Summary
This paper presents a selective survey of the literature on non-stationarity tests, namely standard and efficient unit root tests and stationarity tests, with or without structural changes. We also present the direct relation between non-stationarity tests and four economic theories, such as business cycles, hysteresis, purchasing power parity and convergence.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agiakoglou C, Newbold P (1992) Empirical evidence on Dickey-Fuller type tests. Journal of Time Series Analysis 6: 471–483
Agiakoglou C, Newbold P (1996) The balance between size and power in Dickey-Fuller tests with data-dependent rules for the choice of truncation lag. Economics Letters 52: 229–234
Altissimo F, Corradi V (2003) Strong rules for detecting the number of breaks in a time series. Journal of Econometrics 117: 207–244
Amsler C, Lee J (1995) An LM test for a unit-root in the presence of a structural change. Econometric Theory 11: 359–368
Arellano C, Pantula SG (1995) Testing for trend stationarity versus difference stationarity. Journal of Time Series Analysis 16: 147–164
Ayat L, Burridge P (2000) Unit root tests in the presence of uncertainty about the nonstochastic trend. Journal of Econometrics 95: 71–96
Badillo R, Belaire-Franch J, Contreras D (2002) Spurious rejection of the stationarity hypothesis in the presence of a break point. Applied Economics 34: 1917–1923
Bai J (1997) Estimating multiple breaks one at the time. Econometric Theory 13: 315–352
Bai J (1999) Likelihood ratio tests for multiple structural changes. Journal of Econometrics 91: 299–323
Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66: 47–78
Bai J, Perron P (2003) Computation and analysis of multiple structural change models. Journal of Applied Econometrics 18: 1–22
Balke NS, Fomby TB (1994) Large shocks, small shocks, and economic fluctuations: Outliers in macroeconomic time series. Journal of Applied Econometrics 9: 181–200
Banerjee A, Lumsdaine RL, Stock JH (1992) Recursive and sequential tests of the unit-root and trend-break hypotheses: theory and international evidence. Journal of Business and Economic Statistics 10: 271–287
Barro RJ (1991) Economic growth in a cross section of countries. Quarterly Journal of Economics 106: 407–443
Barro RJ, Sala-i-Martin X (1992) Convergence. Journal of Political Economy 100: 223–251
Baumol WJ (1986) Productivity growth, convergence, and welfare: What the long-run data show. American Economic Review 76: 1072–1085
Bernard AB, Durlauf SN (1995) Convergence in international output. Journal of Applied Econometrics 10: 97–108
Bernard AB, Durlauf SN (1996) Interpreting tests of the convergence hypothesis. Journal of Econometrics 71: 161–173
Bhargava A (1986) On the theory of testing for unit roots in observed time series. Review of Economic Studies 53: 369–384
Blanchard O, Summers L (1986) Hysteresis and the European unemployment problem. In Fischer (ed) NBER macroeconomic annual MIT Press, Cambridge
Blanchard O, Summers L (1987) Hysteresis in unemployment. European Economic Review 31: 288–295
Bradley MD, Jansen DW (1995) Unit roots and infrequent large shocks: New international evidence on output growth. Journal of Money, Credit, and Banking 27: 876–893
Burridge P, Taylor AMR (2000) On the power of GLS-type unit root tests. Oxford Bulletin of Economics and Statistics 62: 633–645
Busetti F, Harvey AC (2001) Testing for the presence of a random walk in series with structural breaks. Journal of Time Series Analysis 22: 127–150
Busetti F, Taylor AMR (2003) Variance shifts, structural breaks, and stationarity tests. Journal of Business and Economic Statistics 21: 510–531
Caner M, Kilian L (2001) Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate. Journal of International Money and Finance 20: 639–657
Carlino G, Mills L (1993) Are US regional economies converging? A time series analysis. Journal of Monetary Economics 32: 335–346
Carrion JL (2003) Breaking date misspecification error for the level shift KPSS test. Economics Letters 81: 365–371
