Rutger Lit

Intraday Stochastic Volatility in Discrete Price Changes: the Dynamic Skellam Model

ABSTRACT We study intraday stochastic volatility for four liquid stocks traded on the New York Stock Exchange using a new dynamic Skellam model for high-frequency tick-by-tick discrete price changes. Since the likelihood function is analytically intractable, we rely on numerical methods for its evaluation. Given the high number of observations per series per day (1000 to 10,000), we adopt computationally efficient methods including Monte Carlo integration. The intraday dynamics of volatility and the high number of trades without price impact require nontrivial adjustments to the basic dynamic Skellam model. In-sample residual diagnostics and goodness-of-fit statistics show that the final model provides a good fit to the data. An extensive day-to-day forecasting study of intraday volatility shows that the dynamic modified Skellam model provides accurate forecasts compared to alternative modeling approaches. Supplementary materials for this article are available online.

The Dynamic Skellam Model with Applications

We introduce a dynamic statistical model for Skellam distributed random variables. The Skellam distribution can be obtained by taking differences between two Poisson distributed random variables. We treat cases where observations are measured over time and where possible serial correlation is modeled via stochastically time-varying intensities of the underlying Poisson counts. The likelihood function for our model is analytically intractable and we evaluate it via a multivariate extension of numerically accelerated importance sampling techniques. We illustrate the new model by two empirical studies and verify whether our framework can adequately handle large data sets. First, we analyze long univariate high-frequency time series of U.S. stock price changes, which evolve as discrete multiples of a fixed tick size of one dollar cent. In a second illustration, we analyze the score differences between rival soccer teams using a large, unbalanced panel of seven seasons of weekly matches in the German Bundesliga.In both empirical studies, the new model provides interesting and non-trivial dynamics with a clear interpretation.

Forecasting Football Match Results in National League Competitions Using Score-Driven Time Series Models

We develop a new dynamic multivariate model for the analysis and the forecasting of football match results in national league competitions. The proposed dynamic model is based on the score of the predictive observation mass function for a high-dimensional panel of weekly match results. Our main interest is to forecast whether the match result is a win, a loss or a draw for each team. To deliver such forecasts, the dynamic model can be based on three different dependent variables: the pairwise count of the number of goals, the difference between the number of goals, or the category of the match result (win, loss, draw). The different dependent variables require different distributional assumptions. Furthermore, different dynamic model specifications can be considered for generating the forecasts. We empirically investigate which dependent variable and which dynamic model specification yield the best forecasting results. In an extensive forecasting study, we consider match results from six large European football competitions and we validate the precision of the forecasts for a period of seven years for each competition. We conclude that our preferred dynamic model for pairwise counts delivers the most precise forecasts and outperforms benchmark and other competing models.

The analysis and forecasting of ATP tennis matches using a high-dimensional dynamic model

We propose a basic high-dimensional dynamic model for tennis match results with time varying player-specific abilities for different court surface types. Our statistical model can be treated in a likelihood-based analysis and is capable of handling high-dimensional datasets while the number of parameters remains small. In particular, we analyze 17 years of tennis matches for a panel of over 500 players, which leads to more than 2000 dynamic strength levels. We find that time varying player-specific abilities for different court surfaces are of key importance for analyzing tennis matches. We further consider several other extensions including player-specific explanatory variables and the accountance of specific configurations for Grand Slam tournaments. The estimation results can be used to construct rankings of players for different court surface types. We finally show that our proposed model can also be effective in forecasting. We provide evidence that our model significantly outperforms existing models in the forecasting of tennis match results.

Model-based Business Cycle and Financial Cycle Decomposition for Europe and the United States

Abstract: We introduce a model-based rather than a pure filtering approach to estimate the financial cycle from a panel of economic and financial time series for four large developed economies. The possible existence and dynamics of a financial cycle have gained momentum following the 2008 financial crisis and the subsequent European sovereign debt crisis. Cyclical fluctuations in macrofinancial variables appear to be not only caused by business cycle fluctuations but also by other secular swings in financial aggregates. It is widely established that such “financial cycles” have a typical length of between 10 and 30 years, which is substantially longer than a typical business cycle. Therefore, estimating the dynamics of such cycles is an important step in surveilling systemic stability.

Model-based Business Cycle and Financial Cycle Decomposition for Europe and the U.S

We develop a multivariate unobserved components model to extract business cycle and financial cycle indicators from a panel of economic and financial time series of four large developed economies. Our model is flexible and allows for the inclusion of cycle components in different selections of economic variables with different scales and with possible phase shifts. We find clear evidence of the presence of a financial cycle with a length that is approximately twice the length of a regular business cycle. Moreover, cyclical movements in credit related variables largely depend on the financial cycle, and only marginally on the business cycle. Property prices appear to have their own idiosyncratic dynamics and do not substantially load on business or financial cycle components. Systemic surveillance policies should therefore account for the different dynamic components in typical macro financial variables.