Ivan Paya










Department of Economics

Lancaster University



P: (+44) (0)1524 593504

F: (+44) (0)1524 594244
E: i.paya@lancaster.ac.uk


I am a Professor of Economics at Lancaster University, UK. I am also a member of the Executive Committee of the Society for Nonlinear Dynamics and Econometrics (SNDE). You can find a chronological list of my publications as well as more details about my background and profile in my vitae, departmental and Ideas webpages.

In this site I have organized my research by topic (Time Series Econometrics, International Economics/Finance, Forecasting, and Decision Theory) and have provided a brief comment on what the papers are about. Some articles could be placed in more than one area but I have located them according to their main contribution.


Time Series Econometrics


My work on time series econometrics is related to the issues of temporal aggregation, persistence, linearity tests, and model specification with special emphasis on nonlinear models.

This paper (“Temporal aggregation of an ESTAR process: Some implications for purchasing power parity adjustment”, Journal of Applied Econometrics 2006, 21, 655-668) investigates the effects of temporal aggregation on unit root and linearity tests, on the estimation of nonlinear autoregressive models, and their impulse response functions. The application is on real exchange rates and the purchasing power parity (PPP) puzzle where most studies typically use temporally aggregated data. This work is complemented here (“Sampling of nonlinear models: Evidence on speed of adjustment in index futures markets”, Journal of Futures Markets 2011, 31, 192-203), where sampling rather than arithmetic averages is considered, and examines the implications of speeds of adjustment to shocks within the cost-of-carry model for future prices. Within the framework of nonlinear autoregressive models, this letter (“Deterministic impulse response in a nonlinear model. An analytic expression”, Economics Letters 2007, Vol. 95, pp. 315-319) analyses the persistence of an ESTAR model and derives an analytical expression for its impulse response function (IRF).


Macroeconomic models are generally silent with respect to what frequency the data should be sampled. Models at different levels of time aggregation are interpreted as being theoretically equivalent. However, persistence is not invariant to the frequency domain. Moreover, there is no unique definition of inflation persistence, and alternative measures of persistence are affected differently by time aggregation. This issue is examined here (“On the relationship between inflation persistence and temporal aggregation”, Journal of Money, Credit and Banking 2007, 39, 1521-1531) with an application to the US inflation rate. In a different paper, (“Inflation dynamics in the U.S.: Global but not local mean reversion”, Journal of Money, Credit and Banking 2010, 42, 135-150) we examine the mean reversion properties of the US inflation rate and propose a parsimonious nonlinear univariate representation of the inflation process for the last 60 years. The empirical results confirm a number of the key features such as global stationarity, local unit root behavior, and lower persistence in the moderation period.


Some of my research has examined further issues related to linearity tests and model specification. This paper (Specifying smooth transition regression models in the presence of conditional heteroskedasticity of unknown form”, Studies in Nonlinear Dynamics and Econometrics 2010, 14) examines the impact of conditional heteroskedasticity on linearity tests and model specification procedures, including several HCCME and bootstrap versions of the tests. This recent working paper assesses the performance of linear and nonlinear causality tests in the presence of multivariate conditional heteroskedasticity, exogenous volatility regressors, and additive volatility outliers. In this article, (Nonlinear dynamics in economics and finance and unit root testingEuropean Journal of Finance, August 2011) we illustrate the flexibility of STR models to encompass nonlinearities, complex dynamics, multiple equilibria, structural breaks and spurious trends that resemble more closely the properties of economic and financial time series. We also re-assess the power of some unit root test in the presence of nuisance parameters typically encountered in the literature. A slightly older work that attempts to develop a methodology for testing hypotheses of linearity and unit roots against alternatives such as non-linear models with multiple equilibria, and explosive processes can be found here (LUMS_WP, 2009/10).


International Economics/Finance


One of my research lines has been to empirically investigate exchange rate determination and the adjustment mechanism of real exchange rates. I am currently also working on econometric methods to detect rational speculative bubbles in asset markets.

This paper (“Real exchange rates and time-varying trade costs”. Journal of International Money and Finance 2011, 30, 1157-1179) re-examines the empirical modelling of PPP deviations in the presence of commodity market frictions. We first show that a specific type of STR models can closely approximate the functional form of the theoretical adjustment mechanism derived by Dumas (1992) for the case of constant as well as changing trade costs. Second, we develop, for the first time, an empirical model of the real exchange rate which allows for changes in the degree of market integration. By employing a long span of data on the Dollar-Sterling real exchange rate and a micro-founded proxy for trade frictions, we provide novel evidence of a significant relationship between the persistence of the real exchange rate and the level of trade costs.


We had previously documented the significance of a time-varying equilibrium and a nonlinear adjustment process in the real exchange rate Dollar-Sterling for over a century of data in this article (“A new analysis of the determinants of the real dollar-sterling exchange rate: 1871-1994”, Journal of Money, Credit and Banking 2006, 38, 1971-1990). The nonlinear adjustment to shocks, or impulse response functions, at which the real exchange rate reverts to the equilibrium level determined by measures of productivity differentials was found to be faster than those obtained in models that do not include the structural determinants of the real rate. This empirical evidence provides a further contribution to explaining the PPP puzzle.

The first paper in the literature (“Further evidence on PPP adjustment speeds: The case of real effective exchange rates and the EMS”, Oxford Bulletin of Economics and Statistics 2003, 65, 421-437) that provided evidence of both reversion to a non-constant level of the real exchange rate and smooth-time-varying autoregressive adjustment used higher frequency data and was applied to the currencies within the EMS as well as real effective exchange rates. Evidence for the Dollar-Yen exchange rate, with a more unrefined proxy for productivity differentials, can be found here (“PPP adjustments speeds in high frequency data when equilibrium real exchange rates is proxied by a time trend”, The Manchester School, 2003, 71, Sup 1, 39-53,). In this paper (“Nonlinear purchasing power parity under the gold standard”, Southern Economic Journal 2004, 71, 302-313) we analysed fourteen real exchange rates and their mean reversion properties under the Gold standard.