Carrion JL, Sansó A, Artís M (1998) Stationarity tests in the presence of structural breaks. Working Paper DOCT 98R04, Department of Econometrics, Statistics and Spanish Economy, University of Barcelona
Carrion JL, Sansó A, Artís M (2003) The KPSS test with two structural breaks. Technical Report, Department of Econometrics, Statistics and Spanish Economy, University of Barcelona
Cass DM (1965) Optimum growth in an aggregate model of capital accumulation. Review of Economic Studies 32: 233–240
Cassel G (1916) The present situation of the foreign exchanges. Economic Journal 26: 62–65
Cassel G (1918) Abnormal deviations in international exchange. Economic Journal 28: 413–415
Chan KH, Hayya JC, Ord JK (1977) A note on trend removal methods: the case of polynomial regression versus variate differencing. Econometrica 45: 737–744
Chen C, Liu LM (1993) Joint estimation of model parameters and outlier effects in time series. Journal of the American Statistical Association 88: 284–297
Choi I (1994) Residual based tests for the null of stationary with applications to U.S. macroeconomic time series. Econometric Theory 10: 720–746
Christiano LJ (1992) Searching for a break in GNP. Journal of Business and Economic Statistics 10: 271–287
Clements MP, Hendry DF (2001) Forecasting with difference-stationary and trend-stationary models. Econometrics Journal 4: 1–9
Clemente J, Montañés A, Reyes M (1998) Testing for a unit root in variables with a double change in the mean. Economics Letters 59: 175–182
Darné O (2004) The effects of additive outliers on stationarity tests: A Monte Carlo study. Economics Bulletin 3: 1–8
Darné O, Diebolt C (2004) Unit roots and infrequent large shocks: New international evidence on output. Journal of Monetary Economics 51: 1449–1465
DeJong DN, Nankervis JC, Savin NE, Whiteman CH (1992) The power problems of unit root tests in time series with autoregressive errors. Journal of Econometrics 53: 323–343
Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with unit root. Journal of the American Statistical Association 74: 427–481
Dickey DA, Fuller WA (1981) Likelihood ratio statistics for autoregressive time series with unit root. Econometrica 49: 1057–1072
Dickey DA, Gonzalez-Farias G (1992) A new maximum likelihood approach to testing for unit roots. Proceedings of the Business and Economic Statistics Section, American Statistical Association
Dornbusch R (1976) Expectations and exchange rate dynamics. Journal of Political Economy 84: 1161–1176
Dufour JM, King M (1991) Optimal invariant tests for the autocorrelation coefficient in linear regressions with stationary and nonstationary errors. Journal of Econometrics 47: 115–143
Edison HJ, Gagnon JE, Melick WR (1996) Understanding the empirical literature on purchasing power parity: The Post-Bretton Woods era. Journal of International Money and Finance 16: 1–17
Elliott G (1999) Efficient tests for a unit root when the initial observation is drawn from its unconditional distribution. International Economic Review 40: 767–783
Elliott G, Rothenberg TJ, Stock JH (1996) Efficient tests for an autoregressive unit root. Econometrica 64: 813–836
Everaert G (2001) Infrequent large shocks to unemployment: New evidence on alternative persistence perspectives. Labour 15: 555–577
Franses PH, Haldrup N (1994) The effects of additive outliers on tests for unit roots and cointegration. Journal of Business and Economic Statistics 12: 471–478
Frenkel JA (1976) A monetary approach to the exchange rate: Doctrinal aspects and empirical evidence. Scandinavian Journal of Economics 78: 200–224
Frenkel JA (1978) Purchasing power parity: Doctrinal perspective and evidence from the 1920s. Journal of International Economics 8: 169–191
Friedman M (1968) The role of monetary policy. American Economic Review 58: 1–17
Froot KA, Rogoff K (1995) Perspectives on PPP and long-run real exchange rates. In Grossman and Rogoff (eds) Handbook of international economics, North-Holland, Amsterdam
Fuller WA (1976) Introduction to statistical time series. John Wiley, New York.
