Unbiasedness of Prediction under Linex Loss Function in Autoregressive Moving Average Models

The asymmetric loss function is used in a situation where a positive error may be more serious than a negative error of the same magnitude or vice versa. One of the most commonly used asymmetric loss functions is the linex loss. The linex unbiased predictor has been developed and applied to real world applications. This study investigated how the linex unbiased prediction behaves when time series processes, AR(p), MA(q) and ARMA (p,q), parameters are unknown and being estimated, with different levels of variance, forecast step, shape parameter and series length. It started with deriving the predictor for each time series process, computing this predictor, and then discussing its properties. Empirical studies of the behavior of this predictor were investigated by using the Monte Carlo simulation. The results of this study showed that, a simpler time series model produced values that were closer to the condition of linex unbiasedness than a complex model. The condition of linex unbiasedness was affected by the variance but not the sign of the linex loss function shape parameter. For any time series model and any condition, as series length increased, the condition of linex unbiasedness values approached zero. When the time series parameters are unknown, the prediction is asymptotically linex unbiased

Application of Signal Processing Methods in Energy and Water Sustainability Optimization.

Ph.D. Thesis. University of Hawaiʻi at Mānoa 2017

Properties of Optimal Forecasts

Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors should be serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results, we show in this paper that all the standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. Our theoretical results suggest that many of the conclusions in the empirical literature concerning suboptimality of forecasts could be premature. We extend the properties that an optimal forecast should have to a more general setting than previously considered in the literature. We also present results on forecast error properties that may be tested when the forecaster's loss function is unknown, and introduce a change of measure, following which the optimum forecast errors for general loss functions have the same properties as optimum errors under MSE lossforecast evaluation, loss function, rationality, efficient markets

The performance of serial correlation preliminary test estimators under asymmetry loss functions

The risk performances, under the symmetric squared error loss function, of the estimators of the regression coefficients after a preliminary test for serial correlation have been widely investigated in the literature. However, it is well known that the use of the symmetric loss functions is inappropriate in estimation problems where underestimation and overestimation have different consequences. We consider the Linear Exponential and Bounded Linear Exponential loss functions which allows for asymmetry. The risks of the estimators are derived and numerically evaluated by using simulations

Using Asymmetric Loss Functions in Time Series Econometrics

This thesis serves the purpose of examining the role of asymmetric loss functions in time series analysis. Asymmetric loss functions can sometimes be interpreted as mathematical representations of risk-averse or risk-seeking behavior of economic agents. This thesis shows how these functions may be used for forecasting certain economic variables. It contains methodological work, statistical simulations as well as empirical studies. It is based on four articles, one of which is currently under review. The thesis is structured as follows

The performance of serial correlation preliminary test estimators under asymmetry loss functions

The risk performances, under the symmetric squared error loss function, of the estimators of the regression coefficients after a preliminary test for serial correlation have been widely investigated in the literature. However, it is well known that the use of the symmetric loss functions is inappropriate in estimation problems where underestimation and overestimation have different consequences. We consider the Linear Exponential and Bounded Linear Exponential loss functions which allows for asymmetry. The risks of the estimators are derived and numerically evaluated by using simulations.The National Research Foundation of South Africa for the grant TTK1206151317.http://www.sastat.org.za/journal/informationhttp://reference.sabinet.co.za/sa_epublication/sasjam201

A Time-Varying Expectations Formation Mechanism

We propose an expectations formation mechanism (EFM) aimed to explain the median – hence lay – forecaster’s year-ahead inflation predictions. The EFM is a time-varying combination of long-run expectations, current inflation and uncertainty with weights naively calibrated according to inflation dynamics. Earning fixed income, in fact, the median forecaster has an aversion toward underestimation that increases with inflation. To allow for occasional – albeit unintentional – cost-minimizing calibrations, the EFM nests various forecasting rules. Data from the Michigan Survey of Consumers sustains the argued behavior and contributes to interpret some puzzling price dynamics such as the missing disinflation and reflation

A Time-Varying Expectations Formation Mechanism

We propose an expectations formation mechanism (EFM) aimed to explain the median – hence lay – forecaster’s year-ahead inflation predictions. The EFM is a time-varying combination of long-run expectations, current inflation and uncertainty with weights naively calibrated according to inflation dynamics. Earning fixed income, in fact, the median forecaster has an aversion toward underestimation that increases with inflation. To allow for occasional – albeit unintentional – cost-minimizing calibrations, the EFM nests various forecasting rules. Data from the Michigan Survey of Consumers sustains the argued behavior and contributes to interpret some puzzling price dynamics such as the missing disinflation and reflation