We consider a time series model with autoregressive conditional heteroscedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the...

In this paper, we present two robust estimates for ARCH(p) models: A - and filtered A-estimates. These are defined by the minimization of conveniently robustified likelihood functions. The robustification is achieved by replacing the mean square error of the standardized observations with the...

This paper develops the idea of renewal time sampling, a novel sampling scheme constructed from stopping times of semimartingales. Based on this new sampling scheme we propose a class of volatility estimators named renewal based volatility estimators. In this paper we show that: (1) The spot...

Many high frequency economic or financial time series display two empirical characteristics: high kurtosis and positive autocorrelation in the centred and squared observations. The first-order autocorrelation is typically low, and the autocorrelation function decays slowly. These series are...

This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications, the inference methods, and the main areas of application of these models in financial econometrics

This paper introduces ARCHModels.jl, a package for the Julia programming language that implements a number of univariate and multivariate ARCH-type models. This model class is the workhorse tool for modelling the conditional volatility of financial assets. Their distinguishing feature is that...

We establish consistency and asymptotic normality of the quasi-maximum likelihood estimator in the linear ARCH model. Contrary to existing literature we allow the parameters to be in the region where no stationary version of the process exists

We explore some aspects of the analysis of latent component structure in non-stationary time series based on time-varying autoregressive (TVAR) models that incorporate uncertainty on model order. Our modelling approach assumes that the AR coefficients evolve in time according to a random walk...

The Japanese version of this paper can be found at "http://ssrn.com/abstract=2710516" http://ssrn.com/abstract=2710516.Many macroeconomic study argued macroeconomic models should be aggregated by micro processes models ("micro-foundation") and many micro-founded macroeconomic models were built....

The estimation for time series models with heavy-tailed innovations has been widely discussed in the literature, while the corresponding goodness-of-fit tests have attracted less attention. This is mainly because the commonly used autocorrelation function in constructing goodness-of-fit tests...