density forecasts since June 2008. We employ two approaches, Probability Integral Transform (PIT) and Ranked Probability Score (RPS). First, we apply Berkowitz's (2001) test to individual density forecasts produced every June. We fail to reject the independency in FY 2010 and 2011 real GDP growth rates. As for CPI inflation rates, we reject the independency in all the samples during FY 2008 to 2011, but fail to reject it if the sample is limited to a half with better forecast performance.
The result may ensure individual densities coincide with unobserved true data generation process of the actual outcomes. Second, we calculate RPS, following Kenny, Kostka, and Masera (2012), and compare the Mean Probability Distribution (MPD), the average of individual densities, with three benchmarks -- Uniform, Normal and Naive distributions -- and individual density forecasts. The MPD turns out to be a "good" density: it beats the benchmarks in most cases and ranks about fifth out of around 35 participants every year. Subjective judgments added to the MPD are likely to deteriorate the performance in the case of CPI inflation rate, but to improve in the case of real GDP growth rate.