Resampling in State Space Models∗
نویسنده
چکیده
Resampling the innovations sequence of state space models has proved to be a useful tool in many respects. For example, while under general conditions, the Gaussian MLEs of the parameters of a state space model are asymptotically normal, several researchers have found that samples must be fairly large before asymptotic results are applicable. Moreover, problems occur if the any of parameters are near the boundary of the parameter space. In such situations, the bootstrap applied to the innovation sequence can provide an accurate assessment of the sampling distributions of the parameter estimates. We have also found that a resampling procedure can provide insight into the validity of the model. In addition, the bootstrap can be used to evaluate conditional forecast errors of state space models. The key to this method is the derivation of a reverse-time innovations form of the state space model for generating conditional data sets. We will provide some theoretical insight into our procedures that show why resampling works in these situations, and we provide simulations and data examples that demonstrate our claims.
منابع مشابه
Reachability checking in complex and concurrent software systems using intelligent search methods
Software system verification is an efficient technique for ensuring the correctness of a software product, especially in safety-critical systems in which a small bug may have disastrous consequences. The goal of software verification is to ensure that the product fulfills the requirements. Studies show that the cost of finding and fixing errors in design time is less than finding and fixing the...
متن کاملRecursive Monte Carlo Filters: Algorithms and Theoretical Analysis
Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform the computations in general state space models. We discuss and compare the accept-reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept-reject version, and we compare ...
متن کاملMeasuring the Searched Space to Guide Efficiency: The Principle and Evidence on Constraint Satisfaction
Searched Space DEFINITION 1 State space: The total state space an evolutionary algorithm is able to search in is defined as . We assume all are equal, thus we know that and . DEFINITION 2 Searched space of an algorithm: The searched space is the set of points taken from the state space that is visited by a particular evolutionary algorithm during a run. DEFINITION 3 Resampling ratio: First we d...
متن کاملModeling Stock Return Volatility Using Symmetric and Asymmetric Nonlinear State Space Models: Case of Tehran Stock Market
Volatility is a measure of uncertainty that plays a central role in financial theory, risk management, and pricing authority. Turbulence is the conditional variance of changes in asset prices that is not directly observable and is considered a hidden variable that is indirectly calculated using some approximations. To do this, two general approaches are presented in the literature of financial ...
متن کاملTowards Smooth Particle Filters for Likelihood Estimation with Multivariate Latent Variables
In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling ste...
متن کامل