In-sample Fit Research Articles

A Model for Highly Fluctuating Spatio-Temporal Infection Data, with Applications to the COVID Epidemic.

Spatio-temporal models need to address specific features of spatio-temporal infection data, such as periods of stable infection levels (endemicity), followed by epidemic phases, as well as infection spread from neighbouring areas. In this paper, we consider a mixture-link model for infection counts that allows alternation between epidemic phases (possibly multiple) and stable endemicity, with higher AR1 coefficients in epidemic phases. This is a form of regime-switching, allowing for non-stationarity in infection levels. We adopt a generalised Poisson model appropriate to the infection count data and avoid transformations (e.g., differencing) to alternative metrics, which have been adopted in many studies. We allow for neighbourhood spillover in infection, which is also governed by adaptive regime-switching. Compared to existing models, the observational (in-sample) model is expected to better reflect the balance between epidemic and endemic tendencies, and short-term extrapolations are likely to be improved. Two case study applications involve COVID area-time data, one for 32 London boroughs (and 96 weeks) since the start of the COVID epidemic, the other for a shorter time span focusing on the epidemic phase in 144 areas of Southeast England associated with the Alpha variant. In both applications, the proposed methods produce a better in-sample fit and out-of-sample short term predictions. The spatial dynamic implications are highlighted in the case studies.

TREE-BASED MACHINE LEARNING METHODS FOR MODELING AND FORECASTING MORTALITY

AbstractMachine learning has recently entered the mortality literature in order to improve the forecasts of stochastic mortality models. This paper proposes to use two pure, tree-based machine learning models: random forests and gradient boosting, based on the differenced log-mortality rates to produce more accurate mortality forecasts. These forecasts are compared with forecasts from traditional, stochastic mortality models and with forecasts from random forests and gradient boosting variants of the stochastic models. The comparisons are based on the Model Confidence Set procedure. The results show that the pure, tree-based models significantly outperform all other models in the majority of cases considered. To address the lack of interpretability issue associated with machine learning models, we demonstrate how to extract information about the relationships uncovered by the tree-based models. For this purpose, we consider variable importance, partial dependence plots, and variable split conditions. Results from the in-sample fit suggest that tree-based models can be very useful tools for detecting patterns within and between variables that are not commonly identifiable with traditional methods.

Modelling Trade Durations Using Dynamic Logarithmic Component ACD Model with Extended Generalised Inverse Gaussian Distribution

This paper proposes a logarithmic version of the two-component ACD (LogCACD) model with no restrictions on the sign of the model parameters while allowing the expected durations to be decomposed into the long- and short-run components to capture the dynamics of these durations. The extended generalised inverse Gaussian (EGIG) distribution is used for the error distribution as its hazard function consists of a roller-coaster shape for certain parameters’ values. An empirical application from the trade durations of International Business Machines stock index has been carried out to investigate this proposed model. Extensive comparisons are carried out to evaluate the modelling and forecasting performances of the proposed model with several benchmark models and different specifications of error distributions. The result reveals that the LogCACDEGIG(1,1) model gives the best in-sample fit based on the Akaike information criterion and other criteria. Furthermore, the estimated parameters obtained through the maximum likelihood estimation confirm the existence of the roller-coaster-shaped hazard function. The examination of LogCACDEGIG(1,1) model also provides the best out-of-sample forecasts evaluated based on the mean square forecast error using the Hansen’s model confidence set. Lastly, different levels of time-at-risk forecasts are provided and tested with Kupiec likelihood ratio test.

A closed-form solution for the stochastic volatility model with applications on international stock markets

This paper proposes a closed-form estimator for the stochastic volatility (SV) model. Compared to the usual maximum likelihood estimation (MLE), which is difficult to perform without appropriate approximations, the proposed method can be easily implemented and does not require the use of any numerical optimizer or starting values for iterations. Moreover, closed-form estimates can be supplied as initial values to MLE, for instance, conducted with a novel Laplace approximation. Denoted by MLE-C, this method consistently outperforms other estimators including the Markov chain Monte Carlo (MCMC). This is confirmed with simulation studies consisting of various combinations of true parameters and sample sizes. Our empirical data include daily returns of S&P 500, Nikkei 225 and DAX 100 over 2011–2020. The SV model estimated by MLE-C almost uniformly beats the popular GARCH counterparty, based on both the in-sample fit and out-of-sample forecasting criteria. Value-at-Risk analyses further demonstrate the capability of the SV model to accurately describe the tail behaviors of negative returns.

