## Working Papers > Time Series Applications

Sharp Breaks or Smooth Shifts? An Investigation of the Evolution of Commodity Prices.

Walter Enders and Matt Holt

Walter Enders and Matt Holt

*(American Journal of Agricultural Economics*2012)**Abstract**This paper explores the behavior of real commodity prices over a 50–year period. Attention is given to how the shifting means for various commodity prices have changed with a special emphasis on behavior since the mid 2000s. To identify structural changes in commodity prices, we estimate shifting–mean autoregressions by using: the Bai and Perron (1998) procedure for determining structural breaks; low frequency Fourier functions; and a procedure that specifies shifts to be smooth logistic functions of time. We find that the pattern in the timing of shifts is suggestive of the causal factors underlying the recent boom.

An Historical Analysis of the Taylor Curve

Eric Olson and Walter Enders

(

Eric Olson and Walter Enders

(

*Journal of Money Credit and Banking*: forthcoming)**Abstract**Taylor (1979) shows that there is a permanent tradeoff between the volatility of the output gap and the volatility of inflation. Although a number of papers argue that the so-called Taylor curve is a policy menu, Friedman (2006) points out that it is more likely to serve as an efficiency locus that can be used to gauge the appropriateness of monetary policy. Using data from 1875 onward, we examine the efficiency of U.S. monetary policy by measuring the orthogonal distance between the observed volatilities of the output gap and inflation from the Taylor curve. In addition, we identify time periods in which the variability of the U.S. economy changed by observing shifts in this efficiency frontier.

Sources of the Great Moderation: A Time-Series Analysis of GDP Subsectors.

Walter Enders and Jun Ma

(Journal of Economic Dynamics and Control: 2011)

Walter Enders and Jun Ma

(Journal of Economic Dynamics and Control: 2011)

**Abstract**Recent work finds evidence that the volatility of the U.S. economy has fallen dramatically since the mid-1980s. We trace the timing of this so called "Great Moderation" across many subsectors of the economy in order to better understand its root cause. We find that the interest rate sensitive sectors generally experience a much earlier volatility decline than other large sectors of the economy. The changes in financial deregulation and Federal Reserve stabilization policies that occurred during the early 1980s support the view that improved monetary policy may have played an important role in stabilizing real economic activity.

In-Sample and Out-of-Sample Properties of Linear and Nonlinear Taylor Rules

Walter Enders and Ting Qin

(

Walter Enders and Ting Qin

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*Journal of Macroeconomics*30, 2008. pp. 428-43.)**Abstract:**This paper examines the in-sample and out-of-sample properties of linear and nonlinear Taylor rules using real-time U.S. data. We find that (i) in-sample and out-of-sample performance measures generally select the same functional form for the Taylor rule and that (ii) the form of the Taylor rule differs across the pre-Greenspan and Greenspan sample periods. However, when we compare the out-of-sample forecasting performance of the Taylor rules to those of univariate models of the federal funds rate, we find it quite interesting that the univariate models forecast better than the Taylor rules after 1979 (but not before 1979).

Forecasting Persistent Data with Possible Structural Breaks: Old School and New School Lessons Using OECD Unemployment Rates

Walter Enders and Ruxandra Prodan

( In D. Rapach and M. Wohar, eds.

Walter Enders and Ruxandra Prodan

( In D. Rapach and M. Wohar, eds.

*Forecasting in the Presence of Structural Breaks and Model Uncertainty*. (Emerald: Bingley, U.K.) 2008. pp. 231-69. )**Abstract:**In contrast to recent forecasting developments, Old School forecasting techniques, such as exponential smoothing and the Box-Jenkins methodology, do not attempt to explicitly model or to estimate breaks in a time series. Adherents of the New School methodology argue that once breaks are well-estimated, it is possible to control for regime shifts when forecasting. We compare the forecasts of monthly unemployment rates in 10 OECD countries using various Old School and New School methods. Although each method seems to have drawbacks and no one method dominates the others, the Old School methods often outperform the New School methods for forecasting the unemployment rates.

