Spurious Long Memory in Commodity Futures: Implications for Agribusiness Option Pricing

Long memory, and more precisely fractionally integration, has been put forward as an explanation for the persistence of shocks in a number of economic time series data as well as to reconcile misleading findings of unit roots in data that should be stationary. Recent evidence suggests that long memory characterizes not commodity futures prices but rather price volatility (generally defined as $L_p$ norms of price logreturns). One implication of long memory in volatility is the mispricing of options written on commodity futures, the consequence of which is that fractional Brownian motion should replace geometric Brownian motion as the building block for option pricing solutions. This paper asks whether findings of long memory in volatility might be spurious and caused either by fragile and inaccurate estimation methods and standard errors, by correlated short memory dynamics, or by alternative data generating processes proven to generate the illusion of long memory. We find that for nine out of eleven agricultural commodities for which futures contracts are traded, long memory is spurious but is not caused by the effect of short memory. Alternative explanations are addressed and implications for option pricing are highlighted.Q13, Q14, Marketing, C52, C53, G12, G13,

The Persistence of Inflation in OECD Countries: A Fractionally Integrated Approach

The statistical properties of inflation and, in particular, its degree of persistence and stability over time is a subject of intense debate, and no consensus has been achieved yet. The goal of this paper is to analyze this controversy using a general approach, with the aim of providing a plausible explanation for the existing contradictory results. We consider the inflation rates of twenty-one OECD countries which are modeled as fractionally integrated (FI) processes. First, we show analytically that FI can appear in inflation rates after aggregating individual prices from firms that face different costs of adjusting their prices. Then, we provide robust empirical evidence supporting the FI hypothesis using both classical and Bayesian techniques. Next, we estimate impulse response functions and other scalar measures of persistence, achieving an accurate picture of this property and its variation across countries. It is shown that the application of some popular tools for measuring persistence, such as the sum of the AR coefficients, could lead to erroneous conclusions if fractional integration is present. Finally, we explore the existence of changes in inflation inertia using a novel approach. We conclude that the persistence of inflation is very high (although nonpermanent) in most postindustrial countries and that it has remained basically unchanged over the last four decades.

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

Combining long memory and level shifts in modeling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons

How Can We Define The Concept of Long Memory? An Econometric Survey

In this paper we discuss different aspects of long mzmory behavior and specify what kinds of parametric models follow them. We discuss the confusion which can arise when empirical autocorrelation function of a short memory process decreases in an hyperbolic way.Long-memory, Switching, Estimation theory, Spectral

An econometric approach to macroeconomic risk. A cross country study

A contribution to the study of volatility and country risk is made in order to achieve a successful crosscountry comparison. We present a methodology for the evaluation of country risk that include endogenous detection of multiple structural breaks (also identifying its different kinds), determination of persistence of shocks through their structural-break free fractional integration order and determination of the adjusted volatility which best characterizes the economy. This methodology is applied to developed and emerging countries' GDPs (taking 9 countries from each group). Although the former have fewer structural breaks than the latter, these breaks are extremely relevant in 14 of the 18 countries. This affects the calculation of the series persistence and volatility. Comparing a traditional risk indicator to our suggested one we find that the cluster of reference of 60% of the countries changes. Most countries present fractional integration (long memory) being the distribution between both groups heterogeneous. Country volatility varies strongly if we isolate structural breaks that present a probabilistic distribution different from intrinsic GDP volatility. Clusters arrangement is different with some risk country evaluation methodologies.Risk, Volatility, Persistence, Structural breaks, Forescastability, Macroeconomic variables, Cross country analysis

Long memory of volatility measures in time series

The authors analyse relations between the long memory parameter of conditional variance and estimates of the long memory in squared residuals in FIGARCH models. The investigations are performed by means of simulations FIGARCH(0, d, 0) and FIGARCH(1, d, 1) models for selected parameters. Simulation results suggest, that estimates of the conditional variance long memory and the long memory in squared residuals can considerable differ. Moreover, only for small d positive relationship between the long memory estimates of squared residuals and the fractional integration parameter d of FIGARCH model can be observed.FIGARCH, long memory, simulations

Inflation persistence in the Franc Zone: evidence from disaggregated prices

In sub-Saharan Africa, where inflation persistence is likely to have deleterious welfare consequences, little attempt has been made to study this phenomenon. Using data over 1989:11-2002:09, this paper investigates persistence in disaggre- gated (food and non-food) inflation for thirteen Communaute Financiere Africaine (CFA) member states using fractional integration (FI) methods. The results show that both inflation series are characterized by mean-reversion and finite variance, however it also exposes some asymmetry in inflation persistence across member states in both sectors. In Chad and Niger, the phenomenon is found to exist in both sectors. With uniform monetary policy across member states, implications for Monetary Policy, Nominal Convergence and Optimal Currency Area are then discussed.Fractional integration, inflation persistence, Franc Zone

Structural breaks and long memory in US inflation rates: do they matter for forecasting?

There is substantial evidence that several economic time series variables experience occasional structural breaks. At the same time, for some of these variables there is evidence of long memory. In particular, it seems that inflation rates have both features. One cause for this finding may be that the two features are difficult to distinguish using currently available econometric tools. Indeed, various recent studies show that neglecting occasional breaks may lead to a spurious finding of long-memory properties. In this paper we focus on this issue within the context of out-of-sample forecasting. First, we show that indeed data with breaks can be viewed as long-memory data. Next, we compare time series models with structural breaks, models with long-memory and linear autoregressive models for 23 monthly US inflation rates in terms of out-of-sample forecasting for various horizons. A key finding is that the linear models do not perform as well as the other two, and that the model with breaks and the model with long memory perform about equally well. We also examine their joint performance by combining the forecasts. A by-product of our empirical analysis is that we can relate the value of the long-memory parameter with the number of detected breaks, in which case we find a strong positive relationship.Long memory;US inflation rates;forecast performance;Occasional breaks