Univariate Time Series Properties Research Articles

Equilibrium exchange rate determination and multiple structural changes

The large appreciation and depreciation of the US Dollar in the 1980s stimulated an important debate on the usefulness of unit root tests in the presence of structural breaks. In this paper, we propose a simple model to describe the evolution of the real exchange rate. We then propose a more general smooth transition (STR) function than has hitherto been employed, which is able to capture structural changes along the (long-run) equilibrium path, and show that this is consistent with our economic model. Our framework allows for a gradual adjustment between regimes and allows for under- and/or over-valued exchange rate adjustments. Using monthly and quarterly data for up to twenty OECD countries, we apply our methodology to investigate the univariate time series properties of CPI-based real exchange rates with both the U.S. Dollar and German Mark as the numeraire currencies. The empirical results show that, for more than half of the quarterly series, the evidence in favor of the stationarity of the real exchange rate was clearer in the sub-sample period post-1980.

Are business cycles stationary fluctuations around a deterministic trend? Empirical evidence from 79 developing countries

There is a large literature that tests the univariate time series properties of the real output series following the seminal work of Nelson and Plosser (1982). Whether or not real output is characterized by a unit root process has important implications. A unit root in real output, for instance, is inconsistent with the notion that business cycles are stationary fluctuations around a deterministic trend. In this paper, we investigate the univariate time series properties of real output for 79 developing countries using the conventional augmented Dickey and Fuller (1979) unit root test, the Zivot and Andrews’ (1992) one structural break unit root test, and the Lumsdaine and Papell (1997) two structural breaks unit root test. Our main finding is that, for 40 countries, real output is stationary around a trend. This indicates that business cycles are stationary fluctuations around a deterministic trend for only 51% of the developing countries in our sample.

Some univariate time series properties of output

Este artículo trata sobre el tamaño de la propiedad de caminata aleatoria del producto de Colombia en dos períodos, 1925-1994 y 1950-1994. PIB y PIB per cápita fueron encontrados ambos integrados de orden uno, un resultado suficientemente conocido. Las secuencias son altamente persistentes, especialmente en el período 1950-1994. El error de pronóstico cuando se presenta una innovación de 1 por ciento a la economía es de 1.5 por ciento en el muy largo plazo, cuando se considera el PIB. La respuesta es de aproximadamente 1.3 por ciento en el caso del PIB per cápita, lo cual parece apoyar la idea de que el crecimiento de la población es una fuente de no estacionaridad para algunos agregados macroeconómicos. Para el periodo más largo (1925-1994) la persistencia es menor. Este resultado introduce algunas dudas sobre el método de estimación del PIB para el periodo 1925-1994. Finalmente evidencia de no linealidad es encontrada solamente en variables filtradas con el procedimiento de Hodrick-Prescott para el periodo 1925-1994. Esto deja abierta la pregunta de si el filtro HP introduce no linealidad en la variable de alta frecuencia que el genera. Palabras Clave: Raíces unitarias, persistencia, no linealidad, función logística, modelos ESTAR y LSTAR.

Unit roots and structural breaks in North American unemployment rates

This paper examines the univariate time-series properties of the unemployment rate in Canada, Mexico, and the United States. Tests are employed that allow for endogenously determined break dates and the results are compared to stationarity tests that assume no break in the data. The structural break unit-root tests contradict the findings of the standard tests. We conclude that North American unemployment rates are trend stationary around a breaking trend.

Estimating strategic price response in a product-differentiated oligopoly: The case of a domestic canned fruit industry

In this article, we empirically estimate the strategic price response in a domestic canned fruit industry using national-level, weekly point-of-purchase scanner data. Augmented Dickey-Fuller tests are used to obtain univariate time series properties of Del Monte and Dole's canned pineapple prices. Johansen's likelihood ratio cointegration test is used to characterize the existence of an industry pricing equilibrium. Vector autoregression and vector error correction models are employed to examine the multivariate time series properties of the two firms' prices. Granger causality tests are used to address the price leadership hypothesis, while impulse response functions are constructed to chronicle the intertemporal price response to an innovation in a rival's price series. The battery of tests indicates that Del Monte follows Dole's pricing decisions in this narrowly defined product market. A thorough understanding of empirical price reactions has far-reaching strategic management implications, such as forecasting a rival's response and avoiding costly price wars. [L110, L200, L660] © 2000 John Wiley & Sons, Inc.

