Jeremy Penzer

Diagnosing Shocks in Time Series

Abstract Efficient means of modeling aberrant behavior in times series are developed. Our methods are based on state-space forms and allow test statistics for various interventions to be computed from a single run of the Kalman filter smoother. The approach encompasses existing detection methodologies. Departures commonly observed in practice, such as outlying values, level shifts, and switches, are readily dealt with. New diagnostic statistics are proposed. Implications for structural models, autoregressive integrated moving average models, and models with explanatory variables are given.

State space models for time series with patches of unusual observations

An alternative to leave-k-out diagnostics for detecting patches of outlying points in time series is developed. We propose that unusual behaviour should be modelled by the addition of shocks. By including shocks in the transition equation of a state space model, we admit the possibility of a persistent change associated with a patch of outliers. Persistent change may take the form of a level shift or a change in seasonal pattern. We provide an efficient mechanism for computing diagnostic statistics associated with the addition of k shocks using a simple adaptation of the Kalman filter. Statistics for detecting unspecified patterns of shocks and an interpretation of the output of the associated smoothing algorithm are derived. Illustrations using real series are given. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

Five Year Prediction of the Number of Hurricanes that make United States Landfall

The insurance industryis interested in five-year predictions of the number of Atlantic hurricanes which will make landfall in the United States. Here we describe a suite of models developed by Risk Management Solutions, Inc. to make such predictions. These models represent a broad spectrum of view-points to be used as a basis for an expert elicitation.

Weather Derivative Pricing and the Normal Distribution: Comparing Three Fitting Schemes using the Out-of-Sample Log-Likelihood Scoring System

Many common weather indices are very close to being normally distributed, and it may be reasonable to assume they are exactly normally distributed for the purpose of pricing weather derivatives. Given that assumption, how should the indices be modelled? We use the expected out-of-sample log-likelihood score to compare 3 schemes: standing normal fitting, adjusted variance normal fitting, and the t-distribution.

Finite sample prediction and interpolation for ARIMA models with missing data

A transformation which allows Cholesky decomposition to be used to evaluate the exact likelihood function of an ARIMA model with missing data has recently been suggested. This method is extended to allow calculation of finite sample predictions of future observations. The output from the exact likelihood evaluation may also be used to estimate missing series values. Copyright