108 research outputs found
Detecting relevant changes in time series models
Most of the literature on change-point analysis by means of hypothesis
testing considers hypotheses of the form H0 : \theta_1 = \theta_2 vs. H1 :
\theta_1 != \theta_2, where \theta_1 and \theta_2 denote parameters of the
process before and after a change point. This paper takes a different
perspective and investigates the null hypotheses of no relevant changes, i.e.
H0 : ||\theta_1 - \theta_2|| ? \leq \Delta?, where || \cdot || is an
appropriate norm. This formulation of the testing problem is motivated by the
fact that in many applications a modification of the statistical analysis might
not be necessary, if the difference between the parameters before and after the
change-point is small. A general approach to problems of this type is developed
which is based on the CUSUM principle. For the asymptotic analysis weak
convergence of the sequential empirical process has to be established under the
alternative of non-stationarity, and it is shown that the resulting test
statistic is asymptotically normal distributed. Several applications of the
methodology are given including tests for relevant changes in the mean,
variance, parameter in a linear regression model and distribution function
among others. The finite sample properties of the new tests are investigated by
means of a simulation study and illustrated by analyzing a data example from
economics.Comment: Keywords: change-point analysis, CUSUM, relevant changes, precise
hypotheses, strong mixing, weak convergence under the alternative AMS Subject
Classification: 62M10, 62F05, 62G1
Misspecification Testing in a Class of Conditional Distributional Models
We propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates. The test is based on the Cramer-von Mises distance between an unrestricted estimate of the joint distribution function of the data, and a restricted estimate that imposes the structure implied by the model. The procedure is straightforward to implement, is consistent against fixed alternatives, has non-trivial power against local deviations of order n^-1/2 from the null hypothesis, and does not require the choice of smoothing parameters. In an empirical application, we use our test to study the validity of various models for the conditional distribution of wages in the US.Cramer-von Mises distance, quantile regression, distributional regression, location-scale model, bootstrap, wage distribution
CUSUM-Type testing for changing parameters in a spatial autoregressive model of stock returns
The paper suggests a CUSUM-type test for time-varying parameters in a recently proposed spatial autoregressive model for stock returns and derives its asymptotic null distribution as well as local power properties. As can be seen from Euro
Stoxx 50 returns, a combination of spatial modelling and change point tests allows
for superior risk forecasts in portfolio management
A generalized functional delta method
We develop a generalized functional delta method, where the considered random function
is not multiplied by a scalar, but by another function. It bases on a generalized Hadamard differentiability between special function spaces. For a certain class of functions, we calculate the Hadamard differential explicitely. We give an example, where the method allows for calculations that are not possible with previous methods
Monitoring stationarity and cointegration
We propose a monitoring procedure to detect a structural change from stationary to integrated
behavior. When the procedure is applied to the residuals of a relationship between
integrated series it thus monitors a structural change from a cointegrating relationship
to a spurious relationship. The cointegration monitoring procedure is based on residuals
from modified least squares estimation, using either Fully Modifi ed, Dynamic or Integrated
Modified OLS. The procedure is inspired by Chu et al. (1996) in that it is based
on parameter estimation on a pre-break \calibration" period only rather than being based
on sequential estimation over the full sample. We investigate the asymptotic behavior of
the procedures under the null, for ( fixed and local) alternatives and in case of parameter
changes. We also study the finite sample performance via simulations. An application to
credit default swap spreads illustrates the potential usefulness of the procedure
Monitoring correlation change in a sequence of random variables
We propose a monitoring procedure to test for the constancy of the correlation
coefficient of a sequence of random variables. The idea of the method is that a
historical sample is available and the goal is to monitor for changes in the correlation
as new data become available. We introduce a detector which is based on the
first hitting time of a CUSUM-type statistic over a suitably constructed threshold
function. We derive the asymptotic distribution of the detector and show that the
procedure detects a change with probability approaching unity as the length of the
historical period increases. The method is illustrated by Monte Carlo experiments
and the analysis of a real application with the log-returns of the Standard & Poor's
500 (S&P 500) and IBM stock assets
Dating multiple change points in the correlation matrix
We propose a nonparametric procedure for detecting and dating multiple change
points in the correlation matrix of a sequence of random variables. The procedure
is based on a test for changes in correlation matrices at an unknown point in time
recently proposed by Wied (2014). Although the procedure requires constant expectations
and variances, only mild assumptions on the serial dependence structure
are assumed. We show the validity of the procedure including the convergence rate
of the change point estimators. Moreover, we illustrate its performance in finite
samples by means of a simulation study and the analysis of a real data example
with financial returns. These examples show that the proposed algorithm has large
power in finite samples
Separate estimation of spatial dependence parameters and variance parameters in a spatial model
This paper suggests a two step estimation procedure for a spatial model with
different kinds of spatial dependence and heteroscedastic innovations. Since
maximum likelihood estimation is cumbersome due to the large number of parameters, we use a generalized method of moments approach to estimate the parameters of spatial correlation which does not need the large number of variance parameters to be known. For illustration purposes, we apply our
estimation procedure to daily stock returns of the Euro Stoxx 50 members. JEL subject classifications: C13, C51, G1
A simple and focused backtest of value at risk
We suggest a simple improvement of recent VaR-backtesting procedures
based on time intervals between VaR-exceedances and show via Monte
Carlo that our test has more power than its competitors against empirically
relevant clustering alternatives
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