Unit Root Properties Research Articles

The unit root property and optimality: a simple proof

Consider a pure exchange overlapping generations (OLG) economy under stationary Markov uncertainty with one good and with sequentially complete markets. It is known that an interior stationary equilibrium allocation at which the agents common matrix of intertemporal rates of substitution has a Perron root which is less than or equal to one is conditionally Pareto optimal (CPO). We provide a simple and direct proof of this fact.

Structural Breaks and Unit Roots: A Further Test of the 
 Sustainability of the Indian Fiscal Deficit

Tests for the sustainability of the public debt typically involve checking for the unit root properties of public expenditure and public revenue. If they are I(1) and not cointegrated or have a cointegration vector different from [1, -1] the public debt is said to be unsustainable. Extant work on debt sustainability in India has indicated that India's fiscal stance is unsustainable. We re-investigate the time series properties of the government of India's revenue and expenditure series by allowing for endogenous structural breaks for two data sets-the British period 1871-1921 and the post independence period 1950-1997. We discover that the revenue and expenditure series (nominal as well as real) are trend stationary with structural breaks, at least for the post independence period. Thus the conclusion that the Indian public debt is unsustainable is not warranted.

A Non-Parametric Examination of Stability in the Euro

Stage three of the introduction programme for the Euro began on January 1, 1999. This in many ways signalled the true beginning of the currency as thereafter the Euro was allowed for trade in foreign exchange markets and also in the issuance of new public debt. However it is already clear that this new currency will become a serious competitor of the Dollar in international usage. To illustrate, forecasts under a number of economic headings suggest that the Euro will be a closer competitor to the Dollar than having the Deutsche Mark as a vehicle currency (Portes and Rey, 1998; and McCauley, 1997). For example, in terms of all foreign exchange transactions, the Euro will be represented 50 to 60% (Dollar - 92%) of the time and the Euro will account for 25% (Dollar - 59%) of world trade invoices (McCauley, 1997). Other forecasts are even more optimistic suggesting equal status for these two currencies (Portes and Rey, 1998). Thus, the Euro is a very important currency for the fundamental welfare of the global economy and any concern over its stability is paramount. The backdrop for this analysis is that participating national currencies of the Euro were previously part of the Exchange Rate Mechanism that unfortunately suffered considerably from currency traders' speculative attack on a number of occasions. These attacks reached their zenith during the 1992/1993 crises leading to a radical revamping of the currency system. Generally, exchange rate fluctuations are measured unconditionally through an average standard deviation value, or conditionally using a GARCH related specification. However, the objective of this paper is to provide a plethora of information on the specific issue of whether speculative activity would unhinge participating governments' confidence in the currency. To achieve this, the paper concentrates on possible large scale exchange rate movements by applying a methodology specifically set-up to provide accurate measures of values located at the tail of the distribution, namely Extreme Value Theory. The findings are mainly encouraging. In many ways, the Euro shows similar characteristics to exchange rate series in general. For instance, the unconditional distribution of the Euro conclusively rejects the assumption of normality as well as having a unit root property and exhibiting volatility clustering. In terms of its stability, this paper finds there is no reason for concern regarding speculative pressure on the Euro. In fact, for a spectrum of probability and quantile measures, it consistently shows less volatility than the Yen. Moreover, the Euro follows a similar risk pattern to the Deutsche Mark, the currency that it is essentially replacing.

Stock returns and economic activity: the UK case

This paper investigates the relationships between real stock returns and a number of financial and economic variables for the UK economy for the period 1980 to 1994. We begin by discussing a theoretical model proposed by Balvers et al. and then re-estimate for the UK what may be regarded as an application of that model by Fama applied to the US market. This reproduces Fama's main results. For the UK we than suggest a slightly, different application of the Balvers model, the most important feature of which is the use of expectational macro-economic variables instead of Fama's use of leading values of industrial production. We then go on to investigate the unit root properties of the data and show that much of the data is indeed characterized by the presence of unit root non stationarity In the light of this, we propose an application of the Phillips-Loretan error-correction model and show that this provides a plausible relationship between real stock returns and most of the financial and economic variables.

Likelihood Ratio Tests for Seasonal Unit Roots

This paper proposes regression‐based likelihood ratio or F tests for the seasonal unit root hypothesis which fully incorporate the implicit restrictions on the parameters associated with the deterministics. These statistics are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. The limiting representations of the statistics are presented for a general seasonal aspect. These limiting representations allow those for other scenarios concerning the deterministics to be simply obtained and provide an explanation for the similarity between critical values in apparently quite different cases of interest. We re‐examine the seasonal unit root properties of the logarithm of monthly seasonally unadjusted real industrial production in Canada.

