Volume 17, Issue 2

We develop a new consistent conditional moment test of functional form based on nuisance parameter indexed sample moments first presented in Bierens. We reduce the nuisance parameter space to known countable sets, which leads to a weighted average conditional moment test in the spirit of Bierens and Ploberger’s integrated conditional moment test (ICM). The weights are possibly stochastic in an arbitrary way, integer-indexed and flexible enough to cover a range of tests from average to higher quantile to maximum tests. The limit distribution under the null and local alternative belong to the same class as the ICM statistic, hence our test is admissible if the errors are Gaussian, and a flat weight leads to the greatest weighted average local power.

This paper contributes to the empirical literature on inflation zone targeting by estimating monetary reaction functions in a non-linear cointegration framework for Brazil, Chile, Colombia and Mexico. Evidence shows that central banks respond linearly to deviations of expected inflation from the target (the inflation gap) in Brazil and Chile. As the inflation gap widens, policy responses become weaker in Colombia and Mexico, a finding that most probably reflects a history of adverse supply shocks rather than a lack of resolve from the monetary authorities. Non-linearity is also found in the central bank’s response to fluctuations in the exchange rate in Brazil and Colombia.

In this paper, we examine the S&P 500 index log-returns on short intraday time scales with three different ARMA-GARCH models. In order to forecast market risk, we describe the innovation process with tempered stable distributions which we compare to commonly used methods in financial modeling. Value-at-risk backtests are provided where we find that models based on the tempered stable innovation assumption significantly outperform traditional models in forecasting risk on short time-scales. In addition to value-at-risk, the idiosyncratic differences in average value-at-risk are compared between the models.

This paper introduces quasi-maximum likelihood estimator for multivariate diffusions based on discrete observations. A numerical solution to the stochastic differential equation is obtained by higher order Wagner-Platen approximation and it is used to derive the first two conditional moments. Monte Carlo simulation shows that the proposed method has good finite sample property for both normal and non-normal diffusions. In an application of estimating stochastic volatility models, we find evidence of closeness between the CEV model and the GARCH stochastic volatility model. This finding supports the discrete time GARCH modeling of market volatility.

We derive the conditions under which time-varying cointegration leads to cointegration spaces that may be time-invariant or, in contrast, time-varying. The model of interest is a vector error correction model with arbitrary time-varying cointegration parameters. We clarify the role of identification and normalization restrictions and show that structural breaks in error-correction models may actually correspond to stable long-run economic relationships, as opposed to a single-equation setup, in which an identification restriction is imposed. Moreover, we show that, in a time-varying cointegrating relationship with a given number of variables and cointegration rank, there is a minimum number of orthogonal Fourier functions that most likely guarantees time-varying cointegrating spaces.

Misspecification of agents’ information sets or expectation formation mechanisms may lead to noncausal autoregressive representations of asset prices. Within the class of linear (vector) autoregressions, annual US stock prices are found to be best described by noncausal models, implying that agents’ expectations are not revealed to an outside observer such as an econometrician observing only realized market data. A simulation study shows that noncausal asset prices are observed when the data are generated by asset-pricing models featuring heterogeneous expectations.

We propose a state space model with Markov switching, whose regimes are associated with the model parameters and regime transition probabilities are modeled using wavelets. The estimation is based on the maximum likelihood method using the EM algorithm and a bootstrap method is proposed in order to assess the distribution of the maximum likelihood estimators. To evaluate the state variables and regime probabilities, the Kalman filter and a probability filter procedure conditional on each possible regime, at each instant, are used. These procedures are evaluated with simulated data and illustrated with the US monthly industrial production index from July 1968 to February 2011.