Fractional cointegration and price discovery in Canadian commodities

Using as a unifying theme commodities important to the Canadian economy, recently developed tools are applied to studying price discovery in the spot and futures markets. For each commodity the fractionally cointegrated vector autoregression (FCVAR) model of Johansen and Neilsen is estimated and tested against the special case of the conventional cointegrated vector autoregression (CVAR). These models characterize the fundamental value of a commodity as the common stochastic trend shared by its cointegrated spot and futures prices, and so price discovery can be analyzed using the permanent-transitory decomposition of Gonzalo and Granger. Model forecasts are evaluated and compared using a distributional result due to Clark and West. The generalization to fractional cointegration is found to be statistically significant. However the economic significance of this generalization—in terms of forecast accuracy and the profitability of mean–variance dynamic trading strategies—is more fragile than may have been appreciated.     

Bayesian prediction with cointegrated vector autoregressions

A complete procedure for calculating the joint predictive distribution of future observations based on the cointegrated vector autoregression is presented. The large degree of uncertainty in the choice of cointegration vectors is incorporated into the analysis via the prior distribution. This prior has the effect of weighing the predictive distributions based on the models with different cointegration vectors into an overall predictive distribution. The ideas of Litterman [Mimeo, Massachusetts Institute of Technology, 1980] are adopted for the prior on the short run dynamics of the process resulting in a prior which only depends on a few hyperparameters. A straightforward numerical evaluation of the predictive distribution based on Gibbs sampling is proposed. The prediction procedure is applied to a seven-variable system with a focus on forecasting Swedish inflation.     

Forecasting and testing in co-integrated systems

This paper examines the behavior of forecasts made from a co-integrated system as introduced by Granger (1981), Granger and Weiss (1983) and Engle and Granger (1987). It is established that a multi-step forecast will satisfy the co-integrating relation exactly and that this particular linear combination of forecasts will have a finite limiting forecast error variance. A simulation study compares the multi-step forecast accuracy of unrestricted vector autoregression with the two-step estimation of the vector autoregression imposing the co-integration restriction.To test whether a system exhibits co-integration, the procedures introduced in Engle and Granger (1987) are extended to allow different sample sizes and numbers of variables.     

Forecasting performance of multivariate time series models with full and reduced rank: an empirical examination

Since Quenouille's influential work on multiple time series, much progress has been made towards the goal of parameter reduction and model fit. Relatively less attention has been paid to the systematic evaluation of out-of-sample forecast performance of multivariate time series models. In this paper, we update the hog data set studied by Quenouille (and other researchers who followed him). We re-estimate his model with extended observations (1867–1966), and generate recursive one- to four-steps-ahead forecasts for the period of 1967 through 2000. These forecasts are compared to forecasts from an unrestricted vector autoregression, a reduced rank regression model, an index model and a cointegration-based error correction model. The error correction model that takes into account both nonstationarity of the data and rank reduction performs best at all four forecasting horizons. However, differences among competing models are statistically insignificant in most cases. No model consistently encompasses the others at all four horizons.     

Cointegration and joint efficiency of international commodity markets

This paper investigates the semi-strong efficiency hypothesis in the international commodity markets of four industrialized countries, using vector autoregression (VAR) and cointegration techniques. Efficiency in these markets requires the corresponding real exchange rates to be martingales with respect to any information set available in the public domain. In the context of a VAR consisting only of real exchange rates, we show that necessary and sufficient conditions for joint efficiency of all the markets under consideration amount to the VAR being of order one (Markovness) and non-cointegrated. On the contrary, in a VAR extended by other potentially “relevant” variables, such as the corresponding real interest rates, non-cointegration and Markovness are only sufficient conditions for the same commodity markets to be characterized as jointly efficient. We also suggest methods for efficiency testing in each individual market within a cointegrated VAR and, finally, we discuss possible long-run linkages among the real exchange rates and real interest rates in association with efficiency in the commodity markets. JEL Classification Number: F31     

Modeling tourism: A fully identified VECM approach

System-based cointegration methods have become popular tools for economic analysis and forecasting. However, the identification of structural relationships is often problematic. Using a theory-directed sequential reduction method suggested by Hall, Henry and Greenslade [Hall, S. G., Henry, S., & Greenslade, J. (2002). On the identification of cointegrated systems in small samples: A modelling strategy with an application to UK wages and prices. Journal of Economic Dynamics and Control, 26, 1517–1537], we estimate a vector error correction model of Hawaii tourism, where both demand and supply-side influences are important. We identify reasonable long-run equilibrium relationships, and Diebold–Mariano tests for forecast accuracy demonstrate satisfactory forecasting performance.     