Time-varying variance and skewness in realized volatility measures

We propose new empirical models to capture the dynamics of the variance and skewness in realized volatility measures. We find that time-variation in variance and skewness of realized measures is a key empirical feature, even after accounting for well-known, stylized facts such as long-memory-type persistence and large incidental observations. Using a broad range of 89 US stocks across different sectors over 2001–2019, we show that these are not incidental phenomena of a few stocks but are widely shared. Accounting for dynamics in the variance and skewness of realized measures results in significantly better in-sample fit and out-of-sample unconditional density and quantile forecasts.

Nowcasting food inflation with a massive amount of online prices

The consensus in the literature on providing accurate inflation forecasts underlines the importance of precise nowcasts. In this paper, we focus on this issue by employing a unique, extensive dataset of online food and non-alcoholic beverages prices gathered automatically from the webpages of major online retailers in Poland since 2009. We perform a real-time nowcasting experiment by using a highly disaggregated framework among popular, simple univariate approaches. We demonstrate that pure estimates of online price changes are already effective in nowcasting food inflation, but accounting for online food prices in a simple, recursively optimized model delivers further gains in the nowcast accuracy. Our framework outperforms various other approaches, including judgmental methods, traditional benchmarks, and model combinations. After the outbreak of the COVID-19 pandemic, its nowcasting quality has improved compared to other approaches and remained comparable with judgmental nowcasts. We also show that nowcast accuracy increases with the volume of online data, but their quality and relevance are essential for providing accurate in-sample fit and out-of-sample nowcasts. We conclude that online prices can markedly aid the decision-making process at central banks.

Prediction of the Fundus Tessellation Severity With Machine Learning Methods.

PurposeTo predict the fundus tessellation (FT) severity with machine learning methods.MethodsA population-based cross-sectional study with 3,468 individuals (mean age of 64.6 ± 9.8 years) based on Beijing Eye Study 2011. Participants underwent detailed ophthalmic examinations including fundus images. Five machine learning methods including ordinal logistic regression, ordinal probit regression, ordinal log-gamma regression, ordinal forest and neural network were used.Main Outcome MeasureFT precision, recall, F1-score, weighted-average F1-score and AUC value.ResultsObserved from the in-sample fitting performance, the optimal model was ordinal forest, which had correct classification rate (precision) of 81.28%, while 34.75, 93.73, 70.03, and 24.82% in each classified group by FT severity. The AUC value was 0.7249. And the F1-score was 65.05%, weighted-average F1-score was 79.64% on the whole dataset. For out-of-sample prediction performance, the optimal model was ordinal logistic regression, which had precision of 77.12% on the validation dataset, while 19.57, 92.68, 64.74, and 6.76% in each classified group by FT severity. The AUC value was 0.7187. The classification accuracy of light FT group was the highest, while that of severe FT group was the lowest. And the F1-score was 54.46%, weighted-average F1-score was 74.19% on the whole dataset.ConclusionsThe ordinal forest and ordinal logistic regression model had the strong prediction in-sample and out-sample performance, respectively. The threshold ranges of the ordinal forest model for no FT and light, moderate, severe FT were [0, 0.3078], [0.3078, 0.3347], [0.3347, 0.4048], [0.4048, 1], respectively. Likewise, the threshold ranges of ordinal logistic regression model were ≤ 3.7389, [3.7389, 10.5053], [10.5053, 13.9323], > 13.9323. These results can be applied to guide clinical fundus disease screening and FT severity assessment.

