Forecasting the daily federal funds rate

This paper compares two alternative one-day-ahead forecasts of tomorrow's federal funds rate. The first forecast is a simple random walk forecast in which the forecast of tomorrow's federal funds rate is taken to be today's federal funds rate. The second forecast is an ARIMA model forecast that was allowed to vary with changes in the Federal Reserve System's operating procedures. These two forecasts are compared in terms of their general forecast accuracy and the decision support they provide to a financial institution hypothesized to be borrowing $7 million a week in the federal funds market. Even in cases felt to be most favorable to the ARIMA forecasts, the degree of forecast accuracy and decision support superiority of the ARIMA forecasts is found to be quite small.     

The serial correlation structure for a random process with steps

Summary We derive the detailed correlation structure for the simple “staircase model”: a process where white noise is superimposed on a deterministic step function that has equal rises and equal treads. It turns out that this structure is an immediate generalisation of that for a linear trend (which, for discrete data, can be alternatively considered as a step function with equal rises and unit treads). We compare the structure obtained with that for a random walk, and those for a subset of other ARIMA(p, 1,q) models, and those of general ARIMA(p, d, q) processes withd>1.     

Just-in-time inventory systems innovation and the predictability of earnings

Firms that adopt just-in-time (JIT) inventory practices do so in order to realize cost savings and improve product quality, but an unexpected benefit to such firms could be a more predictable earnings stream. We examine the relationship between implementation of just-in-time inventory practices and the predictability of future quarterly earnings for a matched-pair sample of 82 firms, half of which have publicly announced that they have adopted JIT inventory practices. We find that one- and four-step-ahead forecasts of quarterly earnings, using either a Brown–Rozeff [Journal of Accounting Research (1979) 179–189] ARIMA or a seasonal random walk expectation model, are more accurate for the firms that have adopted JIT.     

Forecasting China's foreign exchange reserves using dynamic model averaging: The roles of macroeconomic fundamentals,financial stress and economic uncertainty

We develop models for examining possible predictors of growth of China's foreign exchange reserves that embrace Chinese and global trade, financial and risk (uncertainty) factors. Specifically, by comparing with other alternative models, we show that the dynamic model averaging (DMA) and dynamic model selection (DMS) models outperform not only linear models (such as random walk, recursive OLS-AR(1) models, recursive OLS with all predictive variables models) but also the Bayesian model averaging (BMA) model for examining possible predictors of growth of those reserves. The DMS is the best overall across all forecast horizons. While some predictors matter more than others over the forecast horizons, there are few that stand the test of time. The US–China interest rate differential has a superior predictive power among the 13 predictors considered, followed by the nominal effective exchange rate and the interest rate spread for most of the forecast horizons. The relative predictive prowess of the oil and copper prices alternates, depending on the commodity cycles. Policy implications are also provided.     

The relationship between the Beveridge–Nelson decomposition and other permanent–transitory decompositions that are popular in economics

The Beveridge–Nelson (BN) decomposition is a model-based method for decomposing time series into permanent and transitory components. When constructed from an ARIMA model, it is closely related to decompositions based on unobserved components (UC) models with random walk trends and covariance stationary cycles. The decomposition when extended to I(2)$I\left(2\right)$ models can also be related to non-model-based signal extraction filters such as the HP filter. We show that the BN decomposition provides information on the correlation between the permanent and transitory shocks in a certain class of UC models. The correlation between components is known to determine the smoothed estimates of components from UC models. The BN decomposition can also be used to evaluate the efficacy of alternative methods. We also demonstrate, contrary to popular belief, that the BN decomposition can produce smooth cycles if the reduced form forecasting model is appropriately specified.     

Predicting crude oil prices: Replication of the empirical results in “What do we learn from the price of crude oil?”

In addition to their theoretical analysis of the joint determination of oil futures prices and oil spot prices, Alquist and Kilian (Journal of Applied Econometrics, 2010, 25(4), 539–573) compare the out‐of‐sample accuracy of the random walk forecast with that of forecasts based on oil futures prices and other predictors. The results of my replication exercise are very similar to the original forecast accuracy results, but the relative accuracy of the random walk forecast and the futures‐based forecast changes when the sample is extended to August 2016, consistent with the results of several other recent studies by Kilian and co‐authors.     

