Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series

Bootstrap prediction intervals in State Space models

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.Backward representation, Kalman filter, Local Level Model, Unobserved Components

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.NAIRU, Output gap, Parameter uncertainty, Prediction Intervals, State Space Models

An overview of probabilistic and time series models in finance

In this paper, we partially review probabilistic and time series models in finance. Both discrete and continuous .time models are described. The characterization of the No- Arbitrage paradigm is extensively studied in several financial market contexts. As the probabilistic models become more and more complex to be realistic, the Econometrics needed to estimate them are more difficult. Consequently, there is still much research to be done on the link between probabilistic and time series models

Non-negative matrix factorization for medical imaging

A non-negative matrix factorization approach to dimensionality reduction is proposed to aid classification of images. The original images can be stored as lower-dimensional columns of a matrix that hold degrees of belonging to feature components, so they can be used in the training phase of the classification at lower runtime and without loss in accuracy. The extracted features can be visually examined and images reconstructed with limited error. The proof of concept is performed on a benchmark of handwritten digits, followed by the application to histopathological colorectal cancer slides. Results are encouraging, though dealing with real-world medical data raises a number of issues.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Hopfield networks: from optimization to adaptive control

This paper proposes an adaptative control algorithm, which is designed by adding a parametric identification method to a non-linear controller. The identification module is built upon the Hopfield neural network, resulting in an unconventional network with time-varying weights and biases. The convergence of the estimations of the parameters of a dynamical system was proved in previous work, as long as the system inputs can be freely manipulated to provide persistent excitation. Henceforth the behaviour of the closed-loop system, when the inputs result from the controller equations, is here analyzed in order to assess both the tracking performance of the full adaptive controller and the identification ability of the neural estimator. The algorithm is applied to an idealized robotic system with two joints, whose positions and velocities are required to follow, as closely as possible, a prescribed reference trajectory. The simulation results show a satisfactory control performance, since the demanded trajectory is almost accurately followed. The estimated values also converge to the correct parameters, as long as the controller provides sufficiently rich signals to the system. The results are similar to a conventional least-squares adaptive controller, with a much lower computational cost.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Under which conditions is carrier cooperation possible? A case study in a Seville marketplace

The high volume of traffic originates two well-known problems in many cities: congestion and pollution. In recent years, a social phenomenon is emerging cooperation. This work is aimed at evaluating the circumstances under which transport cooperation is possible between different stakeholders operating in the same geographical area. To this end, a double survey process was conducted in a marketplace situated in the Seville City (Spain) centre. The first survey was designed to know the characteristics of the retailers and their preferences with respect to cooperation and regulations. A relational analysis between retailer features and their willingness to cooperate was carried out. After analysing the motivations for non-cooperation, a mixed proposal was designed and surveyed. Although the research was limited to a marketplace, the relevant data gathered from this double survey process highlights some implications: (a) the importance of personal relations in retailer cooperation; (b) a high volume of freight and the use of vans as on-street warehouses appear as significant motivations for non-cooperation; (c) forcing changes in the statu quo encourages cooperation.Ministerio de Economía y Competitividad (España) TEC2013-47286-C3-3-

Tactile hazardous material information system (THMIS)

In today\u27s work environment, many dangers exist around that can harm workers who are not aware of the hazards in their environment. If these workers happen to be visually impaired, then identifying those hazards with the present labeling systems would be difficult. The Hazardous Material Information System (HMIS) was chosen to be adapted with tactile patterns and numbers. The tactile patterns and numbers would not change the layout and intent of the HMIS, but enhance its effectiveness. Five tactile patterns and five tactile numbers were designed to be recognizable and simple. The patterns and numbers were tested and observed to learn if they could be recognized without being mistaken for another pattern. Twenty subjects volunteered, 14 males and 6 females, to participate in the experiment. The twenty subjects were provided two different sizes of the patterns making a total of 2000 observations. The three most recognizable tactile patterns were chosen out of the five and assigned a color consistent with the HMIS