High-Frequency Quote Volatility Measurement Using a Change-Point Intensity Model

Quote volatility is important in determining the cost of demand in a high frequency (HF) order market. This paper proposes a new model to measure quote volatility based on the point process and price-change duration. Specifically, we built a change-point intensity (CPI) model to describe the dynamics of price-change events for a given level of threshold. The instantaneous volatility of quote price can be calculated at any time according to price-change intensities. Based on this, we can quantify the cost of demanding liquidity for traders with different trading latency by using integrated variances. Furthermore, we use the autoregressive conditional intensity (ACI) model proposed by Russell (1999) as a benchmark comparison. The results suggest that our model has better performance of both in-sample fitness and out-of-sample prediction.

Gaussian process latent class choice models

We present a Gaussian Process – Latent Class Choice Model (GP-LCCM) to integrate a non-parametric class of probabilistic machine learning within discrete choice models (DCMs). Gaussian Processes (GPs) are kernel-based algorithms that incorporate expert knowledge by assuming priors over latent functions rather than priors over parameters, which makes them more flexible in addressing nonlinear problems. By integrating a Gaussian Process within a LCCM structure, we aim at improving discrete representations of unobserved heterogeneity. The proposed model would assign individuals probabilistically to behaviorally homogeneous clusters (latent classes) using GPs and simultaneously estimate class-specific choice models by relying on random utility models. Furthermore, we derive and implement an Expectation-Maximization (EM) algorithm to jointly estimate/infer the hyperparameters of the GP kernel function and the class-specific choice parameters by relying on a Laplace approximation and gradient-based numerical optimization methods, respectively. The model is tested on two different mode choice applications and compared against different LCCM benchmarks. Results show that GP-LCCM allows for a more complex and flexible representation of heterogeneity and improves both in-sample fit and out-of-sample predictive power. Moreover, behavioral and economic interpretability is maintained at the class-specific choice model level while local interpretation of the latent classes can still be achieved, although the non-parametric characteristic of GPs lessens the transparency of the model.

Economic Policy Uncertainty and Conditional Dependence between China and U.S. Stock Markets

In this paper, we investigate the impact of economic policy uncertainty (EPU) on the conditional dependence between China and U.S. stock markets by employing the Copula-mixed-data sampling (Copula-MIDAS) framework. In the case of EPU, we consider the global EPU (GEPU), the American EPU (AEPU), and the China EPU (CEPU). The empirical analysis based on the Shanghai Stock Exchange Composite (SSEC) index in China and the S&P 500 index in the U.S. shows that the tail dependence between China and U.S. stock markets is symmetrical, and the t Copula outperforms alternative Copulas in terms of in-sample goodness of fit. In particular, we find that the t Copula-MIDAS model with EPU dominates the traditional time-varying t Copula in terms of in-sample fitting. Moreover, we observe that both the GEPU and AEPU have a significantly positive impact on the conditional dependence between China and U.S. stock markets, whereas CEPU has no significant impact. The tail dependence between China and U.S. stock markets exhibits an increasing trend, particularly in the recent years.

Multi-population mortality modeling: When the data is too much and not enough

A large number of mortality rates yield estimation issues in a mortality model. The first issue is about the consistency of factor estimates when the number of mortality rates is more than the number of observations. The second issue concerns the heterogeneity among multiple populations or within a single population. We apply the framework of the approximate factor model to resolve these issues. The empirical tests on individual and multiple populations show that incorporating idiosyncratic heteroskedasticities and correlations into estimations improves in-sample fitting and out-of-sample forecasting. By comparing with existing models, we conclude that the improvements come from capturing the heteroskedasticities and correlations in the higher-order idiosyncratic errors.

The Role of Jumps in Realized Volatility Modeling and Forecasting

Abstract Building on an extensive empirical analysis, I investigate the relevance of jumps and signed variations in predicting realized volatility. I show that properly accounting for intra-day volatility patterns and staleness sensibly reduces the identified jumps, in particular for low and moderate liquidity assets. Modeling realized variance using jumps and intra-day return sign improves the in-sample fit of commonly adopted specifications, irrespective of assets liquidity. From a forecasting perspective, the empirical evidence I report shows that most models, independently from their flexibility, are statistically equivalent in many cases. These results are confirmed with different samples, assets liquidity level, forecast horizons, and possible transformations of the dependent and explanatory variables.

