nach oben

Empirical Economics

Erschienen in:

01.09.2014

Exchange rates dynamics revisited: a panel data test of the fractional integration order

verfasst von: Fredrik N. G. Andersson

Erschienen in: Empirical Economics | Ausgabe 2/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We test the possibility that exchange rates from nine developed countries have a unit root against the alternate possibility that they are fractionally integrated. Theoretically, exchange rates are only expected to follow a random walk under restrictive assumptions. However, most traditional unit root tests cannot reject a unit root in exchange rates, and time series tests that allow for fractional integration have given inconclusive results. To increase the power of the test of the integration order we develop two panel data tests of the fractional integration order. Monte Carlo simulations show that these tests are correctly sized and have relatively high power compared to other similar tests. Moreover, our empirical results show that we can reject a unit root in exchange rates with a high probability, but the integration order is close to one. This indicates that exchange rates are mean-reverting, although the reversion is slow, resulting in long swings.

Nächster Artikel Revealing asymmetries in the loss function of WTI oil futures market

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Australia, Canada, the Euro Area, Japan, New Zealand, Norway, Switzerland, Sweden, the United Kingdom, and the United States.

When \(\varepsilon _{nt} \) is integrated of order \(d_{\varepsilon n}\), \(x_{nt} \) is integrated of order \(d_{\varepsilon n}+d_{n}\) (Percival and Walden 2006).

See Percival (2006) or Andersson (2008) for a detailed description of how the transform matrix is constructed.

The exclusion of boundary coefficients results in a loss of information. But, the number of boundary coefficients is small compared to the number of non-boundary coefficients. In our simulations and empirical analysis 89 % of the transform coefficients are non-boundary coefficients when \(T =256\), and 99 % of the transform coefficients are non-boundary coefficients when \(T=4{,}096\).

For more details, see Percival and Walden (2006).

Our simulation shows that each scale should include at least 16 transform coefficients for the Fisher test to be correctly sized.

Bai and Ng (2004) consider different data generating processes where the idiosyncratic component and the common factor can have different integration orders. This case is not considered in the paper since time series estimators of the fractional integration require that the integration orders are the same.

To estimate the factors the data must be stationary. When \(0.5<d<1.5\), it is therefore necessary to take the difference of \(x_{nt}\) to make it stationary before estimating the factors and the idiosyncratic component. Once the factors and the idiosyncratic components have been estimated in first differences they are cumulated back to levels (see Bai and Ng 2004).

Heteroskedastic across cross-sections is easily taken into account by estimating one shock variance for each cross-section.

Nielsen proposes two tests. Under the null \(d_{n}=d\) for all \(n\) in both tests. In the first test under the alternative \(d_{n}=d+\phi \) where \(\phi \ne 0\) In the second test, under the alternative \(d_{n}=d+\phi _{n}\) where \(\phi _{n}\ne 0\) for at least one \(n\). We use the second test.

This is similar as to Bai and Ng (2004).

Simulations not presented in the paper show that the AMLE estimates of the integration order is unbiased for \(\rho <0.5\) when wavelet scales 1–4 are excluded from the estimation.

An alternative wavelet transform that does not impose any restriction on the sample size is the Maximal Overlap Discrete Wavelet Transform. However, this transform does not decorrelate the transform coefficients of fractionally integrated process and can thus not be used in our analysis.

http://research.stlouisfed.org/fred2/.

The estimated integration order for the full sample is 0.643 while the estimated integration order for the truncated sample is 0.859.

Barros et al. (2011) estimates two integration orders: one estimate using all frequencies and one estimate where the high frequencies have been excluded. Similar to our analysis they find no evidence of autocorrelated errors.

The smaller currencies are: AUD, CAD, CHF, GBP, JPY, NOK, NZD, and SEK.

Andersson FNG (2008) Wavelet Analysis of Economic Time Series. Lund Economic Studies 149

Andreas EL, Trevino G (1997) Using Wavelets to Detect Trends. Journal of Atmospheric and Oceanic Technology 14:554–564CrossRef

Bai J, Ng S (2004) A Panic Attack on Unit Roots and Cointegration. Econometrica 72(4):1127–1177CrossRef

Barnhart SW, Szakmary AC (1991) Testing the Unbiased Forward Rate Hypothesis: Evidence on Unit-Roots, Co-Integration, and Stochastic Effects. Journal of Financial and Quantitative Analysis 26:245–267CrossRef

Barros CP, Gil-Alana L, Matousek R (2011) Fractional Integration of Nominal Exchange Rates: Evidence from CEECs in Light of EMU Enlargement. Review of International Economics 19:77–92CrossRef

Belaire-Franch J, Opong KK (2005) Some Evidence of Random Walk Behaviour of EUR Exchange Rates using Ranks and Signs. Journal of Banking and Finance 29:1631–1643CrossRef

Bisaglia L, Procidano I (2003) Improving the Power of Unit Roots Tests Against Fractional Alternatives Using Bootstraps. Statistica LXIII n.3, 589–602

Baillie RT, Bollerslev T (1989) Common Stochastic Trends in a System of Exchange Rates. Journal of Finance 44:167–181CrossRef

Brockwell PJ, Davis RA (1998) Time Series: Theory and Methods. Springer-Verlag

Corbae D, Ouliaris S (1986) Robust Tests for Unit Roots in the Foreign Exchange Market. Economic Letters 22:375–380CrossRef

Cheung YW, Lai KS (1993) A Fractional Cointegration Analysis of Purchasing Power Parity. Journal of Business and Economic Statistics 11:103–112

