Three Essays on the Study of Persistence via Impulse-Response Confidence Bands with Application to Autoregressive Moving Average (ARMA) Processes

Abstract

The two-step simulation-based method introduced in this thesis combines Indirect Inference jointly with Monte Carlo (MC) test methods to deliver identification robust confidence sets for finite samples. In the first chapter, a general framework is introduced, which considers three auxiliary estimating functions: two-sided forward and backward looking regressions with leads and lags, long- autoregressions and empirical autocorrelations. The first simulation stage is incorporated to calibrate parameter estimates. In the second simulation stage, the resulting objective functions are inverted applying the MC test to obtain joint confidence sets. The empirical focus is on Autoregressive Moving Average (ARMA) processes, since identification and boundary issues raise enduring complications for estimation and inference. In particular, simultaneous impulse-responses confidence bands are derived for ARMA processes via confidence set projections. Supporting simulation studies illustrate the accurate size and good power of our method. The following chapters introduce further refinements to our framework with empirical applications. The second chapter investigates the persistence of oil shocks via impulse-response confidence bands. For the particular case of non-Gaussian Stable distribution, the “Local” Monte Carlo (LMC) test method is applied in the second stage, which is based on calibrations of the nuisance parameters of skewness and kurtosis. By studying long and short weekly samples as well as monthly samples, we find that shocks to oil returns are not permanent, since they are able to dissipate in short to middle time frames of approximately twenty periods. Our findings support the usefulness of impulse-responses obtained from asymmetric and heavy tailed distributions as a tool to understand the uncertainty surrounding commonly applied forecasting techniques. Lastly, the third chapter assesses the persistence of shocks on a measure of idiosyncratic risk (MIR) computed for a non-diversifiable portfolio of Telecom stocks. The two-stage simulation based method is applied with a particular refinement; the average of the statistics of the three estimating functions is computed as a forth resulting test statistic to harvest information from the other three. We conclude that a shock to the MIR can be described as having a short-lived large impact and relatively small oscillatory effects, which remain close to zero approximately after eight months.