My research on the FOREX market and its historical perspective includes an examination of the forward premium puzzle in the interwar period. It has been argued that the forward bias will not attract speculative funds until this trading strategy is expected to generate an excess return per unit of risk that exceeds that of other trading strategies. In this letter (The forward premium puzzle in the interwar period and deviations from covered interest parity”, Economics Letters 2010, 108, 55-57) we provide evidence for the Dollar–Sterling exchange rate and found that the degree of bias in the standard Fama regression varies significantly with the deviation from covered interest parity (CIP). In this book chapter (“Ex ante real returns in forward market speculation in the interwar period: Evidence and Prediction” in New Trends in Macroeconomics, 2005 Springer Verlag) we examine the Keynes-Einzig conjecture about deviations from CIP for six currencies against the US Dollar for the period 1921-1936. In particular, we analyse the ex ante real returns to uncovered forward speculation and find that excess returns were predictable, that deviations from covered interest parity (CIP) were large and systematic, and evidence of nonlinear adjustment of CIP.

A comprehensive review of some of the papers discussed above and the rest of the literature on the econometric methods in modelling some of the key relationships which determine the behaviour of exchange rates and the efficacy of models employed to forecast them can be found in this chapter of The Handbook of Econometrics, Palgrave.


I am currently working on a new test to detect rational speculative bubbles using forward rates. The fact that a rational speculative bubble, which is part of the asset price, is also present in the forward rate has implications for EMH tests. We propose a method of bubble detection in the foreign exchange market that is based on the value of the slope coefficient of the Fama and spot-forward regressions. The method is valid for a variety of different data generating processes for fundamentals, including explosive behavior, and provides a date-stamping strategy. We examine the Reichsmark/Dollar exchange rate from the end of 1921 until mid 1923, where the probability of monetary reform is thought to be negligible, and identify the period associated with the presence of rational bubbles.




Research on this area has mainly dealt with the issue of whether nonlinear models can outperform linear ones in forecasting main macroeconomic variables (growth, inflation, real exchange rates, and interest rates) and to what extent forecast evaluation tests are valid when linearity does not hold.

The derivation of most of the recently developed forecast evaluation tests is based on the assumption that the regression models are linear in parameters and the processes are stationary. This recently published article (“Forecast evaluation of nonlinear models: The case of long-span real exchange rates”. Journal of Forecasting, 2012, 31, 580-595) provides evidence into the performance of forecast evaluation measures when one of the alternative (nesting) models is nonlinear or nonstationary. Our results indicate that most tests have good size properties, F-type tests have similar or substantially better power properties than their t-type counterparts, and both appear to exhibit very low power for the comparison of nonlinear with linear AR models. Furthermore, we provide evidence of superior forecast accuracy of nonlinear models of the dollar–sterling and franc–sterling real exchange rates using long spans of data.


With regard to the predictability of real economic activity, this paper (“Predicting real growth and the probability of recession in the Euro-area using the yield spread”, International Journal of Forecasting 2005, 21, 261-277) examines the predictive power of the term structure of interest rates using linear as well as nonlinear models for the Euro area. Significant nonlinearity with respect to time and past annual growth is detected, outperforming the linear model in out-of-sample forecasts of 1-year-ahead annual growth. Furthermore, probit models that use the EMU and US yield spreads are successful in predicting EMU recessions. The usefulness of the term spread as a leading indicator is also analysed in this article (“The term structure and real economic activity in the US in the inter-war period”, Journal of Macroeconomics 2005, 27, 331-343) for the case of the US in the interwar period. We find stronger significance of the spread in periods of deflationary price instability. Our results suggest that (i) the term spread has significant explanatory power in predicting medium-term growth (including the onset of the Great Depression), (ii) the information content of the term structure is robust, but not invariant to regime changes, and (iii) evidence of non-linearity in the relationship.


One of the papers discussed above (“Inflation dynamics in the U.S.: Global but not local mean reversion”, Journal of Money, Credit and Banking 2010, 42, 135-150) also include an analysis on the forecasting performance of four alternative univariate models of the US inflation, namely, a linear AR process, a random walk, an IMA/UC, and the ESTAR model. Results are mixed and the superior specification depends on the forecast horizon and time period.

In a recent article (“Forecasting monetary policy rules in South Africa”. International Journal of Forecasting 2012, 28, 446-455) we have analysed the ability of linear and nonlinear monetary policy rule specifications, as well as nonparametric and semiparametric models, to forecast the nominal interest rate setting that describes the South African Reserve Bank’s (SARB) policy decisions. Our results indicate, first, that asset prices are taken into account when setting interest rates; second, that there are nonlinearities in the monetary policy rule; and third, that forecasts constructed from semiparametric models perform particularly well over the inflation targeting regime.


Decision Theory


In this area I have recently worked on the application of rational expectations models to choice under uncertainty when the distribution of micro and macro aggregates is heavy tailed. Growth models under uncertainty and constant relative risk aversion (CRRA) utility are fragile in explaining consumers’ choice, as equilibrium consumption is dependent on distributional assumptions. In this letter (“On the stability of CRRA utility under high degrees of uncertainty”. Economics Letters 2012, 115, 244-248) we show that, under semi-nonparametric distributions, general equilibrium models are stable, as the existence of expected utility is guaranteed.

Another topic I am currently analysing is the effect of higher-order moments on decision theory within the standard portfolio problem. This issue is now being extended to the area of occupational choice.