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Michael Stanley Smith

Selected Works

Articles 1 - 9 of 9

Full-Text Articles in Econometrics

Inversion Copulas From Nonlinear State Space Models With An Application To Inflation Forecasting, Michael S. Smith, Worapree Ole Maneesoonthorn May 2018

Inversion Copulas From Nonlinear State Space Models With An Application To Inflation Forecasting, Michael S. Smith, Worapree Ole Maneesoonthorn

Michael Stanley Smith

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas …

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Real-Time Macroeconomic Forecasting With A Heteroskedastic Inversion Copula, Ruben Loaiza-Maya, Michael S. Smith May 2018

Real-Time Macroeconomic Forecasting With A Heteroskedastic Inversion Copula, Ruben Loaiza-Maya, Michael S. Smith

Michael Stanley Smith

There is a growing interest in allowing for asymmetry in the density forecasts of macroeconomic variables. 
In multivariate time series, this can be achieved with a copula model, where both serial and cross-sectional dependence is captured by a copula function, and the margins are nonparametric. Yet most existing copulas cannot capture heteroskedasticity well, which is a feature of many economic and financial time series. To do so, we propose a new copula created by the inversion of a multivariate unobserved component stochastic volatility model, and show how to estimate it using Bayesian methods. We fit the copula model to real-time data on five …

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Time Series Copulas For Heteroskedastic Data, Ruben Loaiza-Maya, Michael S. Smith, Worapree Maneesoonthorn Dec 2017

Time Series Copulas For Heteroskedastic Data, Ruben Loaiza-Maya, Michael S. Smith, Worapree Maneesoonthorn

Michael Stanley Smith

We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We suggest copulas for first-order Markov series, and then extend them to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence, including co-movement and spillover in multivariate series. In general, these depend upon the marginal distributions of the series. Using exchange rate returns, we show that the resulting copula models can capture
their marginal distributions more accurately than univariate and multivariate generalized autoregressive conditional heteroskedasticity models, and produce more accurate value-at-risk forecasts.

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Econometric Modeling Of Regional Electricity Spot Prices In The Australian Market, Michael S. Smith, Thomas S. Shively Dec 2017

Econometric Modeling Of Regional Electricity Spot Prices In The Australian Market, Michael S. Smith, Thomas S. Shively

Michael Stanley Smith

Wholesale electricity markets are increasingly integrated via high voltage interconnectors, and inter-regional
trade in electricity is growing. To model this, we consider a spatial equilibrium model of price formation, where constraints on inter-regional flows result in three distinct equilibria in prices. We use this to motivate an econometric model for the distribution of observed electricity spot prices that captures many of their unique empirical characteristics. The econometric model features supply and inter-regional trade cost functions, which are estimated using Bayesian monotonic regression smoothing methodology. A copula multivariate time series model is employed to capture additional dependence --- both cross-sectional and serial --- in …

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Variational Bayes Estimation Of Discrete-Margined Copula Models With Application To Ime Series, Ruben Loaiza-Maya, Michael S. Smith Nov 2017

Variational Bayes Estimation Of Discrete-Margined Copula Models With Application To Ime Series, Ruben Loaiza-Maya, Michael S. Smith

Michael Stanley Smith

We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension $rT$, where $T$ is the number of observations and $r$ is the number of series, and are difficult to estimate using previous methods. 
The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a feature of most ordinal …

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Asymmetric Forecast Densities For U.S. Macroeconomic Variables From A Gaussian Copula Model Of Cross-Sectional And Serial Dependence, Michael S. Smith, Shaun Vahey Dec 2015

Asymmetric Forecast Densities For U.S. Macroeconomic Variables From A Gaussian Copula Model Of Cross-Sectional And Serial Dependence, Michael S. Smith, Shaun Vahey

Michael Stanley Smith

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this paper, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, …

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Some Matlab Routines To Compute Crps And Quantile Weighted Ps, Michael S. Smith Dec 2014

Some Matlab Routines To Compute Crps And Quantile Weighted Ps, Michael S. Smith

Michael Stanley Smith

Three routines to compute the CRPS of Gneiting and Raftery (JASA 2007) and the quantile weighted probability score (QWPS) extension in Gneiting and Ranjan (JBES, 2011). They are based on numerical integration as discussed in the Appendix of Smith and Vahey (2015), and I have found them to be much more accurate than using Monte Carlo approximation to the difference of two expectations, as advocated in Panagiotelis and Smith (IJF, 2008).

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Copula Modelling Of Dependence In Multivariate Time Series, Michael S. Smith Dec 2014

Copula Modelling Of Dependence In Multivariate Time Series, Michael S. Smith

Michael Stanley Smith

Almost all existing nonlinear multivariate time series models remain linear, conditional on a point in time or latent regime. Here, an alternative is proposed, where nonlinear serial and cross-sectional dependence is captured by a copula model. The copula defines a multivariate time series on the unit cube. A drawable vine copula is employed, along with a factorization which allows the marginal and transitional densities of the time series to be expressed analytically. The factorization also provides for simple conditions under which the series is stationary and/or Markov, as well as being parsimonious. A parallel algorithm for computing the likelihood is …

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From Amazon To Apple: Modeling Online Retail Sales, Purchase Incidence And Visit Behavior, Anastasios Panagiotelis, Michael S. Smith, Peter Danaher Dec 2013

From Amazon To Apple: Modeling Online Retail Sales, Purchase Incidence And Visit Behavior, Anastasios Panagiotelis, Michael S. Smith, Peter Danaher

Michael Stanley Smith

In this study we propose a multivariate stochastic model for website visit duration, page views, purchase incidence and the sale amount for online retailers. The model is constructed by composition from carefully selected distributions, and involves copula components. It allows for the strong nonlinear relationships between the sales and visit variables to be explored in detail, and can be used to construct sales predictions. The model is readily estimated using maximum likelihood, making it an attractive choice in practice given the large sample sizes that are commonplace in online retail studies. We examine a number of top-ranked U.S. online retailers, …

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