The effect of parameter uncertainty on forecast variances and confidence intervals for unit root and trend stationary time-series models

In this paper I describe the effect of parameter uncertainty on the way conditional forecast variances grow as the forecast horizon increases. Without parameter uncertainty, forecast variances for the unit root model grow linearly with the forecast horizon while with the trend stationary model they are bounded. With parameter uncertainty, however, I find that for both the unit root and the trend stationary models, forecast variances grow with the square of the forecast horizon so that uncertainty grows at a much faster rate than without parameter uncertainty.     

Properties of optimal forecasts under asymmetric loss and nonlinearity

Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. We establish instead that a suitable transformation of the forecast error—known as the generalized forecast error—possesses an equivalent set of properties. The paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts.     

The use of advance order data in demand forecasting

This paper uses advance order data and historical demand data from a manufacturing shop and from a service operation to develop and test a forecasting methodology for predicting customer demand over a forecast horizon. The proposed methodology uses simple linear regression to model the relationship between a total demand ratio and a partial demand ratio. Comparison of the proposed model to a standard regression approach and a commonly used multiplicative model showed that the proposed model exhibited the greatest forecast accuracy.     

Asymmetry in unemployment rate forecast errors

Asymmetries in unemployment dynamics have been observed in the time series of a number of countries, including the United States. This paper studies asymmetries in unemployment rate forecast errors. We consider conditions under which optimal forecasts will display asymmetrically-distributed errors and how the degree of asymmetry might vary with the forecast horizon. Using data from the U.S. Survey of Professional Forecasters and the Federal Reserve Greenbook, we find substantial evidence of forecast error asymmetry, which tends to increase with the forecast horizon; we also find noteworthy differences in forecasts from these two sources. The results give insight into the abilities of professional forecasters to adapt their forecasts to asymmetry in underlying processes.     

A Dynamic Panel Data Approach to the Forecasting of the GDP of German Länder

Abstract

In this paper, we make multi-step forecasts of the annual growth rates of the real GDP for each of the 16 German Länder simultaneously. We apply dynamic panel models accounting for spatial dependence between regional GDP. We find that both pooling and accounting for spatial effects help to improve the forecast performance substantially. We demonstrate that the effect of accounting for spatial dependence is more pronounced for longer forecasting horizons (the forecast accuracy gain is about 9% for a 1-year horizon and exceeds 40% for a 5-year horizon). We recommend incorporating a spatial dependence structure into regional forecasting models, especially when long-term forecasts are made.     

Monetary policy shocks: We got news!

We assess the role of monetary policy news shocks in the context of a medium scale DSGE model estimated on US data. We estimate several versions of the model and find decisive evidence in favour of the inclusion of monetary policy news shocks over a two-quarter horizon. According to our results, monetary policy news shocks account for a non-negligible fraction of the variance of real variables, especially at shorter forecast horizons. Further, we document that the importance of monetary policy news shocks goes beyond what was observed in recent years. The historical importance of monetary policy news shocks dates back to the 1999–2006 period when the official FOMC statements provided information about both the current policy setting and the expected future policy path. We also show that adding monetary policy news shocks to the model does not lead to identification problems.     

波动率预测:GARCH模型与隐含波动率

在预测未来波动率时,究竟是基于历史数据的时间序列模型还是基于期权价格的隐含波动率模型效率更高?本文对香港恒生指数期权市场所含信息的研究发现,在预测期限较短(一周)时,GARCH(1,1)模型所含信息较多,预测能力最强,但在预测较长期限(一个月)时,隐含波动率所含信息较多,预测能力较强。同时,期权市场交易越活跃,所反映的信息就越全面,隐含波动率的预测能力也就越强。     

Predicting volatility using the Markov-switching multifractal model: Evidence from S&P 100 index and equity options

In this paper, we evaluate the performance of the ability of Markov-switching multifractal (MSM), implied, GARCH, and historical volatilities to predict realized volatility for both the S&P 100 index and equity options. Some important findings are as follows. First, we find that the ability of MSM and GARCH volatilities to predict realized volatility is better than that of implied and historical volatilities for both the index and equity options. Second, equity option volatility is more difficult to be forecast than index option volatility. Third, both index and equity option volatilities can be better forecast during non-global financial crisis periods than during global financial crisis periods. Fourth, equity option volatility exhibits distinct patterns conditional on various equity and option characteristics and its predictability by MSM and implied volatilities depends on these characteristics. And finally, we find that MSM volatility outperforms implied volatility in predicting equity option volatility conditional on various equity and option characteristics.     

