98 research outputs found
A Study of the Allan Variance for Constant-Mean Non-Stationary Processes
The Allan Variance (AV) is a widely used quantity in areas focusing on error
measurement as well as in the general analysis of variance for autocorrelated
processes in domains such as engineering and, more specifically, metrology. The
form of this quantity is widely used to detect noise patterns and indications
of stability within signals. However, the properties of this quantity are not
known for commonly occurring processes whose covariance structure is
non-stationary and, in these cases, an erroneous interpretation of the AV could
lead to misleading conclusions. This paper generalizes the theoretical form of
the AV to some non-stationary processes while at the same time being valid also
for weakly stationary processes. Some simulation examples show how this new
form can help to understand the processes for which the AV is able to
distinguish these from the stationary cases and hence allow for a better
interpretation of this quantity in applied cases
A simple recipe for making accurate parametric inference in finite sample
Constructing tests or confidence regions that control over the error rates in
the long-run is probably one of the most important problem in statistics. Yet,
the theoretical justification for most methods in statistics is asymptotic. The
bootstrap for example, despite its simplicity and its widespread usage, is an
asymptotic method. There are in general no claim about the exactness of
inferential procedures in finite sample. In this paper, we propose an
alternative to the parametric bootstrap. We setup general conditions to
demonstrate theoretically that accurate inference can be claimed in finite
sample
On the Properties of Simulation-based Estimators in High Dimensions
Considering the increasing size of available data, the need for statistical
methods that control the finite sample bias is growing. This is mainly due to
the frequent settings where the number of variables is large and allowed to
increase with the sample size bringing standard inferential procedures to incur
significant loss in terms of performance. Moreover, the complexity of
statistical models is also increasing thereby entailing important computational
challenges in constructing new estimators or in implementing classical ones. A
trade-off between numerical complexity and statistical properties is often
accepted. However, numerically efficient estimators that are altogether
unbiased, consistent and asymptotically normal in high dimensional problems
would generally be ideal. In this paper, we set a general framework from which
such estimators can easily be derived for wide classes of models. This
framework is based on the concepts that underlie simulation-based estimation
methods such as indirect inference. The approach allows various extensions
compared to previous results as it is adapted to possibly inconsistent
estimators and is applicable to discrete models and/or models with a large
number of parameters. We consider an algorithm, namely the Iterative Bootstrap
(IB), to efficiently compute simulation-based estimators by showing its
convergence properties. Within this framework we also prove the properties of
simulation-based estimators, more specifically the unbiasedness, consistency
and asymptotic normality when the number of parameters is allowed to increase
with the sample size. Therefore, an important implication of the proposed
approach is that it allows to obtain unbiased estimators in finite samples.
Finally, we study this approach when applied to three common models, namely
logistic regression, negative binomial regression and lasso regression
A penalized two-pass regression to predict stock returns with time-varying risk premia
We develop a penalized two-pass regression with time-varying factor loadings.
The penalization in the first pass enforces sparsity for the time-variation
drivers while also maintaining compatibility with the no-arbitrage restrictions
by regularizing appropriate groups of coefficients. The second pass delivers
risk premia estimates to predict equity excess returns. Our Monte Carlo results
and our empirical results on a large cross-sectional data set of US individual
stocks show that penalization without grouping can yield to nearly all
estimated time-varying models violating the no-arbitrage restrictions.
Moreover, our results demonstrate that the proposed method reduces the
prediction errors compared to a penalized approach without appropriate grouping
or a time-invariant factor model
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