- A. Harvey and R. Ito (2017) Modeling Time Series With Zero Observations, Nuffield College Economics Working Paper 2017-W01, Oxford University.
- Abstract: We consider situations in which a significant proportion of observations in a time series are zero, but the remaining observations are positive and measured on a continuous scale. We propose a new dynamic model in which the conditional distribution of the observations is constructed by shifting a distribution for non-zero observations to the left and censoring negative values. The key to generalizing the censoring approach to the dynamic case is to have (the logarithm of) the location/scale parameter driven by a filter that depends on the score of the conditional distribution. An exponential link function means that seasonal effects can be incorporated into the model and this is done by means of a cubic spline (which can potentially be timevarying). The model is fitted to daily rainfall in northern Australia and compared with a dynamic zero-augmented model.
- R. Ito (2017) Long Memory and Fractional Differencing: Revisiting Clive W. J. Granger's Contributions and Further Developments, European Journal of Pure and Applied Mathematics, 10:82-103. In "Sir Clive W.J. Granger Memorial Special Issue on Econometrics" edited by D. Hendry and J. Castle.
- Abstract: In 1980, Sir Clive W. J. Granger discovered the fractional differencing operator and its fundamental properties in discrete-time mathematics, which sparked an enormous literature concerning
the fractionally integrated autoregressive moving average models. Fractionally integrated models capture a type of long memory and have useful theoretical properties, although scientists can find them difficult to estimate or intuitively interpret. His introductory papers from 1980, one of which with Roselyne Joyeux, show his early and deep understanding of this subject by showing
that familiar short memory processes can produce long memory effects under certain conditions. Moreover, fractional differencing advanced our understanding of cointegration and the properties of traditional Dickey-Fuller tests, and motivated the development of new unit-root tests against fractional alternatives. This article honors his significant contributions by identifying key areas of research he inspired and surveying recent developments in them.
- R. Ito (2016) Asymptotic Theory for Beta-t-GARCH, Cambridge Working Papers in Economics CWPE1607, University of Cambridge. [Revisory resubmission at Econometric Theory].
- Abstract: The dynamic conditional score (DCS) models with variants of Student's t innovation are gaining popularity in volatility modeling, and studies have found that they outperform GARCH-type models of comparable specifications. DCS is typically estimated by the method of maximum likelihood, but there is so far limited asymptotic theories for justifying the use of this estimator for non-Gaussian distributions. This paper develops asymptotic theory for Beta-t-GARCH, which is DCS with Student's t innovation and the benchmark volatility model of this class. We establish the necessary and sufficient condition for strict stationarity of the first-order Beta-t-GARCH using one simple moment equation, and show that its MLE is consistent and asymptotically normal under this condition. The results of this paper theoretically justify applying DCS with Student's t innovation to heavy-tailed data with a high degree of kurtosis, and performing standard statistical inference for model selection using the estimator. Since GARCH is Beta-t-GARCH with infinite degrees of freedom, our results imply that Beta-t-GARCH can capture the size of the tail or the degree of kurtosis that is too large for GARCH.
- (Link to faculty website for CWPE1607)
- R. Ito (2016) Spline-DCS for Forecasting Trade Volume in High-Frequency Finance, Cambridge Working Papers in Economics CWPE1606, University of Cambridge. [Supplementary material.]
- Abstract: We develop the spline-DCS model and apply it to trade volume prediction, which remains a highly non-trivial task in high-frequency finance. Our application illustrates that the spline-DCS is computationally practical and captures salient empirical features of the data such as the heavy-tailed distribution and intra-day periodicity very well. We produce density forecasts of volume and compare the model's predictive performance with that of the state-of-the-art volume forecasting model, named the component-MEM, of Brownlees et al. (2011). The spline-DCS significantly outperforms the component-MEM in predicting intra-day volume proportions.
- (Link to faculty website for CWPE1606)
- R. Ito (2013) Modeling Dynamic Diurnal Patterns in High Frequency Financial Data, Cambridge Working Papers in Economics CWPE1315, University of Cambridge.
- Abstract: We introduce the spline-DCS model with a dynamic cubic spline as a way of capturing periodic behavior in financial data that evolves over time. Our empirical application provides evidence for changing diurnal patterns in the high-frequency financial data we study. We illustrate that this generalization can lead to an improvement in the quality of the fit of the model to the empirical distribution of data, especially in the tail region, for an extended out-of-sample period. Moreover, it can lead to a substantial improvement in predicting intra-day volume proportions, which is a key ingredient in high-frequency trading algorithms. Our novel approach gives new insights into regular trading behavior and how it responds to changing market conditions.
- (Link to faculty website for CWPE1315)