Bayes Inference for Technological Substitution Data with Data-based Transformation

Bayesian inference via Gibbs sampling is studied for forecasting technological substitutions. The Box–Cox transformation is applied to the time series AR(1) data to enhance the linear model fit. We compute Bayes point and interval estimates for each of the parameters from the Gibbs sampler. The unknown parameters are the regression coefficients, the power in the Box–Cox transformation, the serial correlation coefficient, and the variance of the disturbance terms. In addition, we forecast the future technological substitution rate and its interval. Model validation and model choice issues are also addressed. Two numerical examples with real data sets are given.©1997 John Wiley & Sons, Ltd.     

A modified sequential Monte Carlo procedure for the efficient recursive estimation of extreme quantiles

Many applications in science involve finding estimates of unobserved variables from observed data, by combining model predictions with observations. The sequential Monte Carlo (SMC) is a well‐established technique for estimating the distribution of unobserved variables that are conditional on current observations. While the SMC is very successful at estimating the first central moments, estimating the extreme quantiles of a distribution via the current SMC methods is computationally very expensive. The purpose of this paper is to develop a new framework using probability distortion. We use an SMC with distorted weights in order to make computationally efficient inferences about tail probabilities of future interest rates using the Cox–Ingersoll–Ross (CIR) model, as well as with an observed yield curve. We show that the proposed method yields acceptable estimates about tail quantiles at a fraction of the computational cost of the full Monte Carlo.     

Forecasting Forward Defaults with the Discrete‐Time Hazard Model

For predicting forward default probabilities of firms, the discrete‐time forward hazard model (DFHM) is proposed. We derive maximum likelihood estimates for the parameters in DFHM. To improve its predictive power in practice, we also consider an extension of DFHM by replacing its constant coefficients of firm‐specific predictors with smooth functions of macroeconomic variables. The resulting model is called the discrete‐time varying‐coefficient forward hazard model (DVFHM). Through local maximum likelihood analysis, DVFHM is shown to be a reliable and flexible model for forward default prediction. We use real panel datasets to illustrate these two models. Using an expanding rolling window approach, our empirical results confirm that DVFHM has better and more robust out‐of‐sample performance on forward default prediction than DFHM, in the sense of yielding more accurate predicted numbers of defaults and predicted survival times. Thus DVFHM is a useful alternative for studying forward default losses in portfolios. Copyright © 2013 John Wiley & Sons, Ltd.     

On a family of finite moving‐average trend filters for the ends of series

A family of finite end filters is constructed using a minimum revisions criterion and based on a local dynamic model operating within the span of a given finite central filter. These end filters are equivalent to evaluating the central filter with unavailable future observations replaced by constrained optimal linear predictions. Two prediction methods are considered: best linear unbiased prediction and best linear biased prediction where the bias is time invariant. The properties of these end filters are determined. In particular, they are compared to X‐11 end filters and to the case where the central filter is evaluated with unavailable future observations predicted by global ARIMA models as in X‐11‐ARIMA or X‐12‐ARIMA. Copyright © 2002 John Wiley & Sons, Ltd.     

Can panel data really improve the predictability of the monetary exchange rate model?

A common explanation for the inability of the monetary model to beat the random walk in forecasting future exchange rates is that conventional time series tests may have low power, and that panel data should generate more powerful tests. This paper provides an extensive evaluation of this power argument to the use of panel data in the forecasting context. In particular, by using simulations it is shown that although pooling of the individual prediction tests can lead to substantial power gains, pooling only the parameters of the forecasting equation, as has been suggested in the previous literature, does not seem to generate more powerful tests. The simulation results are illustrated through an empirical application. Copyright © 2007 John Wiley & Sons, Ltd.     

On Selecting a Power Transformation in Time-Series Analysis

The primary aim of this paper is to select an appropriate power transformation when we use ARMA models for a given time series. We propose a Bayesian procedure for estimating the power transformation as well as other parameters in time series models. The posterior distributions of interest are obtained utilizing the Gibbs sampler, a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is illustrated with two real data sets. The performance of the proposed procedure is compared with other competing procedures. © 1997 John Wiley & Sons, Ltd.     

Forecasting economic time series that require a power transformation: Case of state tax receipts

In this study, time series analysis is applied to the problem of forecasting state income tax receipts. The data series is of special interest since it exhibits a strong trend with a high multiplicative seasonal component. An appropriate model is identified by simultaneous estimation of the parameters of the power transformation and the ARMA model using the Schwarz (1978) Bayesian information criterion. The forecasting performance of the time series model obtained from this procedure is compared with alternative time series and regression models. The study illustrates how an information criterion can be employed for identifying time series models that require a power transformation, as exemplified by state tax receipts. It also establishes time series analysis as a viable technique for forecasting state tax receipts.     

