We offer a novel way of thinking about the modelling of the time-varying distributions of financial asset returns. Borrowing ideas from symbolic data analysis, we consider data representations beyond scalars and vectors. Specifically, we consider a quantile function as an observation, and develop a new class of dynamic models for quantile-function-valued (QF-valued) time series. In order to make statistical inferences and account for parameter uncertainty , we propose a method whereby a likelihood function can be constructed for QF-valued data, and develop an adaptive MCMC sampling algorithm for simulating from the posterior distribution. Compared to modelling realised measures,modelling the entire quantile functions of intra-daily returns allows one to gain more insight into the dynamic structure of price movements. Via simulations, we show that the proposed MCMC algorithm is effective in recovering the posterior distribution, and that the posterior means are reasonable point estimates of the model parameters. For empirical studies, the new model is applied to analysing one-minute returns of major international stock indices. Through quantile scaling, we further demonstrate the usefulness of our method by forecasting one-step-ahead the Value-at-Risk of daily returns.
Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we develop a time-series model for forecasting quantile-function-valued (QF-valued) daily summaries for intra-daily returns. We call this model the dynamic quantile function (DQF) model. Instead of a histogram, we propose to use a g-and-h quantile function to summarise the distribution of intra-daily returns. We work with a Bayesian formulation of the DQF model in order to make statistical inference while accounting for parameter uncertainty ; an efficient MCMC algorithm is developed for sampling-based posterior inference. Using ten international market indices and approximately 2,000 days of out-of-sample data from each market, the performance of the DQF model compares favourably, in terms of forecasting VaR of intra-daily returns , against the interval-valued and histogram-valued time-series models. Additionally, we demonstrate that the QF-valued forecasts can be used to forecast VaR measures at the daily timescale via a simple quantile regression model on daily returns (QR-DQF). In certain markets, the resulting QR-DQF model is able to provide competitive VaR forecasts for daily returns.
R
We offer a novel way of thinking about the modelling of the time-varying distributions of financial asset returns. Borrowing ideas from
Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of
R
consider data representations beyond scalars and vectors. Specifically, we consider a quantile function as an observation, and develop a new class of dynamic models for
develop a time-series model for forecasting
R
time series. In
daily summaries for intra-daily returns. We call this model the dynamic quantile function (DQF) model. Instead of a histogram, we propose to use a g-and-h quantile function to summarise the distribution of intra-daily returns. We work with a Bayesian formulation of the DQF model in
R
inferences and account
inference while accounting
R
, we propose a method whereby a likelihood function can be constructed for QF-valued data, and develop an adaptive MCMC sampling algorithm for simulating from the posterior distribution. Compared to modelling realised measures,modelling the entire quantile functions of
; an efficient MCMC algorithm is developed for sampling-based posterior inference. Using ten international market indices and approximately 2,000 days of out-of-sample data from each market, the performance of the DQF model compares favourably, in terms of forecasting VaR of
R
allows one to gain more insight into the dynamic structure of price movements. Via simulations, we show that the proposed MCMC algorithm is effective in recovering the posterior distribution, and that the posterior means are reasonable point estimates of the model parameters. For empirical studies, the new model is applied to analysing one-minute returns of major international stock indices. Through quantile scaling, we further demonstrate the usefulness of our method by forecasting one-step-ahead the Value-at-Risk of
, against the interval-valued and histogram-valued time-series models. Additionally, we demonstrate that the QF-valued forecasts can be used to forecast VaR measures at the daily timescale via a simple quantile regression model on daily returns (QR-DQF). In certain markets, the resulting QR-DQF model is able to provide competitive VaR forecasts for