Detecting nonlinearity in time series by model selection criteria

This article analyzes the use of model selection criteria for detecting nonlinearity in the residuals of a linear model. Model selection criteria are applied for finding the order of the best autoregressive model fitted to the squared residuals of the linear model. If the order selected is not zero, this is considered as an indication of nonlinear behavior. The BIC and AIC criteria are compared to some popular nonlinearity tests in three Monte Carlo experiments. We conclude that the BIC model selection criterion seems to offer a promising tool for detecting nonlinearity in time series. An example is shown to illustrate the performance of the tests considered and the relationship between nonlinearity and structural changes in time series.     

Performance of information criteria for selection of Hawkes process models of financial data

We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling. The information criteria are Akaike’s information criterion, the Bayesian information criterion and the Hannan–Quinn criterion. Since we work with simulated data, we are able to measure the performance of model selection by the success rate of the IC in selecting the model that was used to generate the data. In particular, we are interested in the relation between correct model selection and underlying sample size. The analysis includes realistic sample sizes and parameter sets from recent literature where parameters were estimated using empirical financial intra-day data. We compare our results to theoretical predictions and similar empirical findings on the asymptotic distribution of model selection for consistent and inconsistent IC.     

Statistical analysis of corruption data and using the Internet to reduce corruption

Corruption is a serious problem in Asia and elsewhere. The Harrison and Vinod (1992) confidence interval for the marginal excess burden (MEB) of taxation is used to estimates the economic harm arising from corruption. One dollar of corruption is estimated to impose a burden of $1.67, which becomes very large when compounded over time. After a brief review of economic theory, this paper uses data on sixteen socio-economic and political variables. A cross-sectional study reveals the relevance of “red tape” and “efficiency of judiciary.” A subset regression using Mallows’ Cp and Akaike information criteria reveals relevance of schooling and income inequality. International aid and cooperation in exposing and fighting corruption and innovative uses of the Internet for information exchange are claimed to be hopeful new tools to fight corruption in the new century.     

Data transforms with exponential smoothing methods of forecasting

In this paper, transforms are used with exponential smoothing, in the quest for better forecasts. Two types of transforms are explored: those which are applied to a time series directly, and those which are applied indirectly to the prediction errors. The various transforms are tested on a large number of time series from the M3 competition, and ANOVA is applied to the results. We find that the non-transformed time series is significantly worse than some transforms on the monthly data, and on a distribution-based performance measure for both annual and quarterly data.     

基于 Copula 的债务抵押债券定价

针对债务抵押债券（ CDO）的定价问题,应用时点改变结构来描述相关资产的动态相关性,通过Copula函数来刻画各个阶段的违约相关结构。针对不同Copula函数的特征,采用AIC准则选择最适合的Copula函数来描述违约相关结构。通过对构建的CDO产品定价研究表明,在不同阶段违约相关结构是不同的,从而求得的CDO各系列定价和期望损失也是不同的。     

Combining exponential smoothing forecasts using Akaike weights

Simple forecast combinations such as medians and trimmed or winsorized means are known to improve the accuracy of point forecasts, and Akaike’s Information Criterion (AIC) has given rise to so-called Akaike weights, which have been used successfully to combine statistical models for inference and prediction in specialist fields, e.g., ecology and medicine. We examine combining exponential smoothing point and interval forecasts using weights derived from AIC, small-sample-corrected AIC and BIC on the M1 and M3 Competition datasets. Weighted forecast combinations perform better than forecasts selected using information criteria, in terms of both point forecast accuracy and prediction interval coverage. Simple combinations and weighted combinations do not consistently outperform one another, while simple combinations sometimes perform worse than single forecasts selected by information criteria. We find a tendency for a longer history to be associated with a better prediction interval coverage.     

Estimating the Kullback–Liebler risk based on multifold cross‐validation

This paper concerns a class of model selection criteria based on cross‐validation techniques and estimative predictive densities. Both the simple or leave‐one‐out and the multifold or leave‐m‐out cross‐validation procedures are considered. These cross‐validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.     

USING MODEL SELECTION ALGORITHMS TO OBTAIN RELIABLE COEFFICIENT ESTIMATES

This review surveys a number of common model selection algorithms (MSAs), discusses how they relate to each other and identifies factors that explain their relative performances. At the heart of MSA performance is the trade‐off between type I and type II errors. Some relevant variables will be mistakenly excluded, and some irrelevant variables will be retained by chance. A successful MSA will find the optimal trade‐off between the two types of errors for a given data environment. Whether a given MSA will be successful in a given environment depends on the relative costs of these two types of errors. We use Monte Carlo experimentation to illustrate these issues. We confirm that no MSA does best in all circumstances. Even the worst MSA in terms of overall performance – the strategy of including all candidate variables – sometimes performs best (viz., when all candidate variables are relevant). We also show how (1) the ratio of relevant to total candidate variables and (2) data‐generating process noise affect relative MSA performance. Finally, we discuss a number of issues complicating the task of MSAs in producing reliable coefficient estimates.     

How to handle missing data in regression models using information criteria*

An important application of multiple regression is predictor selection. When there are no missing values in the data, information criteria can be used to select predictors. For example, one could apply the small‐sample‐size corrected version of the Akaike information criterion (AIC), the (AICC). In this article, we discuss how information criteria should be calculated when the dependent variable and/or the predictors contain missing values. Therewith, we extensively discuss and evaluate three models that can be employed to deal with the missing data, that is, to predict the missing values. The most complex model, that is, the model with all available predictors, outperforms the other models. These results also apply to more general hypotheses than predictor selection and also to structural equation modeling (SEM) models.     

A statistical comparison of the short-term interest rate models for Japan,U.S., and Germany

We propose a simple and practical model selection method for continuous time models. We apply the method to several continuous time short-term interest rate models using discrete time series data of Japan, U.S. and Germany. All the models can be easily estimated from discrete observations, and their performances can be evaluated in a uniform statistical framework. The models that allow dependence of volatility on the level of interest rates tend to perform well empirically. The degree of volatility dependence on the interest rate levels seems to be different across the countries. For the German data, we observe that a model with nonlinear drift performs better than the best linear drift model.