Deviations of Exchange Rates from Purchasing Power Parity: A Story Featuring Two Monetary Unions

We examine the mean-reverting properties of real exchange rates, by comparing the unit root properties of a group of international real exchange rates with two groups of intra-national real exchange rates. Strikingly, we find that while the international real rates taken as a group are mean-reverting, the intra-national rates are not. This is consistent with the view that while monetary shocks may be mean-reverting over the medium-term, underlying real factors do generate long-term trends in real exchange rates.

Additional critical values and asymptotic representations for seasonal unit root tests

This paper is concerned with tests for seasonal unit roots in a univariate time series process. The paper extends the procedures and tables of critical values due to Hylleberg et al. (1990) and Ghysels et al. (1994) to obtain tests which are similar (exactly and asymptotically) with respect to both the initial values of the process and the possibility of differential seasonal drift under the null hypothesis of a seasonal unit root. Representations are derived for the limiting distributions of the test statistics in this and other cases of interest. These representations provide an explanation for the similarity between critical values for the statistics in different scenarios. The seasonal unit root properties of real seasonally unadjusted UK non-durable consumption expenditure are re-examined.

Deviations of Exchange Rates from Purchasing Power Parity: A Story Featuring Two Monetary Unions

We examine the mean-reverting properties of real exchange rates, by comparing the unit root properties of a group of international real exchange rates with two groups of intra-national real exchange rates. Strikingly, we find that while the international real rates taken as a group are mean-reverting, the intra-national rates are not. This is consistent with the view that while monetary shocks may be mean-reverting over the medium-term, underlying real factors do generate long-term trends in real exchange rates.

Deviations of Exchange Rates From Purchasing Power Parity: A Story Featuring Two Monetary Unions

We examine the mean-reverting properties of real exchange rates, by comparing the unit root properties of a group of international real exchange rates with two groups of intra-national real exchange rates. Strikingly, we find that while the international real rates taken as a group appear mean-reverting, the intra-national rates are not. This is consistent with the view that while monetary shocks may be mean-reverting over the medium term, underlying real factors do generate long-term trends in real exchange rates.

Testing for a unit root in time series with trend breaks

This paper examines the implications of structural breaks for the unit-root property of some post-World War II macroeconomic time series. Based on sequential methods, trend breaks are found for 8 out of the 17 series considered. Conditional on a single break, the augmented Dickey-Fuller test rejects the no-break unit-root null for 5 series. Further, allowing for multiple breaks as opposed to a single break yields little gain against the null. The evidence against the null is much stronger based on recursive instead of sequential tests and weaker based on Phillips-Perron instead of augmented Dickey-Fuller statistics.

Modeling the U.S. demand for imports through cointegration and error correction

The purpose of this paper is to provide new estimates of the aggregate demand for both total and non-oil merchandise imports of the United States over the last two decades. To this aim we have applied recent and by now widely used cointegration techniques in order to estimate the long-run equilibrium relationship. Then we have imposed this long-run result as an error-correction mechanism to the dynamic model. The estimate of the long- and short-run income and price elasticities of imports is important to assess the potential role of the United States as “engine” of world growth, as suggested by the “locomotive” theory. Furthermore, it is important to evaluate whether and to what extent the United States faces an external constraint on growth and how exchange-rate movements affect the trade balance. This paper is structured as follows: after a brief introduction, Section 2 provides a review of the theoretical framework of the imperfect substitutes model on which ground lies our estimates. In Section 3 unit root properties of the data, the Engle-Granger two-step procedure and the Johansen methodology for estimating and testing cointegrating vectors are presented. Section 4 contains the econometric evidence on short-run income and price elasticities. In Section 5 the analysis is restricted to import demand of non-oil products. Empirical results are summarized in the last section.

Testing for unit roots with very high frequency spot exchange rate data

This paper Borno Statetests for unit roots in very high frequency spot exchange rate series, which have recently become available. The results suggest that the daily and hourly exchange rate series have a unit root, and most minute-by-minute series have a unit root without trend. In contrast, the continuous time exchange rate series have a unit root with trend, except the Tuesday series, which is trend stationary. However, after temporally aggregating the continuous time series into thirty-second, one-minute, five-minute, ten-minute, fifteen-minute, twenty-minute, thirty-minute and hourly series, we find a unit root in all the series. The results are consistent with the notion that temporal aggregation preserves the unit root property in time series.