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on Econometrics |
| By: | Alain Hecq; Daniel Velasquez-Gaviria |
| Abstract: | This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the innovations. Instead, we use the information of higher-order cumulants, combining the spectrum and the bispectrum in a minimum distance estimation. We show how to circumvent the nonlinearity of the parameters and the multimodality in the noncausal and mixed models by selecting the appropriate initial values in the estimation. In addition, we propose a method of identification using a simple comparison criterion based on the global minimum of the estimation function. By means of a Monte Carlo study, we find unbiased estimated parameters and a correct identification as the data depart from normality. We propose an empirical application on eight monthly commodity prices, finding noncausal and mixed causal-noncausal dynamics. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.13830&r=ecm |
| By: | Bodnar, Taras (Stockholm University); Mazur, Stepan (Örebro University School of Business); Nguyen, Hoang (Örebro University School of Business) |
| Abstract: | In the paper we consider the optimal portfolio choice problem under parameter uncertainty when the covariance matrix of asset returns is singular. Very useful stochastic representations are deduced for the characteristics of the expected utility optimal portfolio. Using these stochastic representations, we derive the moments of higher order of the estimated expected return and the estimated variance of the expected utility optimal portfolio. Another line of applications leads to their asymptotic distributions obtained in the high-dimensional setting. Via a simulation study, it is shown that the derived high-dimensional asymptotic distributions provide good approximations of the exact ones even for moderate sample sizes. |
| Keywords: | singular Wishart distribution; mean-variance portfolio; Moore-Penrose inverse |
| JEL: | G11 |
| Date: | 2022–12–06 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:oruesi:2022_015&r=ecm |
| By: | Mathur, Maya B |
| Abstract: | Background: Complete-case analyses can be biased if missing data are not missing completely at random. Methods: We propose simple sensitivity analyses that apply to complete-case estimates of treatment effects; these analyses use only simple summary data and obviate specifying the mechanism of missingness and making distributional assumptions. Bias arises when: (1) treatment effects differ between retained and non-retained participants; or (2) among non-retained participants, the estimate is biased because conditioning on retention has induced a backdoor path. We thus bound the overall treatment effect on the difference scale by specifying: (1) the unobserved treatment effect among non-retained participants; (2) the strengths of association that unobserved variables have with the exposure and with the outcome among retained participants (``induced confounding associations''). Working with the former sensitivity parameter subsumes certain existing methods of worst-case imputation, while also accommodating less conservative assumptions (e.g., that the treatment is not detrimental even among non-retained participants). We propose analogs to the E-value for confounding that represent, for a specified treatment effect among non-retained participants, the strength of induced confounding associations required to reduce the treatment effect to the null or to any other value. Results: We apply the methods to a published randomized trial on financial incentives for smoking cessation. Conclusion: These methods could help characterize the robustness of complete-case analyses to potential bias due to missing data. The methods can also be used for general selection bias when the probability of selection is known. |
| Date: | 2022–06–03 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:e9bzc&r=ecm |
| By: | Guljanov, Gaygysyz; Mutschler, Willi; Trede, Mark |
| Abstract: | The Skewed Kalman Filter is a powerful tool for statistical inference of asymmetrically distributed time series data. However, the need to evaluate Gaussian cumulative distribution functions (cdf) of increasing dimensions, creates a numerical barrier such that the filter is usually applicable for univariate models and under simplifying conditions only. Based on the intuition of how skewness propagates through the state-space system, a computationally efficient algorithm is proposed to prune the overall skewness dimension by discarding elements in the cdfs that do not distort the symmetry up to a pre-specified numerical threshold. Accuracy and efficiency of this Pruned Skewed Kalman Filter for general multivariate state-space models are illustrated through an extensive simulation study. The Skewed Kalman Smoother and its pruned implementation are also derived. Applicability is demonstrated by estimating a multivariate dynamic Nelson-Siegel term structure model of the US yield curve with Maximum Likelihood methods. We find that the data clearly favors a skewed distribution for the innovations to the latent level, slope and curvature factors. |
| Keywords: | state-space models; skewed Kalman filter; skewed Kalman smoother; closed skew-normal; dimension reduction; yield curve; term structure; dynamic Nelson-Siegel |
| Date: | 2022–12 |
| URL: | http://d.repec.org/n?u=RePEc:cpm:dynare:078&r=ecm |
| By: | Li, Chenxing; Maheu, John M; Yang, Qiao |
