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This chapter develops a predictive approach to Granger causality (GC) testing that utilizes k -fold cross-validation and posterior simulation to perform out-of-sample testing. A Monte Carlo study indicates that the cross-validation predictive procedure has improved power in comparison to previously available out-of-sample testing procedures, matching the performance of the in-sample F-test while retaining the credibility of post- sample inference. An empirical application to the Phillips curve is provided evaluating the evidence on GC between inflation and unemployment rates.

We investigate predictive abilities of nonlinear models for stock returns when density forecasts are evaluated and compared instead of the conditional mean point forecasts. The aim of this paper is to show whether the in-sample evidence of strong nonlinearity in mean may be exploited for out-of-sample prediction and whether a nonlinear model may beat the martingale model in out-of-sample prediction. We use the Kullback–Leibler Information Criterion (KLIC) divergence measure to characterize the extent of misspecification of a forecast model. The reality check test of White (2000) using the KLIC as a loss function is conducted to compare the out-of-sample performance of competing conditional mean models. In this framework, the KLIC measures not only model specification error but also parameter estimation error, and thus we treat both types of errors as loss. The conditional mean models we use for the daily closing S&P 500 index returns include the martingale difference, ARMA, STAR, SETAR, artificial neural network, and polynomial models. Our empirical findings suggest the out-of-sample predictive abilities of nonlinear models for stock returns are asymmetric in the sense that the right tails of the return series are predictable via many of the nonlinear models, while we find no such evidence for the left tails or the entire distribution.

Value at risk (VaR) and expected shortfall (ES) are popular market risk measurements. The former is not coherent but robust, whereas the latter is coherent but less interpretable, only conditionally backtestable and less robust. In this chapter, we compare an innovative artificial neural network (ANN) model with a time series model in the context of forecasting VaR and ES of the univariate time series of four asset classes: US large capitalization equity index, European large cap equity index, US bond index, and US dollar versus euro exchange rate price index for the period of January 4, 1999, to December 31, 2018. In general, the ANN model has more favorable backtesting results as compared to the autoregressive moving average, generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) time series model. In terms of forecasting accuracy, the ANN model has much fewer in-sample and out-of-sample exceptions than those of the ARMA-GARCH model.

In this chapter we discuss model selection and predictive accuracy tests in the context of parameter and model uncertainty under recursive and rolling estimation schemes. We begin by summarizing some recent theoretical findings, with particular emphasis on the construction of valid bootstrap procedures for calculating the impact of parameter estimation error. We then discuss the Corradi and Swanson (2002) (CS) test of (non)linear out-of-sample Granger causality. Thereafter, we carry out a series of Monte Carlo experiments examining the properties of the CS and a variety of other related predictive accuracy and model selection type tests. Finally, we present the results of an empirical investigation of the marginal predictive content of money for income, in the spirit of Stock and Watson (1989), Swanson (1998) and Amato and Swanson (2001).

The causal relationship between money and income (output) has been an important topic and has been extensively studied. However, those empirical studies are almost entirely on Granger-causality in the conditional mean. Compared to conditional mean, conditional quantiles give a broader picture of an economy in various scenarios. In this paper, we explore whether forecasting conditional quantiles of output growth can be improved using money growth information. We compare the check loss values of quantile forecasts of output growth with and without using past information on money growth, and assess the statistical significance of the loss-differentials. Using U.S. monthly series of real personal income or industrial production for income and output, and M1 or M2 for money, we find that out-of-sample quantile forecasting for output growth is significantly improved by accounting for past money growth information, particularly in tails of the output growth conditional distribution. On the other hand, money–income Granger-causality in the conditional mean is quite weak and unstable. These empirical findings in this paper have not been observed in the money–income literature. The new results of this paper have an important implication on monetary policy, because they imply that the effectiveness of monetary policy has been under-estimated by merely testing Granger-causality in conditional mean. Money does Granger-cause income more strongly than it has been known and therefore information on money growth can (and should) be more utilized in implementing monetary policy.

In the last few decades, there has been growing interest in forecasting with computer intelligence, and both fuzzy time series (FTS) and artificial neural networks (ANNs) have gained particular popularity, among others. Rather than the conventional methods (e.g., econometrics), FTS and ANN are usually thought to be immune to fundamental concepts such as stationarity, theoretical causality, post-sample control, among others. On the other hand, a number of studies significantly indicated that these fundamental controls are required in terms of the theory of forecasting, and even application of such essential procedures substantially improves the forecasting accuracy. The aim of this paper is to fill the existing gap on modeling and forecasting in the FTS and ANN methods and figure out the fundamental concepts in a comprehensive work through merits and common failures in the literature. In addition to these merits, this paper may also be a guideline for eliminating unethical empirical settings in the forecasting studies.

We model international short-term capital flow by identifying technical trading rules in short-term capital markets using Genetic Programming (GP). The simulation results suggest that the international short-term markets was quite efficient during the period of 1997–2002, with most GP generated trading strategies recommending buy-and-hold on one or two assets. The out-of-sample performance of GP trading strategies varies from year to year. However, many of the strategies are able to forecast Taiwan stock market down time and avoid making futile investment. Investigation of Automatically Defined Functions shows that they do not give advantages or disadvantages to the GP results.

Demand forecasting has long been an imperative tenet in production planning especially in a make-to-order environment where a typical manufacturer has to balance the issues of holding excessive safety stocks and experiencing possible stockout. Many studies provide pragmatic paradigms to generate demand forecasts (mainly based on smoothing forecasting models.) At the same time, artificial neural networks (ANNs) have been emerging as alternatives. In this chapter, we propose a two-stage forecasting approach, which combines the strengths of a neural network with a more conventional exponential smoothing model. In the first stage of this approach, a smoothing model estimates the series of demand forecasts. In the second stage, general regression neural network (GRNN) is applied to learn and then correct the errors of estimates. Our empirical study evaluates the use of different static and dynamic smoothing models and calibrates their synergies with GRNN. Various statistical tests are performed to compare the performances of the two-stage models (with error correction by neural network) and those of the original single-stage models (without error-correction by neural network). Comparisons with the single-stage GRNN are also included. Statistical results show that neural network correction leads to improvements to the forecasts made by all examined smoothing models and can outperform the single-stage GRNN in most cases. Relative performances at different levels of demand lumpiness are also examined.

We examine the role of structural breaks in forecasting stock return volatility. We begin by testing for structural breaks in the unconditional variance of daily returns for the S&P 500 market index and ten sectoral stock indices for 9/12/1989–1/19/2006 using an iterative cumulative sum of squares procedure. We find evidence of multiple variance breaks in almost all of the return series, indicating that structural breaks are an empirically relevant feature of return volatility. We then undertake an out-of-sample forecasting exercise to analyze how instabilities in unconditional variance affect the forecasting performance of asymmetric volatility models, focusing on procedures that employ a variety of estimation window sizes designed to accommodate potential structural breaks. The exercise demonstrates that structural breaks present important challenges to forecasting stock return volatility. We find that averaging across volatility forecasts generated by individual forecasting models estimated using different window sizes performs well in many cases and appears to offer a useful approach to forecasting stock return volatility in the presence of structural breaks.