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.     

Two are better than one: Volatility forecasting using multiplicative component GARCH-MIDAS models

We examine the properties and forecast performance of multiplicative volatility specifications that belong to the class of generalized autoregressive conditional heteroskedasticity–mixed-data sampling (GARCH-MIDAS) models suggested in Engle, Ghysels, and Sohn (Review of Economics and Statistics, 2013, 95, 776–797). In those models volatility is decomposed into a short-term GARCH component and a long-term component that is driven by an explanatory variable. We derive the kurtosis of returns, the autocorrelation function of squared returns, and the R² of a Mincer–Zarnowitz regression and evaluate the QMLE and forecast performance of these models in a Monte Carlo simulation. For S&P 500 data, we compare the forecast performance of GARCH-MIDAS models with a wide range of competitor models such as HAR (heterogeneous autoregression), realized GARCH, HEAVY (high-frequency-based volatility) and Markov-switching GARCH. Our results show that the GARCH-MIDAS based on housing starts as an explanatory variable significantly outperforms all competitor models at forecast horizons of 2 and 3 months ahead.     

Simple Identification and Specification of Cointegrated Varma Models

We bring together some recent advances in the literature on vector autoregressive moving‐average models, creating a simple specification and estimation strategy for the cointegrated case. We show that in this case with fixed initial values there exists a so‐called final moving‐average representation. We prove that the specification strategy is consistent. The performance of the proposed method is investigated via a Monte Carlo study and a forecasting exercise for US interest rates. We find that our method performs well relative to alternative approaches for cointegrated series and methods which do not allow for moving‐average terms. Copyright © 2014 John Wiley & Sons, Ltd.     

Do TFP and the relative price of investment share a common I(1) component?

Results from cointegration tests clearly suggest that TFP and the relative price of investment (RPI) are not cointegrated. Evidence on the alternative possibility that they may nonetheless contain a common I(1) component generating long-horizon co-variation between them crucially depends on the fact that (i) structural breaks are, or are not allowed for, and (ii) the precise nature and timing of such breaks. Not allowing for breaks, evidence points towards the presence of a common component inducing positive long-horizon covariation, which is compatible with the notion that the technology transforming consumption goods into investment goods is non-linear, and the RPI is also impacted upon by neutral shocks. Allowing for breaks, evidence suggests that long-horizon covariation is either nil or negative.Assuming, for illustrative purposes, that the two series contain a common component inducing negative long-horizon covariation, evidence based on structural VARs shows that this common shock (i) plays an important role in macroeconomic fluctuations, explaining sizeable fractions of the forecast error variance of main macro series, and (ii) generates ‘disinflationary booms’, characterized by transitory increases in hours, and decreases in inflation.     

Forecasting using a periodic transfer function: with an application to the UK price of ferrous scrap

The familiar concept of cointegration enables us to determine whether or not there is a long-run relationship between two integrated time series. However, this may not capture short-run effects such as seasonality. Two series which display different seasonal effects can still be cointegrated. Seasonality may arise independently of the long-run relationship between two time series or, indeed, the long-run relationship may itself be seasonal. The market for recycled ferrous scrap displays these features: the US and UK scrap prices are cointegrated, yet the local markets exhibit different forms of seasonality. The paper addresses the problem of using both cointegrating and seasonal relationships in forecasting time series through the use of periodic transfer function models. We consider the problems of testing for cointegration between series with differing seasonal patterns and develop a periodic transfer function model for the US and UK scrap markets. Forecast comparisons with other time series models suggest that forecasting efficiency may be improved by allowing for periodicity but that such improvement is by no means guaranteed. The correct specification of the periodic component of the model is critical for forecast accuracy.     

Testing for the cointegration rank when some cointegrating directions are changing

We develop some tests for characterizing the cointegration space of a cointegrated vector autoregressive model when its long-run parameters are modified by a structural break at a known date. We first consider the case in which the break does not affect the loading factors and second the more general one in which all long-run parameters change. For each configuration, we design procedures to test for the cointegration rank as for the number of directions which are changing between the two regimes. For the simplest case, the cointegration rank test is also extended to the case of an unknown date of shift.     