| Abstract: | This paper extends the Bayesian semiparametric stochastic volatility (SV-DPM) model of Jensen and Maheu (2010). Instead of using a Dirichlet process mixture (DPM) to model return innovations, we use an infinite hidden Markov model (IHMM). This allows for time variation in the return density beyond that attributed to parametric latent volatility. The new model nests several special cases as well as the SV-DPM. We also discuss posterior and predictive density simulation methods for the model. Applied to equity returns, foreign exchange rates, oil price growth and industrial production growth, the new model improves density forecasts, compared to the SV-DPM, a stochastic volatility with Student-t innovations and other fat-tailed volatility models. |
| Keywords: | stochastic volatility; Markov-switching; MCMC; Bayesian; nonparametric; semiparametric |
| JEL: | C11 C14 C22 C53 C58 |
| Date: | 2022–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:115456&r=ecm |
| By: | Aryan Bhambu; Arabin Kumar Dey |
| Abstract: | In this paper we propose a novel procedure to construct a confidence interval for multivariate time series predictions using long short term memory network. The construction uses a few novel block bootstrap techniques. We also propose an innovative block length selection procedure for each of these schemes. Two novel benchmarks help us to compare the construction of this confidence intervals by different bootstrap techniques. We illustrate the whole construction through S\&P $500$ and Dow Jones Index datasets. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.13915&r=ecm |
| By: | John List; Ian Muir; Gregory Sun |
| Abstract: | This study investigates how to use regression adjustment to reduce variance in experimental data. We show that the estimators recommended in the literature satisfy an orthogonality property with respect to the parameters of the adjustment. This observation greatly simplifies the derivation of the asymptotic variance of these estimators and allows us to solve for the efficient regression adjustment in a large class of adjustments. Our efficiency results generalize a number of previous results known in the literature. We then discuss how this efficient regression adjustment can be feasibly implemented. We show the practical relevance of our theory in two ways. First, we use our efficiency results to improve common practices currently employed in field experiments. Second, we show how our theory allows researchers to robustly incorporate machine learning techniques into their experimental estimators to minimize variance. |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:feb:natura:00763&r=ecm |
| By: | Oshan, Taylor M. |
| Abstract: | This chapter introduces the concept of local versus global models and describes one type of local model, Geographically Weighted Regression, and its recent successor, Multiscale Geographically Weighted Regression. The conceptual basis for this type of model is explained in terms of data-borrowing. An empirical example is given to demonstrate both the value of local regression models and freely available software for their calibration. |
| Date: | 2022–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:hpbd8&r=ecm |
| By: | Damir Filipovi\'c; Puneet Pasricha |
| Abstract: | We introduce an ensemble learning method based on Gaussian Process Regression (GPR) for predicting conditional expected stock returns given stock-level and macro-economic information. Our ensemble learning approach significantly reduces the computational complexity inherent in GPR inference and lends itself to general online learning tasks. We conduct an empirical analysis on a large cross-section of US stocks from 1962 to 2016. We find that our method dominates existing machine learning models statistically and economically in terms of out-of-sample $R$-squared and Sharpe ratio of prediction-sorted portfolios. Exploiting the Bayesian nature of GPR, we introduce the mean-variance optimal portfolio with respect to the predictive uncertainty distribution of the expected stock returns. It appeals to an uncertainty averse investor and significantly dominates the equal- and value-weighted prediction-sorted portfolios, which outperform the S&P 500. |
| Date: | 2022–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2212.01048&r=ecm |
| By: | Mogens Fosgerau; Julien Monardo; André de Palma (Université de Cergy-Pontoise, THEMA) |
| Abstract: | We introduce the inverse product differentiation logit (IPDL) model, a micro-founded inverse market share model for differentiated products that captures market segmentation according to one or more characteristics. The IPDL model generalizes the nested logit model to allow richer substitution patterns, including complementarity in demand, and can be estimated by linear instrumental variables regression using market-level data. Furthermore, we provide Monte Carlo experiments that compare the IPDL model to the workhorse empirical models of the literature. Lastly, we show the empirical performance of the IPDL model using a well-known dataset on the ready-toeat cereals market. |
| Keywords: | Demand estimation, Inverse demand, Logit, Consumer model, Differentiated products. |
| JEL: | C26 D11 D12 L |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2022-22&r=ecm |
| By: | Marko Mlikota |
