Sequential Monte Carlo Filters with Parameters Learning for Commodity Pricing Models

In this article, an estimation methodology based on the sequential Monte Carlo algorithm is proposed, thatjointly estimate the states and parameters, the relationship between the prices of futures contracts and the spot prices of primary products is determined, the evolution of prices and the volatility of the historical data of the primary market (Gold and Soybean) are analyzed. Two stochastic models for an estimate the states and parameters are considered, the parameters and states describe physical measure (associated with the price) and risk-neutral measure (associated with the markets to futures), the price dynamics in the short-term through the reversion to the mean and volatility are determined, while that in the long term through markets to futures. Other characteristics such as seasonal patterns, price spikes, market dependent volatilities, and non-seasonality can also be observed. In the methodology, a parameter learning algorithm is used, specifically, three algorithms are proposed, that is the sequential Monte Carlo estimation (SMC) for state space modelswith unknown parameters: the first method is considered a particle filter that is based on the sampling algorithm of sequential importance with resampling (SISR). The second implemented method is the Storvik algorithm [19], the states and parameters of the posterior distribution are estimated that have supported in low-dimensional spaces, a sufficient statistics from the sample of the filtered distribution is considered. The third method is (PLS) Carvalho’s Particle Learning and Smoothing algorithm [31]. The cash prices of the contracts with future delivery dates are analyzed. The results indicate postponement of payment, the future prices on different maturity dates with the spot price are highly correlated. Likewise, the contracts with a delivery date for the last periods of the year 2017, the spot price lower than the prices of the contracts with expiration date for 12 and 24 months is found, opposite occurs in the contracts with expiration date for 1 and 6 months.

Inflation and professional forecast dynamics: An evaluation of stickiness, persistence, and volatility

This paper studies the joint dynamics of U.S. inflation and a term structure of average inflation predictions taken from the Survey of Professional Forecasters (SPF). We estimate these joint dynamics by combining an unobserved components (UC) model of inflation and a sticky‐information forecast mechanism. The UC model decomposes inflation into trend and gap components, and innovations to trend and gap inflation are affected by stochastic volatility. A novelty of our model is to allow for time‐variation in inflation‐gap persistence as well as in the frequency of forecast updating under sticky information. The model is estimated with sequential Monte Carlo methods that include a particle learning filter and a Rao–Blackwellized particle smoother. Based on data from 1968 Q4 to 2018 Q3, estimates show that (i) longer horizon average SPF inflation predictions inform estimates of trend inflation; (ii) inflation gap persistence is countercyclical before the Volcker disinflation and acyclical afterwards; (iii) by 1990 sticky‐information inflation forecast updating is less frequent than it was earlier in the sample; and (iv) the drop in the frequency of the sticky‐information forecast updating occurs at the same time persistent shocks become less important for explaining movements in inflation. Our findings support the view that stickiness in survey forecasts is not invariant to the inflation process.

An efficient sequential learning algorithm in regime-switching environments

We provide a novel approach of estimating a regime-switching nonlinear and non-Gaussian state-space model based on a particle learning scheme. In particular, we extend the particle learning method in Liu, J., and M. West. 2001. “Combined Parameter and State Estimation in Simulation-Based Filtering.” In Sequential Monte Carlo Methods in Practice, 197–223. Springer. by constructing a new proposal distribution for the latent regime index variable that incorporates all available information contained in the current and past observations. The Monte Carlo simulation result implies that our approach categorically outperforms a popular existing algorithm. For empirical illustration, the proposed algorithm is used to analyze the underlying dynamics of US excess stock return.

Industry-based equity premium forecasts

Purpose This paper aims to study whether the industry indexes predict the evolution of the broad stock market in the USA. Design/methodology/approach The study uses industry indexes to predict the equity premium in the USA. It considers several types of predictive models: constant coefficients and constant volatility, drifting coefficients and constant volatility, constant coefficients and stochastic volatility and drifting coefficients and stochastic volatility. The models are estimated through the particle learning algorithm, which is suitable for dealing with the problem that an investor faces in practice, given that it allows the investor to revise the parameters as new information arrives. The individual forecasts are combined based on their past performance. Findings The results reveal that models exhibit significant predictive ability. The models with constant volatility exhibit better performance, at the statistical level, but the models with stochastic volatility generate higher gains for a mean–variance investor. Practical implications This study’s findings are valuable not only for finance researchers but also for private investors and mutual fund managers, who can use these forecasts to improve the performance of their portfolios. Originality/value To the best of the knowledge of the author, this is the first paper that uses particle learning and combination of forecasts to predict the equity premium in the USA based on industry indexes. The study shows that the models generate valuable forecasts over the long time span that is considered.