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.     

Analysts' utilization of historical earnings information

This study examines whether security analysts (in)efficiently utilize the information contained in past series of annual and quarterly earnings in producing earnings forecasts. To do so, it investigates whether equal-weighted combinations of security analysts' forecasts with forecasts from statistical models based on historical earnings are superior, both in terms of being a better surrogate for the market's expectations of earnings and of accuracy, to forecasts from either one of these two sources. The empirical findings indicate that, although analysts' forecasts are superior to forecasts from statistical models, performance can be improved—both in terms of accuracy and also of being a better surrogate for market earnings expectations—by combining analysts' forecasts with forecasts from statistical models based on past quarterly earnings. Improvements in proxying for market earnings expectations were obtained even when analysts' forecasts made in June of the forecast year were used in the combinations. An implication of these findings is that investors can improve their investment decisions by using an average of the mean analysts' forecasts and the forecast produced by a time-series model of quarterly earnings in their investment decisions.     

The relationship between forecast dispersion and forecast uncertainty: Evidence from a survey data—arch model

This paper examines empirically the relationship between measures of forecast dispersion and forecast uncertainty from data on inflation expectations from the Livingston survey series and the Survey Research Center (SRC) survey series. Because the survey series do not provide probabilistic forecasts of inflation, we derive measures of inflation uncertainty by modelling the conditional variance of the inflation forecast errors from the survey series as an autoregressive conditional heteroscedastic (ARCH) process. The analysis is complicated by the fact that the overlap of forecast horizons for the survey series does not preclude the model's disturbance terms from displaying autocorrelation, and also places a restriction on the specification for the ARCH measures of inflation uncertainty. We estimate the model using Hansen's (1982) generalized method of moments (GMM) procedure to account for the presence of serial correlation and conditional heteroscedasticity in the disturbance terms. The results generally support the hypothesis that the measures of forecast dispersion across survey respondents are positively and statistically significantly associated with the measures of inflation uncertainty. However, the appropriateness of using forecast dispersion measures as proxies for inflation uncertainty is sensitive to the choice of the survey series.     

Forecast revisions of Mexican inflation and GDP growth

We analyze the forecasts of inflation and GDP growth contained in the Banco de México’s Survey of Professional Forecasters for the period 1995–2009. The forecasts are for the current and the following year, and comprise an unbalanced three-dimensional panel with multiple individual forecasters, target years, and forecast horizons. The fixed-event nature of the forecasts enables us to examine their efficiency by looking at the revision process. The panel structure allows us to control for aggregate shocks and to construct a measure of the news that impacted expectations in the period under study. We find that respondents anchor to their initial forecasts, updating their revisions smoothly as they receive more information. In addition, they do not seem to use publicly-known information in an efficient manner. These inefficiencies suggest clear areas of opportunity for improving the accuracy of the forecasts, for instance by taking into account the positive autocorrelation found in forecast revisions.     

Anchoring the yield curve using survey expectations

The dynamic behavior of the term structure of interest rates is difficult to replicate with models, and even models with a proven track record of empirical performance have underperformed since the early 2000s. On the other hand, survey expectations can accurately predict yields, but they are typically not available for all maturities and/or forecast horizons. We show how survey expectations can be exploited to improve the accuracy of yield curve forecasts given by a base model. We do so by employing a flexible exponential tilting method that anchors the model forecasts to the survey expectations, and we develop a test to guide the choice of the anchoring points. The method implicitly incorporates into yield curve forecasts any information that survey participants have access to—such as information about the current state of the economy or forward‐looking information contained in monetary policy announcements—without the need to explicitly model it. We document that anchoring delivers large and significant gains in forecast accuracy relative to the class of models that are widely adopted by financial and policy institutions for forecasting the term structure of interest rates.     

Least squares learning and the US Treasury bill rate

Understanding how agents formulate their expectations about Fed behavior is important for market participants because they can potentially use this information to make more accurate estimates of stock and bond prices. Although it is commonly assumed that agents learn over time, there is scant empirical evidence in support of this assumption. Thus, in this paper we test if the forecast of the three month T-bill rate in the Survey of Professional Forecasters (SPF) is consistent with least squares learning when there are discrete shifts in monetary policy. We first derive the mean, variance and autocovariances of the forecast errors from a recursive least squares learning algorithm when there are breaks in the structure of the model. We then apply the Bai and Perron (1998) test for structural change to a forecasting model for the three month T-bill rate in order to identify changes in monetary policy. Having identified the policy regimes, we then estimate the implied biases in the interest rate forecasts within each regime. We find that when the forecast errors from the SPF are corrected for the biases due to shifts in policy, the forecasts are consistent with least squares learning.     