Forecasting the term structures of Treasury and corporate yields using dynamic Nelson-Siegel models

We extend Diebold and Li’s dynamic Nelson-Siegel three-factor model to a broader empirical prospective by including the evaluation of the state space approach and by using nine different ratings for corporate bonds. We find that the dynamic Nelson-Siegel factor AR(1) model outperforms other competitors on the out-of-sample forecast accuracy, especially on the investment-grade bonds for the short-term forecast horizon and on the high-yield bonds for the long-term forecast horizon. The dynamic Nelson-Siegel factor state space model, however, becomes appealing on the high-yield bonds in the short-term forecast horizon, where the factor dynamics are more likely time-varying and parameter instability is more probable in the model specification.     

Modeling the accuracy of certain regional predictions

A model is hypothesized specifying forecast error as a function of specific ‘year effects’, particular dates of forecast, and ‘time span effects’, length of projection horizon. Model estimation methodology is presented and empirical application is made to inaccuracies arising in the RAS procedure for projecting bivariate region/industry employment arrays for two sets of regional data. In both applications, the model is found to explain a large proportion of variation in forecast errors, and estimation results permit isolation of pure time effects on deterioration of model accuracy and quantification of relative ‘year effects’.     

Content horizons for univariate time-series forecasts

This paper investigates the maximum horizon at which conditioning information can be shown to have value for univariate time series forecasts. In particular, we consider the problem of determining the horizon beyond which forecasts from univariate time series models of stationary processes add nothing to the forecast implicit in the unconditional mean. We refer to this as the content horizon for forecasts, and provide a formal definition of the corresponding forecast content function at horizons s=1,… S. This function depends upon parameter estimation uncertainty as well as on autocorrelation structure of the process. We show that for autoregressive processes it is possible to give an asymptotic expression for the forecast content function, and show by simulation that the expression gives a good approximation even at modest sample sizes. The results are applied to the growth rate of GDP and to inflation, using US and Canadian data.     

The term structure of volatility predictability

Volatility forecasting is crucial for portfolio management, risk management, and pricing of derivative securities. Still, little is known about the accuracy of volatility forecasts and the horizon of volatility predictability. This paper aims to fill these gaps in the literature. We begin this paper by introducing the notions of spot and forward predicted volatilities and propose describing the term structure of volatility predictability by spot and forward forecast accuracy curves. Then, we perform a comprehensive study of the term structure of volatility predictability in stock and foreign exchange markets. Our results quantify the volatility forecast accuracy across horizons in two major markets and suggest that the horizon of volatility predictability is significantly longer than that reported in earlier studies. Nevertheless, the aforesaid horizon is observed to be much shorter than the longest maturity of traded derivative contracts.     

A UNIFYING VIEW ON MULTI‐STEP FORECASTING USING AN AUTOREGRESSION

Abstract This paper unifies two methodologies for multi‐step forecasting from autoregressive time series models. The first is covered in most of the traditional time series literature and it uses short‐horizon forecasts to compute longer‐horizon forecasts, while the estimation method minimizes one‐step‐ahead forecast errors. The second methodology considers direct multi‐step estimation and forecasting. In this paper, we show that both approaches are special (boundary) cases of a technique called partial least squares (PLS) when this technique is applied to an autoregression. We outline this methodology and show how it unifies the other two. We also illustrate the practical relevance of the resultant PLS autoregression for 17 quarterly, seasonally adjusted, industrial production series. Our main findings are that both boundary models can be improved by including factors indicated from the PLS technique.     

Forecasting economic time series using targeted predictors

This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non-linear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to ‘targeted predictors’ selected using hard and soft thresholding rules. Our three main findings can be summarized as follows. First, we find improvements at all forecast horizons over the current diffusion index forecasts by estimating the factors using fewer but informative predictors. Allowing for non-linearity often leads to additional gains. Second, forecasting the volatile one month ahead inflation warrants a high degree of targeting to screen out the noisy predictors. A handful of variables, notably relating to housing starts and interest rates, are found to have systematic predictive power for inflation at all horizons. Third, the targeted predictors selected by both soft and hard thresholding changes with the forecast horizon and the sample period. Holding the set of predictors fixed as is the current practice of factor forecasting is unnecessarily restrictive.     

Evolution of forecast disagreement in a Bayesian learning model

We estimate a Bayesian learning model with heterogeneity aimed at explaining expert forecast disagreement and its evolution over horizons. Disagreement is postulated to have three components due to differences in: (i) the initial prior beliefs, (ii) the weights attached on priors, and (iii) interpreting public information. The fixed-target, multi-horizon, cross-country feature of the panel data allows us to estimate the relative importance of each component precisely. The first component explains nearly all to 30% of forecast disagreement as the horizon decreases from 24 months to 1 month. This finding firmly establishes the role of initial prior beliefs in generating expectation stickiness. We find the second component to have barely any effect on the evolution of forecast disagreement among experts. The importance of the third component increases from almost nothing to 70% as the horizon gets shorter via its interaction with the quality of the incoming news. We propose a new test of forecast efficiency in the context of Bayesian information processing and find significant heterogeneity in the nature of inefficiency across horizons and countries.     