A comparison of the forecasting performance of WEFA and ARIMA time series methods

This paper examines the forecasting performance of the Wharton model (MARK III) over the period 1973 through 1975 and compares it with that of ARIMA models' performance over the same period. Despite strong intimation in the literature to the contrary, we find that this econometric model, at least, exhibits greater accuracy in every respect relative to ARIMA methods, in terms of its forecasts cum constant adjustments. When constant adjustments are disallowed then its forecasts are still more accurate than ARIMA forecasts over a 4- and 8-quarter forecasting horizon, but less accurate over a 1-quarter horizon. The comparison was carried out over twenty three macrovariables, under a slight handicap for the Wharton Model, in that the latter's parameters were estimated over a sample ending in 1969.3 while the ARIMA models were reidentified and reestimated as of the quarter immediately preceding the forecast.     

Bayesian Comparison of ARIMA and Stationary ARMA Models

Time series analysts have long been concerned with distinguishing stationary "generating processes" from processes for which differencing is required to induce stationarity. In practical applications, this issue is addressed almost invariably through formal hypothesis testing. In this paper, we explore some aspects of the Bayesian approach to the problem, leading to the calculation of posterior odds ratios. Interesting features arise in the simplest possible variant of the problem, where a choice has to be made between a random walk and a stationary first order autoregressive model. We discuss in detail the analysis of this case, and also indicate how our approach extends to the more general comparison of an ARIMA model with a stationary competitor.     

Varianzquotiententests und Random Walk Verhalten internationaler Aktienmärkte

Variance ratio tests can be considered the state-of-the-art methodology for testing stock markets for random walk behavior. This article reviews recent developments in the area. Furthermore, it analyzes whether the recent financial crisis has influenced the random walk behavior of international stock markets. Our findings based on individual and multiple variance ratio tests can be summarized as follows: (i) There appears to be less evidence against the random walk hypothesis in industrialized markets than there is in emerging markets. (ii) Industrialized countries’ stock market behavior seems to be less affected by the financial crisis than the one of emerging markets. (iii) The choice of individual or multiple variance ratio test does not crucially influence our main conclusions.     

On the choice between two delta-hedging strategies

This paper studies the choice between two popular hedging strategies by assuming that the hedge position (delta) follows a Markov chain with boundary conditions. We give the formula for long-run cost per unit time under two different cost structures: (I) a fixed transaction cost and (II) a non-fixed transaction cost. Then, we consider the case where the hedge position follows a random walk; we show that (i) re-balancing delta to the initial position is always more cost-efficient than re-balancing it to the edge for a fixed transaction cost; (ii) under certain conditions, re-balancing delta to the initial position is less cost-efficient than re-balancing it to the edge for a non-fixed transaction cost. In addition, we quantify the magnitude of the efficiency in both cases.     

Forecasting Bitcoin with technical analysis: A not-so-random forest?

This paper uses data sampled at hourly and daily frequencies to predict Bitcoin returns. We consider various advanced non-linear models based on a multitude of popular technical indicators that represent market trend, momentum, volume, and sentiment. We run a robust empirical exercise to observe the impact of forecast horizon, model type, time period, and the choice of inputs (predictors) on the forecast performance of the competing models. We find that Bitcoin prices are weakly efficient at the hourly frequency. In contrast, technical analysis combined with non-linear forecasting models becomes statistically significantly dominant relative to the random walk model on a daily horizon. Our comparative analysis identifies the random forest model as the most accurate at predicting Bitcoin. The estimated measures of the relative importance of predictors reveal that the nature of investing in the Bitcoin market evolved from trend-following to excessive momentum and sentiment in the most recent time period.     

A general asymptotic theory for time-series models

This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time–series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.     

Forecasting inflation using time‐varying Bayesian model averaging

This paper presents a Bayesian model averaging regression framework for forecasting US inflation, in which the set of predictors included in the model is automatically selected from a large pool of potential predictors and the set of regressors is allowed to change over time. Using real‐time data on the 1960–2011 period, this model is applied to forecast personal consumption expenditures and gross domestic product deflator inflation. The results of this forecasting exercise show that, although it is not able to beat a simple random‐walk model in terms of point forecasts, it does produce superior density forecasts compared with a range of alternative forecasting models. Moreover, a sensitivity analysis shows that the forecasting results are relatively insensitive to prior choices and the forecasting performance is not affected by the inclusion of a very large set of potential predictors.     

