Econometric Time Series
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Econometric Time Series
2016-07-23
Estimating the Integrated Parameter of the Time-Varying Parameter Self-Exciting Process
http://d.repec.org/n?u=RePEc:arx:papers:1607.05831&r=ets
We introduce and show the existence of a continuous time-varying parameter extension model to the self-exciting point process. The kernel shape is assumed to be exponentially decreasing. The quantity of interest is defined as the integrated parameter over time $T^{-1} \int_0^T \theta_t^* dt$, where $\theta_t^*$ is the time-varying parameter. To estimate it na\"{i}vely, we chop the data into several blocks, compute the maximum likelihood estimator (MLE) on each block, and take the average of the local estimates. Correspondingly, we give conditions on the parameter process and the block length under which we can establish the local central limit theorem, and the boundedness of moments of order $2\kappa$ of the local estimators, where $\kappa > 1$. Under those assumptions, the global estimator asymptotic bias explodes asymptotically. As a consequence, we provide a non-na\"{i}ve estimator, which is constructed as the na\"{i}ve one when applying a first-order bias reduction to the local MLE. We derive such first-order bias formula for the self-exciting process, and provide further conditions under which the non-na\"{i}ve global estimator is asymptotically unbiased. Finally, we obtain the associated global central limit theorem.
Simon Clinet
Yoann Potiron
2016-07
Estimating Aggregate Autoregressive Processes When Only Macro Data are Available
http://d.repec.org/n?u=RePEc:chf:rpseri:rp1443&r=ets
The aggregation of individual random AR(1) models generally leads to an AR(infinity) process. We provide two consistent estimators of aggregate dynamics based on either a parametric regression or a minimum distance approach for use when only macro data are available. Notably, both estimators allow us to recover some moments of the cross-sectional distribution of the autoregressive parameter. Both estimators perform very well in our Monte-Carlo experiment, even with finite samples.
Eric JONDEAU
Florian PELGRIN
Autoregressive process, Aggregation, Heterogeneity
Tests for an end-of-sample bubble in financial time series
http://d.repec.org/n?u=RePEc:not:notgts:16/02&r=ets
In this paper we examine the issue of detecting explosive behaviour in economic and financial time series when an explosive episode is both ongoing at the end of the sample, and of finite length. We propose a testing strategy based on the sub-sampling methods of Andrews (2003), in which a suitable test statistic is calculated on a finite number of end-of-sample observations, with a critical value obtained using sub-sample test statistsics calculated on the remaining observations. This approach also has the practical advantage that, by virtue of how the critical values are obtained, it can deliver tests which are robust to, among other things, conditional heteroskedasticity and serial correlation in the driving shocks. We also explore modifications of the raw statistics to account for unconditional heteroskedasticity using studentisation and a White-type correction. We evaluate the finite sample size and power properties of our proposed procedures, and find that they offer promising levels of power, suggesting the possibility for earlier detection of end-of-sample bubble episodes compared to exisitng procedures.
Sam Astill
David Harvey
Stephen Leybourne
Robert Taylor
Rational bubble; Explosive autoregression; Right-tailed unit root testing: Sub-sampling.