On predicting the semiconductor industry cycle: a Bayesian model averaging approach

The methodologies used in previous studies include the vector autoregressive (VAR) model in Liu (2005, 2007), the Markov regime-switching model in Liu and Chyi (2006) and Liu et al. (2013), the discrete Fourier transform in Tan and Mathews (2010a), the Bayesian VAR model in Chow and Choy (2006) and Aubry and Renou-Maissant (2014), and the vector error-correction model in Aubry and Renou-Maissant (2013).

Recently, Hansen (2007) and Hansen and Racine (2012) introduced Mallows model averaging (MMA) and Jackknife model averaging (JMA), which are asymptotical optimal in the sense of achieving the lowest possible squared error under the assumptions of homoscedastic errors and heteroscedastic errors, respectively. It is shown in Hansen (2007) that when the weight set is rich enough, the optimal model averaging estimator usually outperforms the one obtained from the optimal single model. However, these two approaches, requiring the error term to be independent, preclude the regression model with time-series errors. Besides, they cannot be applied to the high-dimensional case if the number of potential predictors is larger than 20 in a non-nested framework due to computational infeasibility. Therefore, with 70 potential predictors in a non-nested time-series system, we are unable to consider this research stream and must apply Bayesian model averaging to deal with model uncertainty in our study.

As indicated by one of the anonymous referees, both samplers (“birth–death” and “reversible jump”) we discuss here are Reversible Jump Markov Chains. The only difference is the type of model changing moves considered.

A run of 2 million recorded drawings with a burn-in of 1 million discarded drawings generates virtually similar results.

Of course, the chain will not cover the entire model space since this would require sampling all \(2^{70}\) models which is computational prohibitive as we already mentioned. Therefore, as noted in Fernandez et al. (2001b), the sample will not make up a perfect replica of the posterior model distribution. Alternatively, the objective of sampling methods in this context is to explore the model space in order to capture the models with higher posterior probability. Our efficient implementation of the “reversible-jump” sampler allows us to cover a high percentage of the posterior mass and, thus, to also characterize a very substantial amount of the variability inherent in the posterior distribution. In addition, we have run a second Markov chain and obtained a 60% “capture–recapture” ratio of the 10,000 best models. Moreover, to further confirm the convergence of the chain, we have tried five different start values of model dimensions (0, 20, 35, 50, and 70) and received virtually similar results.

For example, Liu (2005) considered 11 predictors, Chow and Choy (2006) 4, Liu (2007) 3 to 10 in different models, and Aubry and Renou-Maissant (2013) 5.

To conserve space, we do not provide the results from these two alternative model priors here. However, these results can be provided upon request.

We thank one of the anonymous referees for this constructive suggestion.

Lasso stands for “least absolute shrinkage and selection operator”.

We use the PLUS package for R to obtain the results for MC+ and SCAD.

The reason why MC+ and SCAD identify so many relevant predictors may be due to the limitation of the Lasso-type method in distinguishing the relevant and irrelevant predictors when there are highly correlated predictors in the dataset, such as IP, NO, TI, or VS in the downstream industries.

At each point in time, we re-estimate the regression, so a new model is selected for the forecast.

Although we have tried adding \(G_{t-1 }\), \(G_{t-2}\), \(G_{t-3}\), and\( G_{t-12}\) into our BMA or BMA* model as potential predictors, the forecast results in terms of MAE and MSE are quite similar to the one presented here.