EXCHANGE RATE FUNDAMENTALS,FORECASTING, AND SPECULATION: BAYESIAN MODELS IN BLACK MARKETS

Although speculative activity is central to black markets for currency, the out‐of‐sample performance of structural models in those settings is unknown. We substantially update the literature on empirical determinants of black market rates and evaluate the out‐of‐sample performance of linear models and non‐parametric Bayesian treed Gaussian process (BTGP) models against the random walk benchmark. Fundamentals‐based models outperform the benchmark in out‐of‐sample prediction accuracy and trading rule profitability measures given future values of fundamentals. In simulated real‐time trading exercises, however, the BTGP achieves superior realized profitability, accuracy and market timing, while linear models do no better than a random walk. Copyright © 2013 John Wiley & Sons, Ltd.     

Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates

It has been documented that random walk outperforms most economic structural and time series models in out-of-sample forecasts of the conditional mean dynamics of exchange rates. In this paper, we study whether random walk has similar dominance in out-of-sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance. We first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out-of-sample setting and provide simulation evidence on its finite sample performance. Then we conduct a comprehensive empirical analysis on the out-of-sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates—Euro/Dollar and Yen/Dollar. It is found that some sophisticated time series models that capture time-varying higher order conditional moments, such as Markov regime-switching models, have better density forecasts for exchange rates than random walk or modified random walk with GARCH and Student-t innovations. This finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out-of-sample applications involving the probability density.     

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.     

A nonsymmetric sequential test

A one-sided testing problem based on an i.i.d. sample of observations is considered. The usual one-sided sequential probability ratio test would be based on a random walk derived from these observations. Here we propose a sequential test where the random walk is replaced by Lindleys random walk which starts anew at zero as soon as it becomes negative. We derive the asymptotics of the expected sample size and the error probabilities of this sequential test. We discuss the advantages of this test for certain nonsymmetric situations.Acknowledgement. The authors thank the referee for helpful comments and suggestions. Their research was supported by the German Research Foundation (DFG) and the Russian Foundation for Basic Research (RFBR).     

Bayesian Model Averaging and exchange rate forecasts

Exchange rate forecasting is hard and the seminal result of Meese and Rogoff [Meese, R., Rogoff, K., 1983. Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of International Economics 14, 3–24] that the exchange rate is well approximated by a driftless random walk, at least for prediction purposes, still stands despite much effort at constructing other forecasting models. However, in several other macro and financial forecasting applications, researchers in recent years have considered methods for forecasting that effectively combine the information in a large number of time series. In this paper, I apply one such method for pooling forecasts from several different models, Bayesian Model Averaging, to the problem of pseudo out-of-sample exchange rate predictions. For most currency–horizon pairs, the Bayesian Model Averaging forecasts using a sufficiently high degree of shrinkage, give slightly smaller out-of-sample mean square prediction error than the random walk benchmark. The forecasts generated by this model averaging methodology are however very close to, but not identical to, those from the random walk forecast.     

General Bayesian time-varying parameter vector autoregressions for modeling government bond yields

US yield curve dynamics are subject to time-variation, but there is ambiguity about its precise form. This paper develops a vector autoregressive (VAR) model with time-varying parameters and stochastic volatility, which treats the nature of parameter dynamics as unknown. Coefficients can evolve according to a random walk, a Markov switching process, observed predictors, or depend on a mixture of these. To decide which form is supported by the data and to carry out model selection, we adopt Bayesian shrinkage priors. Our framework is applied to model the US yield curve. We show that the model forecasts well, and focus on selected in-sample features to analyze determinants of structural breaks in US yield curve dynamics.     

Econometric modeling of urban and other substate areas: An analysis of alternative methodologies

Questions raised by J.R. Meyer and J.W. Millimar on the appropriate level of sophistication in regional econometric models are addressed by comparing the modeling methodologies for each of six diverse substate areas. The methodologies range from aggregated recursive structures driven by an ARIMA time-series model of export-base employment to highly detailed simultaneous equation models. It is found that recursive model accuracy is relatively insensitive to forecast accuracy of the model-driving variable and simultaneous models are more accurate than recursive ones, but relative accuracies of aggregated and detailed simultaneous models are less clear. Population and personal income estimates are improved by disaggregation, but with respect to employment, there is a trade-off in model structure between average employment prediction accuracy over a number of time periods and turning point prediction accuracy.