Forecasting Multivariate Time Series under Present-Value-Model Short- and Long-run Co-movement Restrictions

This paper has two original contributions. First, we show that the present value model (PVM hereafter), which has a wide application in macroeconomics and fi nance, entails common cyclical feature restrictions in the dynamics of the vector error-correction representation (Vahid and Engle, 1993); something that has been already investigated in that VECM context by Johansen and Swensen (1999, 2011) but has not been discussed before with this new emphasis. We also provide the present value reduced rank constraints to be tested within the log-linear model. Our second contribution relates to forecasting time series that are subject to those long and short-run reduced rank restrictions. The reason why appropriate common cyclical feature restrictions might improve forecasting is because it finds natural exclusion restrictions preventing the estimation of useless parameters, which would otherwise contribute to the increase of forecast variance with no expected reduction in bias. We applied the techniques discussed in this paper to data known to be subject to present value restrictions, i.e. the online series maintained and up-dated by Shiller. We focus on three different data sets. The fi rst includes the levels of interest rates with long and short maturities, the second includes the level of real price and dividend for the S&P composite index, and the third includes the logarithmic transformation of prices and dividends. Our exhaustive investigation of several different multivariate models reveals that better forecasts can be achieved when restrictions are applied to them. Moreover, imposing short-run restrictions produce forecast winners 70% of the time for target variables of PVMs and 63.33% of the time when all variables in the system are considered.

A unit root test based on partially adaptive estimation

This paper constructs a unit root test baseei on partially adaptive estimation, which is shown to be robust against non-Gaussian innovations. We show that the limiting distribution of the t-statistic is a convex combination of standard normal and DF distribution. Convergence to the DF distribution is obtaineel when the innovations are Gaussian, implying that the traditional ADF test is a special case of the proposed testo Monte Carlo Experiments indicate that, if innovation has heavy tail distribution or are contaminated by outliers, then the proposed test is more powerful than the traditional ADF testo Nominal interest rates (different maturities) are shown to be stationary according to the robust test but not stationary according to the nonrobust ADF testo This result seems to suggest that the failure of rejecting the null of unit root in nominal interest rate may be due to the use of estimation and hypothesis testing procedures that do not consider the absence of Gaussianity in the data.Our results validate practical restrictions on the behavior of the nominal interest rate imposed by CCAPM, optimal monetary policy and option pricing models.

Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

Efficient semiparametric estimation of quantile treatment effects

This paper presents calculations of semiparametric efficiency bounds for quantile treatment effects parameters when se1ection to treatment is based on observable characteristics. The paper also presents three estimation procedures forthese parameters, alI ofwhich have two steps: a nonparametric estimation and a computation ofthe difference between the solutions of two distinct minimization problems. Root-N consistency, asymptotic normality, and the achievement ofthe semiparametric efficiency bound is shown for one ofthe three estimators. In the final part ofthe paper, an empirical application to a job training program reveals the importance of heterogeneous treatment effects, showing that for this program the effects are concentrated in the upper quantiles ofthe earnings distribution.

Aggregate vs disaggregate data analysis: a paradox in the estimation of money demand function of Japan under the low interest rate policy

We investigate the issue of whether there was a stable money demand function for Japan in 1990's using both aggregate and disaggregate time series data. The aggregate data appears to support the contention that there was no stable money demand function. The disaggregate data shows that there was a stable money demand function. Neither was there any indication of the presence of liquidity trapo Possible sources of discrepancy are explored and the diametrically opposite results between the aggregate and disaggregate analysis are attributed to the neglected heterogeneity among micro units. We also conduct simulation analysis to show that when heterogeneity among micro units is present. The prediction of aggregate outcomes, using aggregate data is less accurate than the prediction based on micro equations. Moreover. policy evaluation based on aggregate data can be grossly misleading.

Bias from ignoring price dispersion in demand estimation

Consumers often pay different prices for the same product bought in the same store at the same time. However, the demand estimation literature has ignored that fact using, instead, aggregate measures such as the “list” or average price. In this paper we show that this will lead to biased price coefficients. Furthermore, we perform simple comparative statics simulation exercises for the logit and random coefficient models. In the “list” price case we find that the bias is larger when discounts are higher, proportion of consumers facing discount prices is higher and when consumers are more unwilling to buy the product so that they almost only do it when facing discount. In the average price case we find that the bias is larger when discounts are higher, proportion of consumers that have access to discount are similar to the ones that do not have access and when consumers willingness to buy is very dependent on idiosyncratic shocks. Also bias is less problematic in the average price case in markets with a lot of bargain deals, so that prices are as good as individual. We conclude by proposing ways that the econometrician can reduce this bias using different information that he may have available.

An evolving possibilistic fuzzy modeling approach for value-at-risk estimation

Market risk exposure plays a key role for nancial institutions risk management. A possible measure for this exposure is to evaluate losses likely to incurwhen the price of the portfolio's assets declines using Value-at-Risk (VaR) estimates, one of the most prominent measure of nancial downside market risk. This paper suggests an evolving possibilistic fuzzy modeling approach for VaR estimation. The approach is based on an extension of the possibilistic fuzzy c-means clustering and functional fuzzy rule-based modeling, which employs memberships and typicalities to update clusters and creates new clusters based on a statistical control distance-based criteria. ePFM also uses an utility measure to evaluate the quality of the current cluster structure. Computational experiments consider data of the main global equity market indexes of United States, London, Germany, Spain and Brazil from January 2000 to December 2012 for VaR estimation using ePFM, traditional VaR benchmarks such as Historical Simulation, GARCH, EWMA, and Extreme Value Theory and state of the art evolving approaches. The results show that ePFM is a potential candidate for VaR modeling, with better performance than alternative approaches.