Tid: 22 februari 1999 kl 1515-1700
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Catalin Starica, Matematisk statistik, Chalmers Tekniska Högskola and The Wharton School, Philadelphia.
Titel: Change of structure in financial, long range dependence and the GARCH model.
Sammanfattning:
Functionals of a two-parameter integrated periodogram have been used for a long time for detecting changes in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram having as limit a Gaussian field. In the case of GARCH(p,q) processes a statistic closely related to the integrated periodogram can be used for the purpose of change detection in the model. We derive a central limit theorem for this statistic under the hypothesis of a GARCH(p,q) sequence with a finite 4th moment. Simulations show that our statistic is quite sensitive to changes of the parameters in the model and that it accurately detects the moment when a change of the model occurs.
When applied to real--life time series our method gives clear evidence of the fast pace of change in the data. One of the straightforward conclusions of our study is the infeasibility of modelling long return series with one GARCH model. The parameters of the model must be updated and we propose a method to detect when the update is needed.
Our study supports the hypothesis of global non--stationarity of the return time series. We bring forth both theoretical and empirical evidence that the long range dependence (LRD) type behaviour of the sample ACF and the periodogram of absolute return series documented in the econometrics literature could be due to the impact of non--stationarity on these statistical instruments.
Contrary to the common-hold belief that the LRD characteristic carries meaningful information about the price generating process, we show that the LRD behaviour could be just an artifact due to structural changes in the data. The effect that the switch to a different regime has on the sample ACF and the periodogram is theoretically explained and empirically documented using time series that were the object of LRD modelling efforts (Standard and Poors 500, DEM/USD FX) in various publications.
Joint work with Thomas Mikosch, University of Groningen.