A two-component realized exponential generalized autoregressive conditional heteroscedasticity model

This paper proposes a two-component realized exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model – an extension of the realized EGARCH model – for the joint modeling of asset returns and realized measures of volatility. The proposed model assumes that the volatility of asset returns consists of two components: a long-run component and a short-run component. The model’s unique ability to capture the long-memory property of volatility distinguishes it from the standard realized EGARCH model. The model is convenient to implement within the framework of maximum likelihood estimation. We apply the two-component realized EGARCH model and a restricted version of the model (the two-component realized EGARCH model with only short-run leverage) to four stock indexes: the Standard & Poor’s 500 index, the Hang Seng index, the Nikkei 225 index and the Deutscher Aktienindex. The empirical study suggests that the two-component realized EGARCH model and its restricted version outperform the realized GARCH model, the realized EGARCH model and the realized heterogeneous autoregressive GARCH model in terms of in-sample fit. Further, an out-of-sample predictive analysis demonstrates that the two-component realized EGARCH model and its restricted version yield more accurate volatility forecasts than the alternatives.

Box-Jenkins Model for Forecasting Malaysia Life Expectancy

Life expectancy is an estimate of how long the average person might be expected to live and is most often quoted for an entire lifetime. Forecasting of future life expectancy is needed to plan for health and social services and pensions. This article attempts to propose the most appropriate time series model based on Box-Jenkins methodology to explain the behavior of Malaysia life expectancy at birth for the purpose of forecasting future life expectancy. Several autoregressive integrated moving average (ARIMA) models were developed to model Malaysia life expectancy on data collected from year 1966 to year 2016. The data which separated by gender are provided by Department of Statistics Malaysia (DOSM) on yearly basis. The results indicate that both ARIMA(1,1,1) and ARIMA(2,2,3) model performed well for both in-sample fitting and out-sample evaluation for male and female respectively with the least value of Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE).

Term structure estimation with liquidity-adjusted Ane Nelson Siegel model: A nonlinear state space approach applied to the Indian bond market

ABSTRACT Efficient term structure estimation in emerging markets is difficult not only because of overall lack of liquidity, but also because of the concentration of liquidity in a few securities. Using the arbitrage-free Affine Nelson-Siegel model, we explicitly incorporate this phenomenon using a proxy for liquidity based on observable data in the bond pricing function and estimate the term structure for Indian Government bond markets in a nonlinear state space setting using the Unscented Kalman Filter. We find strong empirical evidence in support of the extended model with both i) a better in-sample fit to bond prices, and ii) the likelihood ratio test rejecting the restrictions assumed in the standard AFNS specification. In an alternative specification, we also model liquidity as a latent risk factor within the AFNS framework. The estimated latent liquidity factor is found to be strongly correlated with the standard market benchmarks of overall liquidity and the India VIX index.

An Application of Damped Diffusion for Modeling Volatility Dynamics

Abstract This paper proposes a damped constant elasticity variance (CEV) stochastic volatility (DCEV) model, which remedies the possible explosive behavior of the CEV model and also accommodates the mean-reverting dynamics more appropriately than the nonlinear drift (NLD) stochastic volatility model. As the DCEV model maintains the linear drift, an analytic formula is available to efficiently infer latent variances from VIX levels, after which both its physical and risk-neutral parameters can be simultaneously estimated with the maximum-likelihood approach given S&P 500 returns and inferred variances. The DCEV model outperforms the CEV and NLD models in in-sample fitting performance and in out-of-sample variance forecasting under the physical measure. It also exhibits superior ability in out-of-sample option pricing over the CEV and Heston’s (1993) models under the risk-neutral measure. This satisfactory performance demonstrates the suitability of describing volatility dynamics with the DCEV model and the potential of applying this to study other issues.

Arbitrage-free Nelson\u2013Siegel model for multiple yield curves

We propose an affine term structure model that allows for tenor-dependence of yield curves and thus for different risk categories in interbank rates, an important feature of post-crisis interest rate markets. The model has a Nelson–Siegel factor loading structure and thus economically well interpretable parameters. We show that the model is tractable in terms of estimation and provides good in-sample fit and out-of-sample forecasting performance. The proposed model is arbitrage-free across maturities and tenors, and thus perfectly suited for risk management and pricing purposes. We apply our framework to the pricing of caplets in order to illustrate its practical applicability and its suitability for stress testing.