Efficient forecast tests for conditional policy forecasts

Central Banks regularly make forecasts, such as the Fed’s Greenbook forecast, that are conditioned on hypothetical paths for the policy interest rate. While there are good public policy reasons to evaluate the quality of such forecasts, up until now, the most common approach has been to ignore their conditional nature and apply standard forecast efficiency tests. In this paper we derive tests for the efficiency of conditional forecasts. Intuitively, these tests involve implicit estimates of the degree to which the conditioning path is counterfactual and the magnitude of the policy feedback over the forecast horizon. We apply the tests to the Greenbook forecast and the Bank of England’s inflation report forecast, finding some evidence of forecast inefficiency. Nonetheless, we argue that the conditional nature of the forecasts made by central banks represents a substantial impediment to the analysis of their quality—stronger assumptions are needed and forecast inefficiency may go undetected for longer than would be the case if central banks were instead to report unconditional forecasts.     

Applications of machine learning for corporate bond yield spread forecasting

This article considers nine different predictive techniques, including state-of-the-art machine learning methods for forecasting corporate bond yield spreads with other input variables. We examine each method’s out-of-sample forecasting performance using two different forecast horizons: (1) the in-sample dataset over 2003–2007 is used for one-year-ahead and two-year-ahead forecasts of non-callable corporate bond yield spreads; and (2) the in-sample dataset over 2003–2008 is considered to forecast the yield spreads in 2009. Evaluations of forecasting accuracy have shown that neural network forecasts are superior to the other methods considered here in both the short and longer horizon. Furthermore, we visualize the determinants of yield spreads and find that a firm’s equity volatility is a critical factor in yield spreads.     

Accuracy, Bias, and Dispersion in Analysts' Earnings Forecasts: The Case of Cross-Listed Foreign Firms

This paper examines differences in analysts' earnings forecast characteristics for foreign incorporated non-U.S. firms cross-listed in the U.S. stock markets relative to a control sample of purely domestic firms. Examining summary earnings forecasts over the calendar years 1984 through 1989, this paper provides evidence that there are statistically significant differences in bias and accuracy between domestic and cross-listed foreign firms. Consistent with prior research, we find a horizon effect in accuracy; i.e., accuracy improves as we get closer to the actual earnings announcement for both types of firms. However, the differences in accuracy between the cross-listed and domestic firms persist only in the earlier forecast horizons where analysts' forecasts are less accurate for foreign cross-listed firms compared with domestic firms. The evidence is also consistent with analysts' exhibiting less optimism with respect to cross-listed foreign firms compared with the domestic firms. Finally, the paper also documents that there is a greater consensus among analysts for foreign cross-listed firms than for domestic firms.     

GNP forecasts: How credible are they? A sequential test of consistency and rationality

In this study we examine the accuracy in the expectation formation process of a major macroeconomic forecast variable, namely the Gross National Product (GNP). The theoretical foundations are similar to the one used to study exchange rate expectations, i.e. a verification of consistency and rationality in forecast formation. A very reliable and continuos data set, the ASA-NBER survey is used. The Engle-Granger two step cointegration methodology and the Johansen-Juselius canonical correlation's (which has the smallest bias and dispersion) is applied to examine consistency in the gross national product expectation formation process. Our results support (reject) consistency at the short (long) forecast horizon. We then sequentially test for weak and strong form rationality using the Phillips-Hansen fully modified ordinary least squares procedure. This allows for an unrestricted cointegration test correcting for both endogeneity in the data and asymtotic bias in the coefficient estimates. Weak (strong) form rationality is upheld (rejected). This is in line with the literature which rejects orthogonality, but partially supports expectational rationality.     

Auditing Stories about Discomfort: Becoming Comfortable with Comfort Theory

We investigate whether the choice of valuation model affects the forecast accuracy of the target prices that investment analysts issue in their equity research reports, controlling for factors that influence this choice. We examine 490 equity research reports from international investment houses for 94 UK-listed firms published over the period July 2002–June 2004. We use four measures of accuracy: (i) whether the target price is met during the 12-month forecast horizon (met_in); (ii) whether the target price is met on the last day of the 12-month forecast horizon (met_end); (iii) the absolute forecast error (abs_err); and (iv) the forecast error of target prices that are not met at the end of the 12-month forecast horizon (miss_err). Based on met_in and abs_err, price-to-earnings (PE) outperform discounted cash flow (DCF) models, while based on met_end and miss_err the difference in valuation model performance is insignificant. However, after controlling for variables that capture the difficulty of the valuation task, the performance of DCF models improves in all specifications and, based on miss_err, they outperform PE models. These findings are robust to standard controls for selection bias.