  A standard model of (conditional) heteroscedasticity, i.e., the phenomenon
that the variance of a process changes over time, is the Generalized
AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is
especially important for economics and finance. GARCH models are typically
estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild
statistical assumptions. Here, we suggest a finite sample approach, called
ScoPe, to construct distribution-free confidence regions around the QML
estimate, which have exact coverage probabilities, despite no additional
assumptions about moments are made. ScoPe is inspired by the recently developed
Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH
case. ScoPe works by perturbing the score function using randomly permuted
residuals. This produces alternative samples which lead to exact confidence
regions. Experiments on simulated and stock market data are also presented, and
ScoPe is compared with the asymptotic theory and bootstrap approaches.