| Abstract: | Many environments in economics feature a cross-section of agents or units linked by a network of bilateral ties. I develop a framework to study dynamics in these cases. It consists of a vector autoregression in which innovations transmit cross-sectionally via bilateral links and which can accommodate general patterns of how network effects of higher order accumulate over time. In a first application, I take the supply chain network of the US economy as given and document how it drives the dynamics of sectoral prices. By estimating the time profile of network effects, the model allows me to go beyond steady state comparisons and study transition dynamics induced by granular shocks. As a result of different positions in the input-output network, sectors differ in both the strength and the timing of their impact on aggregates. In a second application, I discuss how to approximate cross-sectional processes by assuming that dynamics are driven by a network and in turn estimating the latter. The proposed framework offers a sparse, yet flexible and interpretable method for doing so, owing to networks` ability to summarize complex relations among units by relatively few non-zero bilateral links. Modeling industrial production growth across 44 countries, I obtain reductions in out-of-sample mean squared errors of up to 20% relative to a principal components factor model. |
| Date: | 2022–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.13610&r=ecm |
| By: | Yao Lei Xu; Kriton Konstantinidis; Danilo P. Mandic |
| Abstract: | Analytics of financial data is inherently a Big Data paradigm, as such data are collected over many assets, asset classes, countries, and time periods. This represents a challenge for modern machine learning models, as the number of model parameters needed to process such data grows exponentially with the data dimensions; an effect known as the Curse-of-Dimensionality. Recently, Tensor Decomposition (TD) techniques have shown promising results in reducing the computational costs associated with large-dimensional financial models while achieving comparable performance. However, tensor models are often unable to incorporate the underlying economic domain knowledge. To this end, we develop a novel Graph-Regularized Tensor Regression (GRTR) framework, whereby knowledge about cross-asset relations is incorporated into the model in the form of a graph Laplacian matrix. This is then used as a regularization tool to promote an economically meaningful structure within the model parameters. By virtue of tensor algebra, the proposed framework is shown to be fully interpretable, both coefficient-wise and dimension-wise. The GRTR model is validated in a multi-way financial forecasting setting and compared against competing models, and is shown to achieve improved performance at reduced computational costs. Detailed visualizations are provided to help the reader gain an intuitive understanding of the employed tensor operations. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2211.05581&r=ecm |
| By: | Todd E. Clark; Gergely Ganics; Elmar Mertens |
| Abstract: | This paper presents a new approach to combining the information in point and density forecasts from the Survey of Professional Forecasters (SPF) and assesses the incremental value of the density forecasts. Our starting point is a model, developed in companion work, that constructs quarterly term structures of expectations and uncertainty from SPF point forecasts for quarterly fixed horizons and annual fixed events. We then employ entropic tilting to bring the density forecast information contained in the SPF’s probability bins to bear on the model estimates. In a novel application of entropic tilting, we let the resulting predictive densities exactly replicate the SPF’s probability bins. Our empirical analysis of SPF forecasts of GDP growth and inflation shows that tilting to the SPF’s probability bins can visibly affect our model-based predictive distributions. Yet in historical evaluations, tilting does not offer consistent benefits to forecast accuracy relative to the model-based densities that are centered on the SPF’s point forecasts and reflect the historical behavior of SPF forecast errors. That said, there can be periods in which tilting to the bin information helps forecast accuracy. |
| Keywords: | Term Structure of Expectations; Uncertainty; Survey Forecasts; Fan Charts; Entropic Tilting |
| JEL: | E37 C53 |
| Date: | 2022–11–28 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwq:95196&r=ecm |
| By: | Montes-Galdón, Carlos; Paredes, Joan; Wolf, Elias |
| Abstract: | This paper proposes a new and robust methodology to obtain conditional density forecasts, based on information not contained in an initial econometric model. The methodology allows to condition on expected marginal densities for a selection of variables in the model, rather than just on future paths as it is usually done in the conditional forecasting literature. The proposed algorithm, which is based on tempered importance sampling, adapts the model-based density forecasts to target distributions the researcher has access to. As an example, this paper shows how to implement the algorithm by conditioning the forecasting densities of a BVAR and a DSGE model on information about the marginal densities of future oil prices. The results show that increased asymmetric upside risks to oil prices result in upside risks to inflation as well as higher core-inflation over the considered forecasting horizon. Finally, a real-time forecasting exercise yields that introducing market-based information on the oil price improves inflation and GDP forecasts during crises times such as the COVID pandemic. JEL Classification: C11, C53, E31, E37 |
| Keywords: | Bayesian analysis, forecasting, importance sampling, inflation-at-risk |
| Date: | 2022–12 |
| URL: | http://d.repec.org/n?u=RePEc:ecb:ecbwps:20222754&r=ecm |