Estimation and analysis of the risk premium for commercial property

This paper has two main aims. First, given that an approximately 2 per cent positive differential of property over gilts appears to be the accepted required risk premium, then it is useful to examine the actual values of ex‐post risk premiums of property over both conventional and index‐linked gilts to determine whether this is achieved. Second, the univariate time series properties of the generated risk premiums are analysed to ascertain if there are any stable forecasting attributes embodied in the first and second moments.

Cointegration Analysis of Seasonal Time Series

This paper reviews various recent approaches to cointegration analysis of seasonal time series. In addition to the usual decisions concerning data transformations and univariate time series properties, it is necessary to decide how seasonal variation is included in the multivariate model and how standard cointegration methods should accordingly be modified. Seasonal cointegration and periodic cointegration methods are discussed, as are some of their recent refinements. An overview of further research topics is also provided.

The role of seasonality in economic time series reinterpreting money-output causality in U.S. data

While empirical evidence on the relationship between money and income has mainly been presented using seasonally adjusted data, seasonally unadjusted data are used in this paper to examine the time series behaviour of money, real GNP and industrial production, at both the seasonal and zero frequencies, based on tests of cointegration and seasonal cointegration. Two important conclusions are reached in the paper. First, although the univariate time series properties of M1 and real GNP appear to be very similar at both the seasonal and zero frequencies, seasonal comovements of M1 and real GNP turn out to be different from long-run comovements. Second, when seasonally unadjusted data are used, there appears to be no long-run relationship between money (M1 or M2) and output in the sense that the null of no cointegration cannot be rejected. Moreover, there is evidence of some feedback from output to money so that money is not necessarily exogenous. Consequently, as we might lose a possibly important chain of causation from money to income by ignoring the information concerning seasonal fluctuations, this paper provides further evidence that researchers should use raw data instead of seasonally adjusted data for inference and forecasting purposes.

Empirical evidence on the long-run neutrality hypothesis using low-frequency international data

We use the Backus and Kehoe ( American Economic Review, 1992, 82, 864–888) long, low-frequency data on real GNP/GDP, prices, and money for Australia, Canada, Denmark, Germany, Italy, Japan, Norway, Sweden, the United Kingdom and the United States to examine the long-run neutrality proposition. In doing so, we apply the Fisher and Seater ( American Economic Review, 1993, 83, 402–415) non-structural methodology, paying explicit attention to the univariate time-series properties of the variables. We conclude that the data are generally supportive of the quantity-theoretic proposition that money is long-run neutral.

On the (mis)specification of seasonality and its consequences: An empirical investigation with US data

It is well known that mis-specification of a trend leads to spurious cycles in detrended data (see, e.g., Nelson and Kang (1981)). Seasonal-adjustment procedures make assumptions, either implicitly or explicitly, about roots on the unit circle both at the zero and seasonal frequencies. Consequently, seasonal-adjustment procedures may produce spurious seasonal variation and other statistically undesirable effects. In this paper we document for a large class of widely used US quarterly macroeconomic series the effects of competing seasonal-adjustment procedures on the univariate time-series properties of the adjusted series. We also investigate which procedures are most appropriate given the properties of the data. Overall, we find very significant differences and evidence that several U.S. macroeconomic time series contain a mixture of deterministic and stochastic seasonal components.

Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates

This paper is of interest both for its methodological contribution of new tools for analyzing rational-expectations models and for its substantive conclusions concerning the term structure of interest rates during the monetary experiment of October 1979. The paper studies systems subject to changes in regime, interpreted here as occasional, discrete shifts in the parameters governing the time series behavior of exogenous economic variables. The specification is shown to be quite tractable both theoretically and empirically. The technique is used to analyze yields on three-month Treasury bills and ten-year Treasury bonds during 1962 to 1987. A constant-parameter linear model for short-term rates is shown to be inconsistent both with the univariate time series properties of short rates and with the observed bivariate relation between long and short rates under the expectations hypothesis of the term structure. AN alternative nonlinear model that admits the possibility of changes in regime affords a much better description of the univariate process for short rates. Moreover, the cross-equation restrictions implied by the expectations hypothesis of the term structure are consistent with the nonlinear specification. Indeed, the residuals of the restricted relation have a standard error of only 0.8 basis points. This is a third less than that of a completely unrestricted linear regression of long rates on short rates, and compares with an unconditional standard deviation of long rates of 142 basis points. I conclude that once the recognition by bond traders of changes in regime is taken into account, the expectations hypothesis of the term structure of interest rates holds up fairly well for these data.