Prediction of α‐stable GARCH and ARMA‐GARCH‐M models

The best prediction of generalized autoregressive conditional heteroskedasticity (GARCH) models with α‐stable innovations, α‐stable power‐GARCH models and autoregressive moving average (ARMA) models with GARCH in mean effects (ARMA‐GARCH‐M) are proposed. We present a sufficient condition for stationarity of α‐stable GARCH models. The prediction methods are easy to implement in practice. The proposed prediction methods are applied for predicting future values of the daily SP500 stock market and wind speed data.     

Deletion diagnostics for transformations of time series

Deletion diagnostics are derived for the effect of individual observations on the estimated transformation of a time series. The paper uses the modified power transformation of Box and Cox to provide a parametric family of transformations. Inference about the transformation parameter is made through regression on a constructed variable. The effect of deletion of observations on residuals and on the estimate of the regression parameter are obtained. Index plots of the diagnostic quantities are shown to be highly informative. Structural time series modelling is used, so that the results readily extend to inference about regression on other explanatory variables.     

Bias‐corrected bootstrap prediction regions for vector autoregression

This paper examines small sample properties of alternative bias‐corrected bootstrap prediction regions for the vector autoregressive (VAR) model. Bias‐corrected bootstrap prediction regions are constructed by combining bias‐correction of VAR parameter estimators with the bootstrap procedure. The backward VAR model is used to bootstrap VAR forecasts conditionally on past observations. Bootstrap prediction regions based on asymptotic bias‐correction are compared with those based on bootstrap bias‐correction. Monte Carlo simulation results indicate that bootstrap prediction regions based on asymptotic bias‐correction show better small sample properties than those based on bootstrap bias‐correction for nearly all cases considered. The former provide accurate coverage properties in most cases, while the latter over‐estimate the future uncertainty. Overall, the percentile‐t bootstrap prediction region based on asymptotic bias‐correction is found to provide highly desirable small sample properties, outperforming its alternatives in nearly all cases. Copyright © 2004 John Wiley & Sons, Ltd.     

Transformations and dynamic linear models

The dynamic linear model (DLM) with additive Gaussian errors provides a useful statistical tool that is easily implemented because of the simplicity of updating a normal model that has a natural conjugate prior. If the model is not linear or if it does not have additive Gaussian errors, then numerical methods are usually required to update the distributions of the unknown parameters. If the dimension of the parameter space is small, numerical methods are feasible. However, as the number of unknown parameters increases, the numerial methods rapidly grow in complexity and cost. This article addresses the situation where a state dependent transformation of the observations follows the DLM, but a priori the appropriate transformation is not known. The Box-Cox family, which is indexed by a single parameter, illustrates the methodology. A prior distribution is constructed over a grid of points for the transformation parameter. For each value of the grid the relevant parameter esitmates and forecasts are obtained for the transformed series. These quantities are then integrated by the current distribution of the transformation parameter. When a new observation becomes available, parallel Kalman filters are used to update the distributions of the unknown parameters and to compute the likelihood of the transformation parameter at each grid point. The distribution of the transformation parameter is then updated.     

Regression tree model for prediction of demand with heterogeneity and censorship

In this research we analyze a new approach for prediction of demand. In the studied market of performing arts the observed demand is limited by capacity of the house. Then one needs to account for demand censorship to obtain unbiased estimates of demand function parameters. The presence of consumer segments with different purposes of going to the theater and willingness-to-pay for performance and ticket characteristics causes a heterogeneity in theater demand. We propose an estimator for prediction of demand that accounts for both demand censorship and preferences heterogeneity. The estimator is based on the idea of classification and regression trees and bagging prediction aggregation extended for prediction of censored data. Our algorithm predicts and combines predictions for both discrete and continuous parts of censored data. We show that our estimator performs better in terms of prediction accuracy compared with estimators which account either for censorship or heterogeneity only. The proposed approach is helpful for finding product segments and optimal price setting.     

Some comparisons of the relative power of simple tests for structural change in regression models

The power of Chow, linear, predictive failure and cusum of squares tests to detect structural change is compared in a two-variable random walk model and a once-for-all parameter shift model. In each case the linear test has greatest power, followed by the Chow test. It is suggested that the linear test be used as the basic general test for structural change in time series data, and tests of forecasting performance be confined to the last few observations. Analysis of recursive residuals and recursive parameter estimates should be regarded as forms of exploratory data analysis and tools for understanding discrepancies with previous results rather than a basis for formal tests of structural change.     