The transformed Gram Charlier distribution: Parametric properties and financial risk applications

In this paper we study an extension of the Gram–Charlier (GC) density in Jondeau and Rockinger (2001) which consists of a Gallant and Nychka (1987) transformation to ensure positivity without parameter restrictions. We derive its parametric properties such as unimodality, cumulative distribution, higher-order moments, truncated moments, and the closed-form expressions for the expected shortfall (ES) and lower partial moments. We obtain the analytic k th order stationarity conditions for the unconditional moments of the TGARCH model under the transformed GC (TGC) density. In an empirical application to asset return series, we estimate the tail index; backtest the density, VaR and ES; and implement a comparative analysis based on Hansen’s skewed-t distribution. Finally, we present extensions to time-varying conditional skewness and kurtosis, and a new class of mixture densities based on this TGC distribution. • We obtain the parametric properties of the transformed Gram–Charlier density. • We study the unimodality and obtain the true ranges for skewness and kurtosis. • Closed-form expressions for asymmetric-risk measures are obtained. • We study the power-law tail property for asymmetric GARCH models under our density. • The model performs well in both in-sample fitting and out-of-sample backtesting.

ON COMPLEX ECONOMIC SCENARIO GENERATORS: IS LESS MORE?

AbstractThis article proposes a complex economic scenario generator that nests versions of well-known actuarial frameworks. The generator estimation relies on the Bayesian paradigm and accounts for both model and parameter uncertainty via Markov chain Monte Carlo methods. So, to the questionis less more?, we answer maybe, but it depends on your criteria. From an in-sample fit perspective, on the one hand, a complex economic scenario generator seems better. From the conservatism, forecasting and coverage perspectives, on the other hand, the situation is less clear: having more complex models for the short rate, term structure and stock index returns is clearly beneficial. However, that is not the case for inflation and the dividend yield.

Infection rate models for COVID-19: Model risk and public health news sentiment exposure adjustments.

During the COVID-19 pandemic, governments globally had to impose severe contact restriction measures and social mobility limitations in order to limit the exposure of the population to COVID-19. These public health policy decisions were informed by statistical models for infection rates in national populations. In this work, we are interested in modelling the temporal evolution of national-level infection counts for the United Kingdom (UK-Wales, England, Scotland), Germany (GM), Italy (IT), Spain (SP), Japan (JP), Australia (AU) and the United States (US). We model the national-level infection counts for the period January 2020 to January 2021, thus covering both the pre- and post-vaccine roll-out periods, in order to better understand the most reliable model structure for the COVID-19 epidemic growth curve. We achieve this by exploring a variety of stochastic population growth models and comparing their calibration, with respect to in-sample fitting and out-of-sample forecasting, both with and without exposure adjustment, to the most widely used and reported growth model, the Gompertz population model, often referred to in the public health policy discourse during the COVID-19 pandemic. Model risk as we explore it in this work manifests in the inability to adequately capture the behaviour of the disease progression growth rate curve. Therefore, our concept of model risk is formed relative to the standard reference Gompertz model used by decision-makers, and then we can characterise model risk mathematically as having two components: the dispersion of the observation distribution, and the structure of the intensity function over time for cumulative counts of new infections daily (i.e. the force of infection) attributed directly to the COVID-19 pandemic. We also explore how to incorporate in these population models the effect that governmental interventions have had on the number of infected cases. This is achieved through the development of an exposure adjustment to the force of infection comprised of a purpose-built sentiment index, which we construct from various authoritative public health news reporting. The news reporting media we employed were the New York Times, the Guardian, the Telegraph, Reuters global blog, as well as national and international health authorities: the European Centre for Disease Prevention and Control, the United Nations Economic Commission for Europe, the United States Centres for Disease Control and Prevention, and the World Health Organisation. We find that exposure adjustments that incorporate sentiment are better able to calibrate to early stages of infection spread in all countries under study.