Forecasting crude oil prices with DSGE models

In this study, we conducted an oil prices forecasting competition among a set of structural models, including vector autoregression and dynamic stochastic general equilibrium (DSGE) models. Our results highlight two principles. First, forecasts should exploit the fact that real oil prices are mean reverting over long horizons. Second, models should not replicate the high volatility of the oil prices observed in samples. By following these principles, we show that an oil sector DSGE model performs much better at real oil price forecasting than random walk or vector autoregression.     

Permanent-transitory Decomposition in Var Models With Cointegration and Common Cycles

In this paper we derive permanent-transitory decompositions of non-stationary multiple times series generated by (r)nite order Gaussian VAR(p) models with both cointegration and serial correlation common features. We extend existing analyses to the two classes of reduced rank structures discussed in Hecq, Palm and Urbain (1998). Using the corresponding state space representation of cointegrated VAR models in vector error correction form we show how decomposition can be obtained even in the case where the number of common feature and cointegration vectors are not equal to the number of variables. As empirical analysis of US business fluctuations shows the practical relevance of the approach we propose.     

Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

A fractional cointegration analysis of Fisher hypothesis: evidence from Turkey

This paper examines the validity of Fisher hypothesis in Turkey over the period from 1990:01 through 2010:03 by using cointegration and fractional cointegration approaches. The findings from Engle and Granger cointegration test indicate that inflation and nominal interest rate series are cointegrated. Since the conventional cointegration tests do not provide strong evidence on the long run relationship, we also use fractional cointegration definition suggested by Cheung and Lai (J Bus Econ Stat 11:103–112, 1993) which requires only a mean reverting (d < 1) relationship between the series. The results from fractional cointegration tests based on GPH and Robinson methods show that inflation and nominal interest rate series are fractionally cointegrated. These findings support the validity of the Fisher hypothesis in Turkey.     

ON COMPARING MACROECONOMIC MODELS USING FORECAST ENCOMPASSING TESTS

ABSTRACT It is clearly of interest to macroeconomists to be able to evaluate whether one large-scale macroeconometric model ‘is better’ than another. Although comparisons between models are sometimes invidious, because the purposes for which the models were built differ, it is the case that formal comparisons of two models' statistical properties are rare. This is in spite of considerable theoretical advances in the econometric methodology, namely the development and use of non-nested and encompassing tests. Chong and Hendry (1986) advocate the use of the forecast encompassing regressions, where the outturns are regressed on competing (one-step-ahead) forecasts. This paper reports the findings of applying this rather easy-to-use method of comparing large scale macroeconometric models. The forecast data we use are those published by three macroeconometric modelling groups, namely: Liverpool; the National Institute; and The London Business School. Forecasts for up to three years ahead are published for unemployment, growth, and inflation, throughout the 1980's. Forecast encompassing tests fail to separate one model from another, based on one-year-ahead forecasts. Each model ‘wins’ once. However, the conclusions are not the same as using root-mean-square-forecast-error criteria, illustrating Clements and Hendry's (1994) observation that minimum root-mean-square-forecast-error is neither necessary nor sufficient for a model to have constant parameters, to provide accurate forecasts, or to encompass its rivals.     

Analysis of cointegrated VARMA processes

VARMA (vector autoregressive moving average) processes are proposed for modelling cointegrated variables. For this purpose the echelon form is combined with the error correction form. Procedures for estimating the Kronecker indices which characterize the echelon form and for specifying the cointegration rank are discussed. The asymptotic distribution of the coefficient estimators is given. An example based o n US macroeconomic data illustrates the procedure and demonstrates its feasibility in practice.     

Macroeconomic forecasting using penalized regression methods

We study the suitability of applying lasso-type penalized regression techniques to macroe-conomic forecasting with high-dimensional datasets. We consider the performances of lasso-type methods when the true DGP is a factor model, contradicting the sparsity assumptionthat underlies penalized regression methods. We also investigate how the methods handle unit roots and cointegration in the data. In an extensive simulation study we find that penalized regression methods are more robust to mis-specification than factor models, even if the underlying DGP possesses a factor structure. Furthermore, the penalized regression methods can be demonstrated to deliver forecast improvements over traditional approaches when applied to non-stationary data that contain cointegrated variables, despite a deterioration in their selective capabilities. Finally, we also consider an empirical applicationto a large macroeconomic U.S. dataset and demonstrate the competitive performance of penalized regression methods.