Wind power prediction based on wind speed forecast using hidden Markov model

This study examines a new approach for short-term wind speed and power forecasting based on the mixture of Gaussian hidden Markov models (MoG-HMMs). The proposed approach focuses on the characteristics of wind speed and power in the consecutive hours of previous days. The proposed method is carried out in two steps. In the first step, for the hourly prediction of wind speed, several wind speed features are employed in MoG-HMM, and in the second step, the results obtained from the first step along with their characteristics and wind power features are used to predict wind power estimation. To increase the prediction accuracy, the data used in each step are classified, and then for each class, one HMM with its specific parameters is used. The performance of the proposed approach is examined using real NREL data. The results show that the proposed method is more precise than other examined methods.     

Time series forecasting models involving power transformations

In this paper we discuss procedures for overcoming some of the problems involved in fitting autoregressive integrated moving average forecasting models to time series data, when the possibility of incorporating an instantaneous power transformation of the data into the analysis is contemplated. The procedures are illustrated using series of quarterly observations on corporate earnings per share.     

Probabilistic Forecasts of Wind Power Generation by Stochastic Differential Equation Models

The increasing penetration of wind power has resulted in larger shares of volatile sources of supply in power systems worldwide. In order to operate such systems efficiently, methods for reliable probabilistic forecasts of future wind power production are essential. It is well known that the conditional density of wind power production is highly dependent on the level of predicted wind power and prediction horizon. This paper describes a new approach for wind power forecasting based on logistic‐type stochastic differential equations (SDEs). The SDE formulation allows us to calculate both state‐dependent conditional uncertainties as well as correlation structures. Model estimation is performed by maximizing the likelihood of a multidimensional random vector while accounting for the correlation structure defined by the SDE formulation. We use non‐parametric modelling to explore conditional correlation structures, and skewness of the predictive distributions as a function of explanatory variables. Copyright © 2015 John Wiley & Sons, Ltd.     

On robust estimation of threshold autoregressions

We investigate the effects of additive outliers on the least squares (LS) estimation of threshold autoregressive models. The class of generalized-M (GM) estimates for linear time series is modified and applied to non-linear threshold processes. A Monte Carlo experiment is carried out to study the robust properties of these estimates. Their relative forecasting performances are also examined. The results indicate that the GM method is preferable to the LS estimation when the observations are contaminated by additive outliers. A real example is also given to illustrate the proposed method.     

Finite sample prediction and interpolation for ARIMA models with missing data

A transformation which allows Cholesky decomposition to be used to evaluate the exact likelihood function of an ARIMA model with missing data has recently been suggested. This method is extended to allow calculation of finite sample predictions of future observations. The output from the exact likelihood evaluation may also be used to estimate missing series values. Copyright © 1999 John Wiley & Sons, Ltd.     

Predictions in Overdispersed Series of Counts Using an Approximate Predictive Likelihood

The generalized autoregression model or GARM, originally used to model series of non-negative data measured at irregularly spaced time points (Lambert, 1996a), is considered in a count data context. It is first shown how the GARM can be expressed as a GLM in the special case of a linear model for some transform of the location parameter. The Butler approximate predictive likelihood (Butler, 1986, Rejoinder) is then used to define likelihood prediction envelopes. The width of these intervals is shown to be slightly wider than the Fisher (1959, pp. 128–33) and Lejeune and Faulkenberry (1982) predictive likelihood-based envelopes which assume that the parameters have fixed known values (equal to their maximum likelihood estimates). The method is illustrated on a small count data set showing overdispersion.© 1997 John Wiley & Sons, Ltd.     

One-day prediction of electricity load reflecting future RCS schedule

In a West-Bohemian power distribution company, a ripple control system (RCS) is used as a key tool for controlling peaks of electricity load. The RCS enables the dispatcher to switch off some groups of consumers for short periods of time, or to move their loading period in order to flatten the load diagram. Since the RCS connected consumers form about 20% of the whole load, shifts in the schedule have to be reflected in load predictions. Therefore, the load of RCS-connected consumers has been modelled and isolated from the baseload. Several similar categories of the consumers have been considered in the West Bohemian area, particularly direct heating, storage heating and boilers. Each category has been characterized by a few constants and parameters, namely installed load (a known parameter), the slope of charging and uncharging, and a daily profile of group's load. Thus, a piecewise linear model with jumps was obtained for the RCS part of the load. The baseload was modelled by means of regression on a suitable class of functions. The parameters have been estimated and utilized for a one-day-ahead prediction. This prediction reflects the scheduled times of RCS impulses, and enables dispatchers to influence the predicted diagram by changing this schedule.