Bayesian learning and convergence to rational expectations

In this paper the probability distribution of equilibrium outcomes is assumed to be a continuous but unknown function of agents' forecasts (which are probability measures). Agents start with a prior distribution on the set of mappings from forecasts into probabilities on outcomes. This induces an initial forecast. After observing the equilibrium outcome a posterior distribution is computed which induces a new forecast. The main result is that with probability one the forecasts converge to the set of fixed points of the unknown mapping. This can be interpreted as convergence to rational expectations.     

Inflation forecast contracts

We introduce a new type of incentive contract for central bankers: inflation forecast contracts, which make central bankers׳ remunerations contingent on the precision of their inflation forecasts. We show that such contracts enable central bankers to influence inflation expectations more effectively, thus facilitating more successful stabilization of current inflation. Inflation forecast contracts improve the accuracy of inflation forecasts, but have adverse consequences for output. On balance, paying central bankers according to their forecasting performance improves welfare. Optimal inflation forecast contracts stipulate high rewards for accurate forecasts.     

Forecasting monthly riverflow time series

Mean monthly flows from thirty rivers in North and South America are used to test the short-term forecasting ability of seasonal ARIMA, deseasonalized ARMA, and periodic autoregressive models. The series were split into two sections and models were calibrated to the first portion of the data. The models were then used to generate one-step-ahead forecasts for the second portion of the data. The forecast performance is compared using various measures of accuracy. The results suggest that a periodic autoregressive model, identified by using the partial autocorrelation function, provided the most accurate forecasts     

Improving forecast stability using deep learning

In this paper, we define forecast (in)stability in terms of the variability in forecasts for a specific time period caused by updating the forecast for this time period when new observations become available, i.e., as time passes. We propose an extension to the state-of-the-art N-BEATS deep learning architecture for the univariate time series point forecasting problem. The extension allows us to optimize forecasts from both a traditional forecast accuracy perspective as well as a forecast stability perspective. We show that the proposed extension results in forecasts that are more stable without leading to a deterioration in forecast accuracy for the M3 and M4 data sets. Moreover, our experimental study shows that it is possible to improve both forecast accuracy and stability compared to the original N-BEATS architecture, indicating that including a forecast instability component in the loss function can be used as regularization mechanism.     

Forecast Rationality Tests in the Presence of Instabilities,with Applications to Federal Reserve and Survey Forecasts

This paper proposes a framework to implement regression‐based tests of predictive ability in unstable environments, including, in particular, forecast unbiasedness and efficiency tests, commonly referred to as tests of forecast rationality. Our framework is general: it can be applied to model‐based forecasts obtained either with recursive or rolling window estimation schemes, as well as to forecasts that are model free. The proposed tests provide more evidence against forecast rationality than previously found in the Federal Reserve's Greenbook forecasts as well as survey‐based private forecasts. It confirms, however, that the Federal Reserve has additional information about current and future states of the economy relative to market participants. Copyright © 2015 John Wiley & Sons, Ltd.     

Using scenarios to forecast outcomes of a refugee crisis

The Syrian civil war has led to millions of Syrians fleeing the country, and has resulted in a humanitarian crisis. By considering how such socio-political events may unfold, scenarios can lead to informed forecasts that can be used for decision-making. We examined the relationship between scenarios and forecasts in the context of the Syrian refugee crisis. Forty Turkish students who had been trained to use a brainstorming technique generated scenarios that might follow within six months of the Turkish government banning Syrian refugees from entering the country. The participants generated 3–6 scenarios. Over half were rated as ‘high’ quality in terms of completeness, relevance/pertinence, plausibility, coherence, and transparency (order effects). The scenario quality was unaffected by the scenario quantity. Even though no forecasts were requested, the participants’ first scenarios contained 0–17 forecasts. The mean forecast accuracy was 45%, and this was unaffected by the forecast quantity. Therefore, brainstorming can offer a simple and quick way of generating scenarios and forecasts that can potentially help decision-makers to tackle humanitarian crises.     