Assessing the Importance of Global Shocks versus Country-Specific Shocks

Walter Enders and Kaouthar Souki

(

Walter Enders and Kaouthar Souki

(

*Journal of International Money and Finance*27, 2008. pp. 1420-29.)**Abstract:**A common assumption in the open-economy macroeconomics literature is that global shocks have little influence on current account balances, relative output levels, and real exchange rates. The aim of the paper is to develop an identification scheme that allows for the possibility that global shocks can affect all countries asymmetrically. Toward this end, we use a four-variable structural vector autoregression (VAR) of the Sims-Bernanke type that allows us to obtain a global shock and three country-specific shocks. We find that global shocks explain almost all of the movements in the German/US real exchange rate and sizable portions of the movements in the other real rates. Moreover, global shocks are important in explaining the changes in the bilateral current accounts between the three countries considered. Our decomposition also allows us to measure the extent to which third-country effects are important in explaining bilateral real exchange rates and relative output levels.

A Threshold Model of Real U.S. GDP and the Problem of Constructing Confidence Intervals in TAR Models

Walter Enders, Barry Falk & Pierre L. Siklos

(

Walter Enders, Barry Falk & Pierre L. Siklos

(

*Studies in Nonlinear Dynamics and Econometrics*11, 2007. Article 4.)**Abstract**We estimate real U.S. GDP growth as a threshold autoregressive process, and construct confidence intervals for the parameter estimates. However, there are various approaches that can be used in constructing the confidence intervals. Specifically, standard-t, bootstrap-t, and bootstrap-percentile confidence intervals are simulated for the slope coefficients and the estimated threshold. However, the results for the different methods have very different economic implications. We perform a Monte Carlo experiment to evaluate the various methods.

Using the Aggregate Demand-Aggregate Supply Model to Identify Structural Demand-Side and Supply-Side Shocks: Results Using a Bivariate VAR

James Peery Cover, Walter Enders, & C. James Hueng

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James Peery Cover, Walter Enders, & C. James Hueng

(

*Journal of Money, Credit and Banking*38, 2006. pp. 777–90.)**Abstract:**This paper uses the short-run restrictions implied by a simple aggregate demand-aggregate supply model as an aid in identifying structural shocks. Combined with the Blanchard-Quah restriction, it allows estimation of the slope of the aggregate supply curve, the variances of structural demand and supply shocks, and the extent to which structural demand and supply shocks are correlated. This paper finds that demand and supply shocks are highly correlated and that demand shocks possibly can account for as much as 82% of the long-run forecast error variance of real U.S. GDP.

Unit-Root Tests and Asymmetric Adjustment With an Example Using the Term Structure of Interest Rates

Walter Enders and C. W. J. Granger

Walter Enders and C. W. J. Granger

**Abstract:**This article develops critical values to test the null hypothesis of a unit root against the alternative of stationarity with asymmetric adjustment. Specific attention is paid to threshold and momentum threshold autoregressive processes. The standard Dickey-Fuller tests emerge as a special case. Within a reasonable range of adjustment parameters, the power of the new tests is shown to be greater than that of the corresponding Dickey-Fuller test. The use of the tests is illustrated using the term structure of interest rates. It is shown that the movements toward the long-run equilibrium relationship are best estimated as an asymmetric process.

Identifying aggregate demand and supply shocks in a small open economy

Walter Enders & Stan Hurn

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Walter Enders & Stan Hurn

(

*Oxford Economic Papers*59, 2007. pp. 411-29)**Abstract:**The standard Blanchard-Quah (BQ) decomposition forces aggregate demand and supply shocks to be orthogonal. However, for a variety of reasons, this assumption may be problematic. For example, policy actions may cause positive correlation between demand and supply shocks. This paper employs a modification of the BQ procedure that allows for correlated shifts in aggregate supply and demand. The method is demonstrated using Australian data. It is found that shocks to Australian aggregate demand and supply are highly correlated. The estimated shifts in the aggregate demand and supply curves are then used to measure the effects of inflation targeting on the Australian inflation rate and level of GDP.