Does the Choice of Realized Covariance Measures Empirically Matter? A Bayesian Density Prediction Approach

This paper suggests a new approach to evaluate realized covariance (RCOV) estimators via their predictive power on return density. By jointly modeling returns and RCOV measures under a Bayesian framework, the predictive density of returns and ex-post covariance measures are bridged. The forecast performance of a covariance estimator can be assessed according to its improvement in return density forecasting. Empirical applications to equity data show that several RCOV estimators consistently perform better than others and emphasize the importance of RCOV selection in covariance modeling and forecasting.

Bayesian analysis of mixture autoregressive models covering the complete parameter space

Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for such models offers the additional advantage of incorporating the uncertainty in the estimated models into the predictions. We introduce a new way of sampling from the posterior distribution of the parameters of MAR models which allows for covering the complete parameter space of the models, unlike previous approaches. We also propose a relabelling algorithm to deal a posteriori with label switching. We apply our new method to simulated and real datasets, discuss the accuracy and performance of our new method, as well as its advantages over previous studies. The idea of density forecasting using MCMC output is also introduced.

Analisis Peramalan Peluang Bisnis Tanah Menggunakan Metode Double Exponential Smoothing

PT. JNF is a company engaged in Engineering, Construction, and Project Management, located in South Jakarta. This company wants to develop its business by building housing in the city of Malang, to be precise in the Kedungkandang and Lowokwaru districts. The company needs some data and information about population density and land prices in the area to help the process of their project work. Providing information on data and forecasting results about population density and land prices in the area will help companies facilitate business development. Therefore, companies need an information system that can predict population density data and land prices in Kedungkandang sub-district and Lowokwaru sub-district, which functions to help companies see land business opportunities in Malang for housing development. The method used to make this system is the Double Exponential Smoothing method, because this method has a trend pattern that matches the data pattern of the object to be predicted. The data used are data from 2005 - 2018. The result of population density forecasting for Lowokwaru sub-district is 8713.98 and has a MAPE value of 1.39%, for Kedungkandang sub-district is 4949.07 and has a MAPE value of 2.55%, for the land price of Lowokwaru sub-district is 2777725.18 and has a MAPE value of 3.45 % and Kedungkandang sub-district is 1766560.27 and has a MAPE value of 8.36%. Based on the calculation of the MAPE value the results of the forecast above, it can be concluded that if the greater the constant value, the lower the MAPE value, the best constant value is between 0.6 - 0.9. The land business opportunity in Lowokwaru and Kedungkandang sub-districts is high based on the forecasting results of population density and land prices which tend to increase every year and the land business opportunity value based on ROI (Return of Investment) for the company is 0.38% of the initial capital. Keywords: information systems, forecasting, land business opportunities, land prices, population density, double exponential smoothing.

A Locally Both Leptokurtic and Fat-Tailed Distribution with Application in a Bayesian Stochastic Volatility Model

In the paper, we begin with introducing a novel scale mixture of normal distribution such that its leptokurticity and fat-tailedness are only local, with this “locality” being separately controlled by two censoring parameters. This new, locally leptokurtic and fat-tailed (LLFT) distribution makes a viable alternative for other, globally leptokurtic, fat-tailed and symmetric distributions, typically entertained in financial volatility modelling. Then, we incorporate the LLFT distribution into a basic stochastic volatility (SV) model to yield a flexible alternative for common heavy-tailed SV models. For the resulting LLFT-SV model, we develop a Bayesian statistical framework and effective MCMC methods to enable posterior sampling of the parameters and latent variables. Empirical results indicate the validity of the LLFT-SV specification for modelling both “non-standard” financial time series with repeating zero returns, as well as more “typical” data on the S&P 500 and DAX indices. For the former, the LLFT-SV model is also shown to markedly outperform a common, globally heavy-tailed, t-SV alternative in terms of density forecasting. Applications of the proposed distribution in more advanced SV models seem to be easily attainable.