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We propose to estimate the weight matrix used for forecast reconciliation as parameters in a general linear model in order to quantify its uncertainty. This implies that forecast reconciliation can be formulated as an orthogonal projection…
We consider the well-studied problem of predicting the time-varying covariance matrix of a vector of financial returns. Popular methods range from simple predictors like rolling window or exponentially weighted moving average (EWMA) to more…
Some time series can be hierarchically organized into levels based on certain characteristics, such as geography or other attributes of interest. These series are referred to as hierarchical time series. Typically, forecasts are generated…
We suggest two classes of multivariate GARCH--models which are both easy to estimate and perform well in forecasting the covariance matrix of more than one hundred stocks. We apply methods from random matrix theory (RMT) to determine the…
Several academics have studied the ability of hybrid models mixing univariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and neural networks to deliver better volatility predictions than purely econometric…
A plethora of static and dynamic models exist to forecast Value-at-Risk and other quantile-related metrics used in financial risk management. Industry practice tends to favour simpler, static models such as historical simulation or its…
Forecast reconciliation adjusts independently generated forecasts so that they satisfy some known constraints. While probabilistic forecast reconciliation is well established for linear constraints, some practical forecasting problems…
Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze…
This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the…
Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts which satisfy a given set of linear constraints for a multivariate time series. In this paper we extend…
Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with…
Multivariate GARCH models are important tools to describe the dynamics of multivariate times series of financial returns. Nevertheless, these models have been much less used in practice due to the lack of reliable software. This paper…
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an…
This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling…
The practical importance of coherent forecasts in hierarchical forecasting has inspired many studies on forecast reconciliation. Under this approach, so-called base forecasts are produced for every series in the hierarchy and are…
We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…
Linearly constrained multiple time series may be encountered in many practical contexts, such as the National Accounts (e.g., GDP disaggregated by Income, Expenditure and Output), and multilevel frameworks where the variables are organized…
This paper is concerned with portfolio optimization models for creating high-quality lists of recommended items to balance the accuracy and diversity of recommendations. However, the statistics (i.e., expectation and covariance of ratings)…
In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the…
Forecast reconciliation of multivariate time series is the process of mapping a set of incoherent forecasts into coherent forecasts to satisfy a given set of linear constraints. Commonly used projection matrix based approaches for point…