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.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

The M5 competition: Background,organization, and implementation

The M5 competition follows the previous four M competitions, whose purpose is to learn from empirical evidence how to improve forecasting performance and advance the theory and practice of forecasting. M5 focused on a retail sales forecasting application with the objective to produce the most accurate point forecasts for 42,840 time series that represent the hierarchical unit sales of the largest retail company in the world, Walmart, as well as to provide the most accurate estimates of the uncertainty of these forecasts. Hence, the competition consisted of two parallel challenges, namely the Accuracy and Uncertainty forecasting competitions. M5 extended the results of the previous M competitions by: (a) significantly expanding the number of participating methods, especially those in the category of machine learning; (b) evaluating the performance of the uncertainty distribution along with point forecast accuracy; (c) including exogenous/explanatory variables in addition to the time series data; (d) using grouped, correlated time series; and (e) focusing on series that display intermittency. This paper describes the background, organization, and implementations of the competition, and it presents the data used and their characteristics. Consequently, it serves as introductory material to the results of the two forecasting challenges to facilitate their understanding.     

Forecasting the UK economy: Alternative forecasting methodologies and the role of off-model information

How did DSGE model forecasts perform before, during and after the financial crisis, and what type of off-model information can improve the forecast accuracy? We tackle these questions by assessing the real-time forecast performance of a large DSGE model relative to statistical and judgmental benchmarks over the period from 2000 to 2013. The forecasting performances of all methods deteriorate substantially following the financial crisis. That is particularly evident for the DSGE model’s GDP forecasts, but augmenting the model with a measure of survey expectations made its GDP forecasts more accurate, which supports the idea that timely off-model information is particularly useful in times of financial distress.     

Examining the credibility of macroeconomic forecasts: Null of cointegration approach

In this study we examine the accuracy of forecasts of a select group of major macroeconomic variables, representing both the real and the financial sector of the economy. 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. The empirical measure of accuracy is consistency in the expectation formation process, a precursor to rational forecasts. Here we examine the cointegration properties of the actual and forecast series (at multiple horizons) using the modern null of cointegration approach. A very reliable and continuos data set, the ASA-NBER survey is used. We find evidence of short (long) term expectational consistency (inconsistency) i.e. bandwagon effects and a mean reversion tendency in case of real variables, while the forecasts of financial variables are inconsistent across all forecast horizons.     

Do Analysts Strategically Employ Cash Flow Forecast Revisions to Offset Negative Earnings Forecast Revisions?

We investigate whether analysts use cash flow forecasts to reduce the impact of earnings forecast revisions (EFRs) on market participants. In particular, we focus on conflict between an analyst's concurrent cash flow and earnings forecast revisions. We hypothesize and find that analysts are more likely to issue a positive cash flow forecast revision when they issue a negative earnings forecast revision concurrently, but not the opposite, particularly for Fortune 500 firms. Furthermore, our supplementary analyses suggest that (1) some analysts optimistically bias cash flow forecasts when they issue negative earnings forecast revisions; (2) the market pays less attention to the historical accuracy of analyst cash flow forecasts, so analysts have some latitude to present their cash flow forecasts in an optimistic way; and (3) the market reacts mainly to the direction, not the magnitude, of cash flow forecast revisions. Overall, these findings suggest that analysts may strategically use cash flow forecasts in conjunction with earnings forecasts to maintain good management relationships.     

Central bank’s forecasts and lack of transparency: An assessment of the effect on private expectations in a large emerging economy

We analyze whether the Central Bank of Brazil’s Inflation Reports projections influences the private’s inflation expectations. Specifically, we investigate how the central bank’s inflation forecasts affect the private sector’s inflation expectations through a qualitative and quantitative examination of the disagreement measure between them. Furthermore, we appraise if the lack of transparency resulting from the difference between the central bank’s inflation forecasts and the realized inflation affects the private’s inflation expectations. Although the findings confirm the previous studies that point out that the central bank transparency can affect the readjustment of market expectations, the results do not rule out the possibility of the central bank’s forecast and private’s inflation expectations being affected reciprocally.     

Estimating time series models using the relevant cost function

In many forecasting problems, the forecast cost function is used only in evaluating the forecasts; a second cost function is used in estimating the parameters in the model. In this paper, I explore some of the ways in which the forecast cost function can be used in estimating the parameters and, more generally, in producing the forecasts. I define the optimal forecast and note that it may depend on the entire conditional distribution of the data, which is typically unknown. I then consider three of the steps involved in forming the forecast: approximating the optimal forecast, selecting the model, and estimating any unknown parameters. The forecast cost function forms the basis of the approximation, selection, and estimation. The methods are illustrated using time series models applied to 15 US macroeconomic series and in a small Monte Carlo experiment.