Review of Unbiased FIR Filters, Smoothers, and Predictors for Polynomial Signals

Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples can be found in industrial, scientific and biomedical instrumentation. Depending on the nature of the application the signal estimate is allowed to be a delayed estimate of the original signal or, in the other extreme, no delay is tolerated. These cases are commonly referred to as filtering, prediction, and smoothing depending on the amount of advance or lag between the input data set and the output data set. In this review paper we provide a comprehensive set of design and analysis tools for designing unbiased FIR filters, predictors, and smoothers for slowly varying signals, i.e. signals that can be modeled by low order polynomials. Explicit expressions of parameters needed in practical implementations are given. Real life examples are provided including cases where the method is extended to signals that are piecewise slowly varying. A critical view on recursive implementations of the algorithms is provided

Factor Analysis of a Large DSGE Model

We study the workings of the factor analysis of high-dimensional data using arti…cial series generated from a large, multi-sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allow us to shed some light on the practical bene…ts and limitations of using factor analysis techniques on economic data. We explain in what sense the arti…cial data can be thought of having a factor structure, study the theoretical and fi…nite sample properties of the principal components estimates of the factor space, investigate the substantive reason(s) for the good performance of diffusion index forecasts, and assess the quality of the factor analysis of highly dissagregated data. In all our exercises, we explain the precise relationship between the factors and the basic macroeconomic shocks postulated by the model.Multisector economies, principal components, forecasting, pervasiveness, FAVAR

Predicting Bid-Ask Spreads Using Long Memory Autoregressive Conditional Poisson Models

We introduce a long memory autoregressive conditional Poisson (LMACP) model to model highly persistent time series of counts. The model is applied to forecast quoted bid-ask spreads, a key parameter in stock trading operations. It is shown that the LMACP nicely captures salient features of bid-ask spreads like the strong autocorrelation and discreteness of observations. We discuss theoretical properties of LMACP models and evaluate rolling window forecasts of quoted bid-ask spreads for stocks traded at NYSE and NASDAQ. We show that Poisson time series models significantly outperform forecasts from ARMA, ARFIMA, ACD and FIACD models. The economic significance of our results is supported by the evaluation of a trade schedule. Scheduling trades according to spread forecasts we realize cost savings of up to 13 % of spread transaction costs.Bid-ask spreads, forecasting, high-frequency data, stock market liquidity, count data time series, long memory Poisson autoregression

Tree-Structured Nonlinear Adaptive Signal Processing

In communication systems, nonlinear adaptive filtering has become increasingly popular in a variety of applications such as channel equalization, echo cancellation and speech coding. However, existing nonlinear adaptive filters such as polynomial (truncated Volterra series) filters and multilayer perceptrons suffer from a number of problems. First, although high Order polynomials can approximate complex nonlinearities, they also train very slowly. Second, there is no systematic and efficient way to select their structure. As for multilayer perceptrons, they have a very complicated structure and train extremely slowly Motivated by the success of classification and regression trees on difficult nonlinear and nonparametfic problems, we propose the idea of a tree-structured piecewise linear adaptive filter. In the proposed method each node in a tree is associated with a linear filter restricted to a polygonal domain, and this is done in such a way that each pruned subtree is associated with a piecewise linear filter. A training sequence is used to adaptively update the filter coefficients and domains at each node, and to select the best pruned subtree and the corresponding piecewise linear filter. The tree structured approach offers several advantages. First, it makes use of standard linear adaptive filtering techniques at each node to find the corresponding Conditional linear filter. Second, it allows for efficient selection of the subtree and the corresponding piecewise linear filter of appropriate complexity. Overall, the approach is computationally efficient and conceptually simple. The tree-structured piecewise linear adaptive filter bears some similarity to classification and regression trees. But it is actually quite different from a classification and regression tree. Here the terminal nodes are not just assigned a region and a class label or a regression value, but rather represent: a linear filter with restricted domain, It is also different in that classification and regression trees are determined in a batch mode offline, whereas the tree-structured adaptive filter is determined recursively in real-time. We first develop the specific structure of a tree-structured piecewise linear adaptive filter and derive a stochastic gradient-based training algorithm. We then carry out a rigorous convergence analysis of the proposed training algorithm for the tree-structured filter. Here we show the mean-square convergence of the adaptively trained tree-structured piecewise linear filter to the optimal tree-structured piecewise linear filter. Same new techniques are developed for analyzing stochastic gradient algorithms with fixed gains and (nonstandard) dependent data. Finally, numerical experiments are performed to show the computational and performance advantages of the tree-structured piecewise linear filter over linear and polynomial filters for equalization of high frequency channels with severe intersymbol interference, echo cancellation in telephone networks and predictive coding of speech signals

Comovements in volatility in the euro money market

This paper assesses the sources of volatility persistence in Euro Area money market interest rates and the existence of linkages relating volatility dynamics. The main findings of the study are as follows. Firstly, there is evidence of stationary long memory, of similar degree, in all series. Secondly, there is evidence of fractional cointegration relationships relating all series, except the overnight rate. Two common long memory factors are found to drive the temporal evolution of the volatility processes. The first factor shows how persistent volatility shocks are trasmitted along the term structure, while the second factor points to excess persistent volatility at the longer end of the yield curve, relative to the shortest end. Finally, impulse response analysis and forecast error variance decomposition point to forward transmission of shocks only, involving the closest maturities. JEL Classification: C32, F30, G10fractional integration and cointegration, fractional vector error correction model, liquidity e¤ect, money market interest rates, realized volatility

Factor Analysis of a Large DSGE Model

We study the workings of the factor analysis of high-dimensional data using artificial series generated from a large, multi-sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allow us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the theoretical and finite sample properties of the principal components estimates of the factor space, investigate the substantive reason(s) for the good performance of di¤usion index forecasts, and assess the quality of the factor analysis of highly dissagregated data. In all our exercises, we explain the precise relationship between the factors and the basic macroeconomic shocks postulated by the model

Statistical Tests of the Rank of a Matrix and Their Applications in Econometric Modelling

Testing the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics literature where these tests are required.Multiple time series, Model specification, Tests of rank