Structure Learning and Break Detection in High-Frequency Data

The accurate learning of the underlying structure in high-frequency data has become critical in the analysis of time series for capturing valuable information that facilitates decision-making. The time series data in finance often is large, dynamic, heterogeneous and even structural unstable. Each aspect of these characteristics will add a degree of difficulty in efficient analysis. The goal of this dissertation is to discover the latent structure of dynamic high-frequency data that may have structural breaks, from both univariate and network perspective. We focus our analysis on durations between user-defined events in transaction-by-transaction stock prices from the Trade and Quotes (TAQ) data base at Wharton Research Data Services (WRDS). Our proposed approach can be easily adapted to other models. The dissertation has three main contributions. First, we propose a fast and accurate distribution-free approach using penalized martingale estimating functions on logarithmic autoregressive conditional duration (Log ACD) models. We discuss three approaches for parameter estimation. Our approach employs effective starting values from an approximating time series model and provides investigators accurate fits and predictions that can assist in trading decisions. Second, we propose a sequential monitoring scheme to detect structural breaks in the estimated parameters of a univariate piecewise Log ACD model. Based on martingale estimating function, this scheme does not require any distributional assumption. This monitoring scheme can detect structural breaks and choose model orders at the same time. Assuming data is given, we compare the performance of our scheme with that of a state-of-the-art offline scheme via simulation studies. Third, we propose a framework for detecting structural breaks in dynamic networks of a large number of stocks. In particular, we discover unobserved dynamic network structure from nodal observations governed by both the latent network and time. Our empirical analysis on the 30 most liquid stocks in S&P100 is an exploratory study. Such an analysis would be useful to economists studying the structural breaks in financial networks

Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models

The object of this paper is to produce non-parametric maximum likelihood estimates of forecast distributions in a general non-Gaussian, non-linear state space setting. The transition densities that define the evolution of the dynamic state process are represented in parametric form, but the conditional distribution of the non-Gaussian variable is estimated non-parametrically. The filtering and prediction distributions are estimated via a computationally efficient algorithm that exploits the functional relationship between the observed variable, the state variable and a measurement error with an invariant distribution. Simulation experiments are used to document the accuracy of the non-parametric method relative to both correctly and incorrectly specified parametric alternatives. In an empirical illustration, the method is used to produce sequential estimates of the forecast distribution of realized volatility on the S&P500 stock index during the recent financial crisis. A resampling technique for measuring sampling variation in the estimated forecast distributions is also demonstrated.Probabilistic Forecasting; Non-Gaussian Time Series; Grid-based Filtering; Penalized Likelihood; Subsampling; Realized Volatility.

Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets

This paper investigates the presence of bull and bear market states in stock price dynamics. A new definition of bull and bear market states based on sequences of stopping times tracing local peaks and troughs in stock prices is proposed. Duration dependence in stock prices is investigated through posterior mode estimates of the hazard function in bull and bear markets. We find that the longer a bull market has lasted, the lower is the probability that it will come to a termination. In contrast, the longer a bear market has lasted, the higher is its termination probability. Interest rates are also found to have an important effect on cumulated changes in stock prices: increasing interest rates are associated with an increase in bull market hazard rates and a decrease in bear market hazard rates.

The (mis)specification of discrete duration models with unobserved heterogeneity: a Monte Carlo study

Empirical researchers usually prefer statistical models that can be easily estimated using standard software packages. One such model is the sequential binary model with or without normal random effects; such models can be adopted to estimate discrete duration models with unobserved heterogeneity. But ease of estimation may come at a cost. In this paper we conduct a Monte Carlo simulation to evaluate the consequences of omitting or misspecifying the unobserved heterogeneity distribution in single-spell discrete duration models.discrete duration models, unobserved heterogeneity, Monte Carlo simulations

Forecasting Spikes in Electricity Prices

In many electricity markets, retailers purchase electricity at an unregulated spot price and sell to consumers at a heavily regulated price. Consequently the occurrence of extreme movements in the spot price represents a major source of risk to retailers and the accurate forecasting of these extreme events or price spikes is an important aspect of effective risk management. Traditional approaches to modeling electricity prices are aimed primarily at predicting the trajectory of spot prices. By contrast, this paper focuses exclusively on the prediction of spikes in electricity prices. The time series of price spikes is treated as a realization of a discrete-time point process and a nonlinear variant of the autoregressive conditional hazard (ACH) model is used to model this process. The model is estimated using half-hourly data from the Australian electricity market for the sample period 1 March 2001 to 30 June 2007. The estimated model is then used to provide one-step-ahead forecasts of the probability of an extreme event for every half hour for the forecast period, 1 July 2007 to 30 September 2007, chosen to correspond to the duration of a typical forward contract. The forecasting performance of the model is then evaluated against a benchmark that is consistent with the assumptions of commonly-used electricity pricing models.Electricity Prices, Price Spikes, Autoregressive Conditional Duration, Autoregressive

Quantile hidden semi-Markov models for multivariate time series

This paper develops a quantile hidden semi-Markov regression to jointly estimate multiple quantiles for the analysis of multivariate time series. The approach is based upon the Multivariate Asymmetric Laplace (MAL) distribution, which allows to model the quantiles of all univariate conditional distributions of a multivariate response simultaneously, incorporating the correlation structure among the outcomes. Unobserved serial heterogeneity across observations is modeled by introducing regime-dependent parameters that evolve according to a latent finite-state semi-Markov chain. Exploiting the hierarchical representation of the MAL, inference is carried out using an efficient Expectation-Maximization algorithm based on closed form updates for all model parameters, without parametric assumptions about the states’ sojourn distributions. The validity of the proposed methodology is analyzed both by a simulation study and through the empirical analysis of air pollutant concentrations in a small Italian city

New estimates of the risk and duration of registered unemployment in urban Russia

This paper examines whether deregistration from the employment office decreases unemployment duration. The study is based on Russian individual-level data from the Public Employment Office of Rostov-on-Don combined with information from the 2000 household survey. Using a proportional hazard model, I find a significant excess in job finding rates following employment office deregistration. The predicted risk of getting a job is non-monotonic and tends to decrease at longer duration intervals. An important finding is that only 29% of the unemployed obtained a job simultaneously with deregistering from the Public Employment Office. Others continued to search for job on their own