Siem Jan Koopman

Statistical algorithms for models in state space using SsfPack 2.2

This paper discusses and documents the algorithms of SsfPack 2.2. SsfPack is a suite of C routines for carrying out computations involving the statistical analysis of univariate and multivariate models in state space form. The emphasis is on documenting the link we have made to the Ox computing environment. SsfPack allows for a full range of different state space forms: from a simple time-invariant model to a complicated time-varying model. Functions can be used which put standard models such as ARIMA and cubic spline models in state space form. Basic functions are available for filtering, moment smoothing and simulation smoothing. Ready-to-use functions are provided for standard tasks such as likelihood evaluation, forecasting and signal extraction. We show that SsfPack can be easily used for implementing, fitting and analysing Gaussian models relevant to many areas of econometrics and statistics. Some Gaussian illustrations are given.

Stamp 5.0 : structural time series analyser, modeller and predictor

Part 1: installation procedure for STAMP. Part 2 Tutorials on structural time series modelling: getting started on simple univariate modelling tutorial on components tutorial on interventions and explanatory variables tutorial on multivariate models applications in macroeconomics and finance. Part 3 STAMP tutorials: the basic skills tutorial on graphics tutorial on data input and output tutorial on data transformation and description tutorial on model building and testing. Part 4 Statistical output: descriptive statistics statistical treatment of models model output output from STAMP model estimation selected model and estimation output summary statistics the sample period test hyperparameters variances and standard deviations cycle and AR(1) covariance matrices (multivariate models) factor loading matrices (multivariate models) transformed hyperparameters and standard errors final state analysis of state regression analysis seasonal tests cycle tests data in logs goodness of fit prediction error variance prediction error mean deviation coefficients of determination information criteria - AIC and BIC components series with components detrended seasonally adjusted individual seasonals data in logs joint components residuals correlogram periodogram and spectrum cumulative statistics and graphs distribution statistics heteroskedasticity. Part 5 STAMP manuals: general information STAMP files the information and binary data files (.IN7/.BN7) spreadsheet files (.XLS,.WKS,.WK1) human-readable files (.DAT) the information and ASCII data files (.IN7/.DAT) the print file (.PRN) results file (.OUT) PCX files (.PCX) algebra file (.ALG) forecast file (.STF) configuration file (STAMP.CFG) STAMP output the results window is full printscreen graphics the graphics window printing graphs graphics modes graphics display configuration limitations of STAMP memory management out of memory memory is low memory fragmentation saving memory command-line options session logging and playback lags the database size variable names missing values details of algebra STAMP menus. Part 6 Appendices: giveman file open configuration save configuration exit DataManager convert edit information file reconstruct information file compress information and binary file information video system setup colours install 800 x 600 x 16 HPP, PSP and NCDC GRAFPLUS user manual DOS extender manual STAMP error messages.

Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives

The analysis of non-Gaussian time series using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Monte Carlo Markov chain methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state vector given the observations, and the mean square errors of their estimates, are developed. These methods are extended to cover the estimation of conditional and posterior densities and distribution functions. Choice of importance sampling densities and antithetic variables is discussed. The techniques work well in practice and are computationally effcient. Their use is illustrated by applying to a univariate discrete time series, a series with outliers and a volatility series.

Estimation of stochastic volatility models via Monte Carlo maximum likelihood

This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chi-square disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favorably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Monte Carlo Markov chain (MCMC) method.

Time Series Analysis by State Space Methods: Second Edition

This new edition updates Durbin & Koopmans important text on the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbance terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. Additions to this second edition include the filtering of nonlinear and non-Gaussian series. Part I of the book obtains the mean and variance of the state, of a variable intended to measure the effect of an interaction and of regression coefficients, in terms of the observations. Part II extends the treatment to nonlinear and non-normal models. For these, analytical solutions are not available so methods are based on simulation.

Forecasting Hourly Electricity Demand Using Time-Varying Splines

Abstract A method for modeling a changing periodic pattern is developed. The use of time-varying splines enables this to be done relatively parsimoniously. The method is applied in a model used to forecast hourly electricity demand, with the periodic movements being intradaily or intraweekly. The full model contains other components, including a temperature response, which is also modeled using splines.

Periodic Seasonal Reg-ARFIMA-GARCH Models for Daily Electricity Spot Prices

Novel periodic extensions of dynamic long-memory regression models with autoregressive conditional heteroscedastic errors are considered for the analysis of daily electricity spot prices. The parameters of the model with mean and variance specifications are estimated simultaneously by the method of approximate maximum likelihood. The methods are implemented for time series of 1,200–4,400 daily price observations in four European power markets. Apart from persistence, heteroscedasticity, and extreme observations in prices, a novel empirical finding is the importance of day-of-the-week periodicity in the autocovariance function of electricity spot prices. In particular, the very persistent daily log prices from the Nord Pool power exchange of Norway are effectively modeled by our framework, which is also extended with explanatory variables to capture supply-and-demand effects. The daily log prices of the other three electricity markets—EEX in Germany, Powernext in France, and APX in The Netherlands—are less persistent, but periodicity is also highly significant. The dynamic behavior differs from market to market and depends primarily on the method of power generation: hydro power, power generated from fossil fuels, or nuclear power. The article improves on existing models in capturing the memory characteristics, which are important in derivative pricing and real option analysis.

Diagnostic Checking of Unobserved- Components Time Series Models

Diagnostic checking of the specification of time series models is normally carried out using the innovations—that is, the one-step-ahead prediction errors. In an unobserved-components model, other sets of residuals are available. These auxiliary residuals are estimators of the disturbances associated with the unobserved components. They can often yield information that is less apparent from the innovations, but they suffer from the disadvantage that they are serially correlated even in a correctly specified model with known parameters. This article shows how the properties of the auxiliary residuals may be obtained, how they are related to each other and to the innovations, and how they can be used to construct test statistics. Applications are presented showing how residuals can be used to detect and distinguish between outliers and structural change.

Exact Initial Kalman Filtering and Smoothing for Nonstationary Time Series Models

Abstract This article presents a new exact solution for the initialization of the Kalman filter for state space models with diffuse initial conditions. For example, the regression model with stochastic trend, seasonal and other nonstationary autoregressive integrated moving average components requires a (partially) diffuse initial state vector. The proposed analytical solution is easy to implement and computationally efficient. The exact solution for smoothing is also given. Missing observations are handled in a straightforward manner. All proofs rely on elementary results.

A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations

We propose a new class of observation-driven time-varying parameter models for dynamic volatilities and correlations to handle time series from heavy-tailed distributions. The model adopts generalized autoregressive score dynamics to obtain a time-varying covariance matrix of the multivariate Student t distribution. The key novelty of our proposed model concerns the weighting of lagged squared innovations for the estimation of future correlations and volatilities. When we account for heavy tails of distributions, we obtain estimates that are more robust to large innovations. We provide an empirical illustration for a panel of daily equity returns.