Generalization of the order-restricted information criterion for multivariate normal linear models (pre-print )

The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints.Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic.We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints.If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion.Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model.

Portfolio Management of Copula-Dependent Assets Based on P(Y < X) Reliability Models: Revisiting Frank Copula and Dagum Distributions

Modern portfolio theory indicates that portfolio optimization can be carried out based on the mean-variance model, where returns and risk are represented as the average and variance of the historical data of the stock’s returns, respectively. Several studies have been carried out to find better risk proxies, as variance was not that accurate. On the other hand, fewer papers are devoted to better model/characterize returns. In the present paper, we explore the use of the reliability measure P(Y<X) to choose between portfolios with returns given by the distributions X and Y. Thus, instead of comparing the expected values of X and Y, we will explore the metric P(Y<X) as a proxy parameter for return. The dependence between such distributions shall be modelled by copulas. At first, we derive some general results which allows us to split the value of P(Y<X) as the sum of independent and dependent parts, in general, for copula-dependent assets. Then, to further develop our mathematical framework, we chose Frank copula to model the dependency between assets. In the process, we derive a new polynomial representation for Frank copulas. To perform a study case, we considered assets whose returns’ distributions follow Dagum distributions or their transformations. We carried out a parametric analysis, indicating the relative effect of the dependency of return distributions over the reliability index P(Y<X). Finally, we illustrate our methodology by performing a comparison between stock returns, which could be used to build portfolios based on the value of the the reliability index P(Y<X).

Putting the individual into reliability: Bayesian testing of homogeneous within-person variance in hierarchical models

Measurement reliability is a fundamental concept in psychology. It is traditionally considered a stable property of a questionnaire, measurement device, or experimental task. Although intraclass correlation coefficients (ICC) are often used to assess reliability in repeated measure designs, their descriptive nature depends upon the assumption of a common within-person variance. This work focuses on the presumption that each individual is adequately described by the average within-person variance in hierarchical models. And thus whether reliability generalizes to the individual level, which leads directly into the notion of individually varying ICCs. In particular, we introduce a novel approach, using the Bayes factor, wherein a researcher can directly test for homogeneous within-person variance in hierarchical models. Additionally, we introduce a membership model that allows for classifying which (and how many) individuals belong to the common variance model. The utility of our methodology is demonstrated on cognitive inhibition tasks. We find that heterogeneous within-person variance is a defining feature of these tasks, and in one case, the ratio between the largest to smallest within-person variance exceeded 20. This translates into a tenfold difference in person-specific reliability! We also find that few individuals belong to the common variance model, and thus traditional reliability indices are potentially masking important individual variation. We discuss the implications of our findings and possible future directions. The methods are implemented in the R package vICC

Gamma variance model: Fractional Fourier Transform (FRFT)

The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining the probability density function and its derivatives; and mainly for fitting stochastic model with the fundamental probabilistic relationships of infinite divisibility. The probability density functions are computed, and the distributional proprieties are reviewed for Variance-Gamma (VG) model. The VG model has been increasingly used as an alternative to the Classical Lognormal Model (CLM) in modelling asset prices. The VG model was estimated by the FRFT. The data comes from the SPY ETF historical prices. The Kolmogorov-Smirnov (KS) goodness-of-fit shows that the VG model fits better the cumulative distribution of the sample data than the CLM. The best VG model comes from the FRFT estimation.

A Mean-Variance Optimization Approach for Residential Real Estate Valuation

This paper introduces a new approach to the sales comparison model for the valuation of real estate that can objectively estimate the coefficients associated with the explanatory price variables. The coefficients of the price adjustment process are estimated from the formulation of a quadratic programming model similar to the mean-variance model in the portfolio selection problem and are shown to be independent of the property to be valued. It is also shown that the sales comparison model should minimize the variance of the adjusted prices, and not their coefficient of variation as indicated by some national and international valuation regulations. The paper concludes with a case study on the city of Medellín, Colombia.

Forecasting Inflation Applying ARIMA Model with GARCH Innovation: The Case of Pakistan

Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features. Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied. Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan. Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.