Bayesian Inference

Abstract

The surge in financial innovation and securitization in the beginning of the 21st century has introduced a large amount of new financial assets in exchanges around the world. While accurate inference on these new assets is crucial for market participants, the historical data available for modeling is in many cases too scarce for robust inference with Classical methods. The recently popular Bayesian inference methods possess theoretical advantages over Classical methods regarding small sample situations and could therefore prove out to be advantageous when making inferences on these new assets. This thesis is set to answer the question: does Bayesian inference perform better than its classical counterpart in the task of calculating inferences from a of a recently introduced asset with just a short historical time-series available?

The time-series used in evaluating the inference methods consists of daily observations of the carbon emission certificate futures prices. The time-series is split in two parts; to in-the-sample period and to out-of-the-sample period. Two different GARCH-type models are estimated from the in-the-sample period and forecasts are made for the out-of-the-sample period. Parameters of the models are estimated with both the classical maximum likelihood method and the Bayesian Markov chain Monte Carlo method. Estimates are calculated from samples of length 150, 300 and 596. In-the-sample fit is evaluated by a logarithmic likelihood test of the inferred and simulated densities. Out-of-the sample performance is evaluated by volatility forecasts and standard forecast error statistics.

The empirical results, though fully applicable only on the carbon emission certificate futures returns, show that the volatility forecasting accuracy increases when the model parameters are inferred by the Bayesian methods. The benefit is largest with the smallest sample size of 150 observations. However, the explanatory power of the forecasts is weak and implies that the models may be unable to capture the correct dynamics of the asset.