Choosing Lag Lengths in Nonlinear Dynamic Models

Given that it is quite impractical to use standard model selection criteria in a nonlinear modeling context, the builders of nonlinear models often choose lag length by setting it equal to the lag length chosen for a linear autoregression of the data. This paper studies the performance of this procedure in a variety of circumstances, and then proposes some new and simple model selection procedures, based on linear approximations of the nonlinear forms. The idea here is to apply standard selection criteria to these linear approximations, rather than to autoregressions that make no provision for nonlinear behavior. A simulation study compares the properties of these proposed procedures with the properties of linear selection procedures.Nonlinear time series models, Neural networks, Model selection criteria, Polynomial approximations, Volterra expansions.

Testing for co-jumps in high-frequency financial data: an approach based on first-high-low-last prices

This paper proposes a new test for simultaneous intraday jumps in a panel of high frequency financial data. We utilize intraday first-high-low-last values of asset prices to construct estimates for the cross-variation of returns in a large panel of high frequency financial data, and then employ these estimates to provide a first-high-low-last price based test statistic to detect common large discrete movements (co-jumps). We study the finite sample behavior of our first-high-low-last price based test using Monte Carlo simulation, and find that it is more powerful than the Bollerslev et al (2008) return-based co-jump test. When applied to a panel of high frequency data from the Chinese mainland stock market, our first-high-low-last price based test identifies more common jumps than the return-based test in this emerging market.Covariance, Co-jumps, High-frequency data, First-High-Low-Last price, Microstructure bias, Nonsynchronous trades, Realized covariance, Realized co-range.

Forecasting Under Strucural Break Uncertainty

This paper proposes two new weighting schemes that average forecasts using different estimation windows to account for structural change. We let the weights reflect the probability of each time point being the most-recent break point, and we use the reversed ordered Cusum test statistics to capture this intuition. The second weighting method simply imposes heavier weights on those forecasts that use more recent information. The proposed combination forecasts are evaluated using Monte Carlo techniques, and we compare them with forecasts based on other methods that try to account for structural change, including average forecasts weighted by past forecasting performance and techniques that first estimate a break point and then forecast using the post break data. Simulation results show that our proposed weighting methods often outperform the others in the presence of structural breaks. An empirical application based on a NAIRU Phillips curve model for the United States indicates that it is possible to outperform the random walk forecasting model when we employ forecasting methods that account for break uncertainty.Forecasting with Structural breaks, Parameter Shifts, break Uncertainty, Structural break Tests, Choice of Estimation Sample, Forecast Combinations, NAIRU Phillips Curve.

Nonlinear Correlograms and Partial Autocorrelograms

This paper proposes neural network based measures of predictability in conditional mean, and then uses them to construct nonlinear analogues to autocorrelograms and partial autocorrelograms. In contrast to other measures of nonlinear dependence that rely on nonparametric estimation of densities or multivariate integration, our autocorrelograms are simple to calculate and appear to work well in relatively small samples.Nonlinear autocorrelograms, Nonlinear time series models, Neural networks, Model selection criteria, Nonlinear partial autocorrelograms

Random Walk Smooth Transition Autoregressive Models

This paper extends the family of smooth transition autoregressive (STAR) models by proposing a specification in which the autoregressive parameters follow random walks. The random walks in the parameters can capture structural change within a regime switching framework, but in contrast to the time varying STAR (TV-STAR) speciifcation recently introduced by Lundbergh et al (2003), structural change in our random walk STAR (RW-STAR) setting follows a stochastic process rather than a deterministic function of time. We suggest tests for RW-STAR behaviour and study the performance of RW-STARmodels in an empirical setting. The out-of sample forecasting performance of our RW-STAR models is encouraging - better than AR, LSTAR and TV-STAR specifications with respect to point forecasts and on a par with TV-STAR speciÞcations with respect to forecast density evaluations.Forecast density evaluation, Non-constant parameters, Random walk

Do Jumps Matter? Forecasting Multivariate Realized Volatility allowing for Common Jumps

Realized volatility of stock returns is often decomposed into two distinct components that are attributed to continuous price variation and jumps. This paper proposes a tobit multivariate factor model for the jumps coupled with a standard multivariate factor model for the continuous sample path to jointly forecast volatility in three Chinese Mainland stocks. Out of sample forecast analysis shows that separate multivariate factor models for the two volatility processes outperform a single multivariate factor model of realized volatility, and that a single multivariate factor model of realized volatility outperforms univariate models.Realized Volatility, Bipower Variation, Jumps, Common Factors, Forecasting

Nonlinear Autoregresssive Leading Indicator Models of Output in G-7 Countries

This paper studies linear and nonlinear autoregressive leading indicator models of business cycles in G7 countries. The models use the spread between short-term and long-term interest rates as leading indicators for GDP, and their success in capturing business cycles is gauged by non-parametric shape tests, and their ability to predict the probability of recession. We find that bivariate nonlinear models of output and the interest rate spread can successfully capture the shape of the business cycle in cases where linear models fail. Also, our nonlinear leading indicator models for USA, Canada and the UK outperform other models of GDP with respect to predicting the probability of recession.Business Cycles, Leading Indicators, Model Evaluation, Nonlinear Models, Yield Spreads.

Single Source of Error State Space Approach to the Beveridge Nelson Decomposition

A well known property of the Beveridge Nelson decomposition is that the innovations in the permanent and transitory components are perfectly correlated. We use a single source of error state space model to exploit this property and perform a Beveridge Nelson decomposition. The single source of error state space approach to the decomposition is computationally simple, and in contrast to other methods of performing the Beveridge-Nelson decomposition, it incorporates the direct estimation of the long-run multiplier.Beveridge Nelson decomposition; Long-run multiplier; Single source of error; State-space models.

Forecasting the volatility of Australian stock returns: do common factors help?

This paper develops univariate and multivariate forecasting models for realized volatility in Australian stocks. We consider multivariate models with common features or common factors, and we suggest estimation procedures for approximate factor models that are robust to jumps when the cross-sectional dimension is not very large. Our forecast analysis shows that multivariate models outperform univariate models, but that there is little difference between simple and sophisticated factor models