Choi I (2001) Unit Root Tests for Panel Data. Journal of International Money and Finance 20:249–272CrossRef

Chung CF, Baillie RT (1993) Small Sample Bias in the Conditional Sum of Squares Estimator of Fractionally Integrated Series. Empirical Economics 18:791–806CrossRef

Ciccarelli M, Mojon B (2007) Global Inflation. Kiel Working Paper No. 1337

Craigmile PF, Percival DB (2005) Asympotic Decorrelation of Between-Scale Wavelet Coefficients. IEEE Transactions on Information Theory 51:1039–1048CrossRef

Craigmile PF, Guttorp P, Percival DB (2005) Wavelet-Based Parameter Estimation for Polynomial Contaminated Fractionally Differenced Processes. IEEE Transactions on Signal Processing 53 (8), 3151–3161

Diebold FX, Rudebusch GD (1991) On the Power of Dickey-Fuller Tests against Fractional Alternatives. Economic Letters 35:155–160CrossRef

Engel CM, Hamilton JD (1990) Long swings in the dollar: Are they in the data and do markets know it? American Economic Review 80:689–713

Fama E (1965) The Behavior of Stock Market Prices. Journal of Business 38:34–105CrossRef

Fama E (1970) Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance 25:383–417CrossRef

Fama E (1991) Efficient Capital Markets: II. Journal of Finance 46(5):1575–1617CrossRef

Fan Y, Gencay R (2010) Unit Root Tests with Wavelets. Econometric Theory 26(5):1305–1331CrossRef

Fujihara RA, Mougoue M (1994) Temporal Aggregation and Unit Roots in Nominal Foreign Exchange Rates. Review of Quantitative Finance and Accounting 4:291–303CrossRef

Gencay R, Selcuk F, Whitcher B (2002) An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic Press, London

Geweke J, Porter-Hudak S (1983) The Estimation and Application of Long Memory Models. Journal of Time Series Analysis 4(4):221–237CrossRef

Hassler U, Walters J (1994) On the Power of Unit Root Tests against Fractional Alternatives. Economic Letters 45:1–5CrossRef

Jin HJ, Elder J, Koo WW (2006) A Reexamination of Fractional Integrating Dynamics in Foreign Currency Markets. International Review of Economics and Finance 15:120–135CrossRef

Li Y, Shukur G (2011) Testing for Unit Roots in Panel Data Using a Wavelet Ratio Method. Computational Economics 41(1):59–69CrossRef

Maddala GS, Wu S (1999) A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test. Oxford Bulletin of Economics and Statistics 61:631–652CrossRef

Meese R, Rogoff K (1983) Empirical exchange rate models of the seventies. Do they fit out of sample? Journal of International Economics 14:3–24

Meese RA, Singleton KJ (1982) On Unit Roots and the Empirical Modeling of Exchange Rates. Journal of Finance 37:1029–1035CrossRef

Monacelli T, Sala L (2009) The International Dimension of Inflation: Evidence from Disaggregated Consumer Price Data. Journal of Money, Credit and Banking 41:101–120CrossRef

Nielsen M (1999) Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long Memory Parameter. Journal of Forecasting 18(1):17–33CrossRef

Nielsen MO (2005) Multivariate Lagrange Multiplier Tests for Fractional Integration. Journal of Financial Econometrics 3(3):372–398CrossRef

Percival DB (2006) Wavelet Methods for Time Series. Lund University Lecture Notes

Percival DB, Walden AT (2006) Wavelet Methods for Time Series Analysis. Cambridge University Press

Percival DB, Sardy S, Davison AC (2001) Wavestrapping Time Series: Adaptive Wavelet-Based Bootstrapping. In: Fitzgerald WJ, Smith RL, Walden AT, Young PC (eds) Nonlinear and Nonstationary Signal Processing. Cambridge University Press

Robinson PM (1995) Log-Periodogram Regression of Time Series with Long Range Dependence. The Annals of Statistics 23(3):1048–1072CrossRef

Samuelson P (1965) Proof that Properly Anticipated Prices Fluctuate Randomly. Industrial Management Review 6:41–49

Sephton P (2008) Exchange Rates and Fractional Integration Revisited. Applied Financial Economic Letters 4(6):383–387CrossRef

Shimotsu K, Phillips PCB (2005) Exact Local Whittle Estimation of Fractional Integration. The Annals of Statistics 33(4)

Slutsky E (1925) Über Stochastiche Asymptotem and Grentzwerte. Metron International Journal of Statistics 5(3):1–90

Sowell FB (1992) Maximum Likelihood Estimation of Stationary Univariate Fractionally Integrated Time Series Models. Journal of Econometrics 53:325–371CrossRef

Taylor MP (1995) The Economics of Exchange Rates. Journal of Economic Literature 33(1):13–47

Velasco C (1999) Non-stationary Log-Periodiogram Regression. Journal of Econometrics 91:325–371CrossRef

Titel: Exchange rates dynamics revisited: a panel data test of the fractional integration order
verfasst von: Fredrik N. G. Andersson
Publikationsdatum: 01.09.2014
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 2/2014
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-013-0740-3

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Springer Professional "Wirtschaft+Technik"

Weitere Artikel der Ausgabe 2/2014

The last fifteen years of stagnation in Italy: a business cycle accounting perspective

Heterogeneous returns to personality: the role of occupational choice

The wage effects of subsidized career breaks

Estimating SUR system with random coefficients: the unbalanced panel data case

Measuring the natural rates, gaps, and deviation cycles

Wage spillovers across sectors in Eastern Europe

Premium Partner