Forecasting realized volatility using a long-memory stochastic volatility model : estimation, prediction and seasonal adjustment

In this paper we investigate the relationship between volatility, measured by realized volatility, and trading volume. We show that volume and volatility are long memory but they are not driven by the same latent factor as suggested by the fractional cointegration analysis. We analyze the degree of tail dependence of the two series finding that this is induced by the extreme dependence in the volatility and volume innovations. Tail dependence is particularly interesting, since, it is informative on the specific behavior of the volatility and volume when large surprising news impact the market. We use a fractionally integrated VAR with shock distributions modeled with a mixture of copulae functions to describe the joint dynamics. The model is able to capture the main characteristic of the series, say long memory, marginal non-normality and tail dependence. Once that long memory is removed, past volume are informative about the present volatility, and this result can be exploited for forecasting purposes. This evidence should be therefore taken into account when building a realistic model, linking volatility and volume.

/pdf/long-memory-and-tail-dependence-in-trading-volume-and-2a7mtsdam6.pdf

Long Memory and Tail Dependence in Trading Volume and Volatility

School of Economics and Management

In this contribution, we consider models in discrete time that contain a latent process for volatility. The most well-known model of this type is the Long-Memory Stochastic Volatility (LMSV) model. We describe its main properties, discuss parametric and semiparametric estimation for these models, and give some generalizations and applications.

/pdf/stochastic-volatility-models-with-long-memory-36yjogh69a.pdf

Stochastic Volatility Models with Long Memory

We develop a Bayesian procedure for analyzing stationary long-range dependent
 processes. Specifically, we consider the fractional exponential model (FEXP) to estimate
 the memory parameter of a stationary long-memory Gaussian time series. In particular, we
 propose a hierarchical Bayesian model and make it fully adaptive by imposing a prior
 distribution on the model order. Further, we describe a reversible jump Markov chain
 Monte Carlo algorithm for variable dimension estimation and show that, in our context,
 the algorithm provides a reasonable method of model selection (within each repetition of
 the chain). Therefore, through an application of Bayesian model averaging, we
 incorporate all possible models from the FEXP class (up to a given finite order).
 As a result we reduce the underestimation of uncertainty at the model-selection stage as
 well as achieve better estimates of the long memory parameter. Additionally, we
 establish Bayesian consistency of the memory parameter under mild conditions on the data
 process. Finally, through simulation and the analysis of two data sets, we demonstrate
 the effectiveness of our approach.

/pdf/a-bayesian-approach-to-estimating-the-long-memory-parameter-nfdk0f2738.pdf

A Bayesian approach to estimating the long memory parameter

In this paper, we consider a method (splitting) for calculating the auto- covariances of fractional integrated processes (ARFIMA) and generalized integrated processes (GARMA). The splitting method does not require any restriction on the autoregressive roots, and allows fast calculation of the autocovariances of these processes.

A note on calculating autocovariances of long‐memory processes

In this paper, we consider a method (splitting) for calculating the autocovariances of fractional integrated processes (ARFIMA) and generalized integrated processes (GARMA). The splitting method does not require any restriction on the autoregressive roots, and allows fast calculation of the autocovariances of these processes.

A Note on Calculating Autocovariances of Long-memory Processes

/pdf/bootstrap-cointegration-tests-in-ardl-models-kpe139sp.pdf

Bootstrap cointegration tests in ARDL models

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A note on calculating autocovariances of long‐memory processes

A Note on Calculating Autocovariances of Long-memory Processes

Bootstrap cointegration tests in ARDL models