A Multi-Step Forecast Density

This paper makes two contribution to the literature on density forecasts. First, we propose a novel bootstrap approach to estimate forecasting densities based on nonparametric techniques. The method is based on the Markov Bootstrap that is suitable to resample dependent data. The combination of nonparametric and bootstrap methods delivers density forecasts that are flexible in capturing markovian dependence (linear and nonlinear) occurring in any moment of the distribution. Second, we improve the testing approach to evaluate density forecasts by considering a set of tests for dynamical misspecification such as autocorrelation, heteroskedasticity and neglected nonlinearity. The approach is useful because rejections of the tests give insights into ways to improve the forecasting model. By Monte Carlo simulations we show that the proposed evaluation strategy has much higher power to detect misspecification of the density forecasts compared to previous analysis. The proposed nonparametric-bootstrap forecasting method exhibits the ability to capture correctly the dynamics of linear and nonlinear time series models. We also investigate the performance at higher orders and propose methods to deal with the \u201ccurse of dimensionality\u201d. Finally, we empirically investigate the relevance of the method in out-of-sample forecasting the density of 3 business cycles variables for the US: real GDP, the Coincident Indicator and Industrial Production. The results indicate that the method gives reliable density forecasts for all variables and performs better compared to parametric forecasting methods.

Testing for Nonlinear Structure and Chaos in Economic Time Series: A Comment

This short paper is a comment on ``Testing for Nonlinear Structure and Chaos in Economic Time Series'' by Catherine Kyrtsou and Apostolos Serletis. We summarize their main results and discuss some of their conclusions concerning the role of outliers and noisy chaos. In particular, we include some new simulations to investigate whether economic time series may be characterized by low dimensional noisy chaos.

Behavioral Heterogeneity in Stock Prices

We estimate a dynamic asset pricing model characterized by heterogeneous boundedly rational agents. The fundamental value of the risky asset is publicly available to all agents, but they have different beliefs about the persistence of deviations of stock prices from the fundamental benchmark. An evolutionary selection mechanism based on relative past profits governs the dynamics of the fractions and switching of agents between different beliefs or forecasting strategies. A strategy attracts more agents if it performed relatively well in the recent past compared to other strategies. We estimate the model to annual US stock price data from 1871 until 2003. The estimation results support the existence of two expectation regimes, and a bootstrap F-test rejects linearity in favor of our nonlinear two-type heterogeneous agent model. One regime can be characterized as a fundamentalists regime, because agents believe in mean reversion of stock prices toward the benchmark fundamental value. The second regime can be characterized as a chartist, trend following regime because agents expect the deviations from the fundamental to trend. The fractions of agents using the fundamentalists and trend following forecasting rules show substantial time variation and switching between predictors. The model offers an explanation for the recent stock prices run-up. Before the 90s the trend following regime was active only occasionally. However, in the late 90s the trend following regime persisted and created an extraordinary deviation of stock prices from the fundamentals. Recently, the activation of the mean reversion regime has contributed to drive stock prices back closer to their fundamental valuation.

Nonlinear Mean Reversion in Stock Prices

We investigate evidence for nonlinear mean reversion in yearly S\&P500 data from 1871 until 2001. We find that up to 1990 there is significant evidence of nonlinear mean reversion. In particular, stock prices are characterized by a persistent process close to the fundamental value. However, when prices deviate significantly a mean reverting regime is activated and prices adjust to fundamental values. Instead, the stock price run-up of the late 90s exacerbated the persistence of the deviations and there is no evidence for a mean reverting regime that drives prices back to fundamentals.nonlinear time series, mean reversion

Reducing the Bias of Causality Measures

Measures of the direction and strength of the interdependence between two time series are evaluated and modified in order to reduce the bias in the estimation of the measures, so that they give zero values when there is no causal effect. For this, point shuffling is employed as used in the frame of surrogate data. This correction is not specific to a particular measure and it is implemented here on measures based on state space reconstruction and information measures. The performance of the causality measures and their modifications is evaluated on simulated uncoupled and coupled dynamical systems and for different settings of embedding dimension, time series length and noise level. The corrected measures, and particularly the suggested corrected transfer entropy, turn out to stabilize at the zero level in the absence of causal effect and detect correctly the direction of information flow when it is present. The measures are also evaluated on electroencephalograms (EEG) for the detection of the information flow in the brain of an epileptic patient. The performance of the measures on EEG is interpreted, in view of the results from the simulation study.Comment: 30 pages, 12 figures, accepted to Physical Review

Tests for serial independence and linearity based on correlation integrals

We propose information theoretic tests for serial independence and linearity in time series. The test statistics are based on the conditional mutual information, a general measure of dependence between lagged variables. In case of rejecting the null hypothesis, this readily provides insights into the lags through which the dependence arises. The conditional mutual information is estimated using the correlation integral from chaos theory. The significance of the test statistic is determined with a permutation procedure and a parametric bootstrap in the tests for independence and linearity, respectively. The size and power properties of the tests are examined numerically and illustrated with applications to some benchmark time series.

A chemically etched corrugated feedhorn array for D-band CMB observations

We present the design, manufacturing, and testing of a 37-element array of corrugated feedhorns for Cosmic Microwave Background CMB) measurements between 140 and 170 GHz. The array was designed to be coupled to Kinetic Inductance Detector arrays, either directly (for total power measurements) or through an orthomode transducer (for polarization measurements). We manufactured the array in platelets by chemically etching aluminum plates of 0.3 mm and 0.4 mm thickness. The process is fast, low-cost, scalable, and yields high-performance antennas compared to other techniques in the same frequency range. Room temperature electromagnetic measurements show excellent repeatability with an average cross polarization level about − 20 dB, return loss about − 25 dB, first sidelobes below − 25 dB and far sidelobes below − 35 dB. Our results qualify this process as a valid candidate for state-of-the-art CMB experiments, where large detector arrays with high sensitivity and polarization purity are of paramount importance in the quest for the discovery of CMB polarization B-modes