Fuller WA (1996) Introduction to statistical time series. Second Edition, John Wiley, New York
Hall A (1989) Testing for a unit root in the presence of moving average errors. Biometrika 76: 49–56
Harvey AC (1989) Forecasting, structural time series models and the Kalman filter. Cambridge University Press
Harvey DI, Leybourne SJ, Newbold P (2001) Innovational outlier unit root tests with an endogenously determined break in level. Oxfor Bulletin of Economics and Statistics 63: 559–575
Hecq A, Urbain J-P (1993) Misspecification tests, unit roots and level shifts. Economics Letters 43: 129–135
Hegwood ND, Papell DH (1998) Quasi purchasing power parity. International Journal of Finance and Economics 3: 279–289
Hendry DF, Neale AF (1991) A Monte Carlo study of the effects of structural breaks for unit roots. In Hackl P, Westlund AH (eds) Economic structural change, analysis and forecasting, Springer, Berlin
Hobijn B, Franses PH, Ooms M (1998) Generalizations of the KPSS-test for stationarity. Econometric Institute Report No. 9802/A, Erasmus University Rotterdam
Hwang J, Schmidt P (1996) Alternatives methods of detrending and the power of unit root tests. Journal of Econometrics 71: 227–248
Kim T-H, Leybourne SJ, Newbold P (2000) Spurious rejections by Perron tests in the presence of a break. Oxford Bulletin of Economics and Statistics 62: 433–444
Kim T-H, Leybourne SJ, Newbold P (2002) Unit root tests with a break in innovation variance. Journal of Econometrics 109: 365–387
King ML (1988) Towards a theory of point optimal testing. Econometric Reviews 6: 169–218
Kurozumi E (2002) Testing for stationarity with a break. Journal of Econometrics 108: 63–99
Kwiatkowski D, Phillips P, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationary against the alternative of a unit root: how sure are we that economic time series have a unit root? Journal of Econometrics 54: 159–178
Kydland FE, Prescott EC (1982) Time to build and aggregate fluctuations. Econometrica 50: 1345–1370
Lanne M, Lütkepohl H (2002) Unit root tests for time series with level shifts: A comparison of different proposals. Economics Letters 75: 109–114
Lanne M, Saikkonen P (2003) Reducing size distorsions of parametric stationarity tests. Journal of Time Series Analysis 24: 423–439
Layard R, Nickell S, Jackman R (1991) Unemployment: Macroeconomic performance and the labour market. Oxford University Press, Oxford.
Lee J, Huang CJ, Shin Y (1997) On stationary tests in the presence of structural breaks. Economics Letters 55: 165–172
Lee J, Strazicich M (1999) Minimum LM unit root tests. Mimeo, Department of Economics, University of Central Florida
Lee J, Strazicich M (2001) Break point estimation and spurious rejections with endogenous unit root tests. Oxford Bulletin of Economics and Statistics 68: 535–558
Lee J, Strazicich M (2001) Testing the null of stationarity in the presence of a structural break. Applied Economics Letters 8: 377–382
Lee J, Strazicich M (2003) Minimum LM unit root tests with two structural breaks. Review of Economics and Statistics 85: 1082–1089
Leybourne SJ (1995) Testing for unit roots using forward and reverse Dickey-Fuller regressions. Oxford Bulletin of Economics and Statistics 57: 559–571
Leybourne SJ, McCabe BPM (1994) A consistent test for a unit root. Journal of Business and Economic Statistics 12: 157–166
Leybourne SJ, McCabe BPM (1999) Modified stationarity tests with data-dependent model-selection rules. Journal of Business and Economic Statistics 17: 264–270
Leybourne SJ, Mills TC, Newbold P (1998) Spurious rejections by Dickey-Fuller tests in the presence of a break under the null. Journal of Econometrics 87: 191–203
Leybourne SJ, Newbold P (2000) Behaviour of Dickey-Fuller t-tests when there is a break under the alternatives hypothesis. Econometric Theory 16: 779–789
Long JB, Plosser CI (1983) Real business cycle. Journal of Political Economy 91: 39–69
Li Q, Papell D (1999) Convergence of international output: Time series evidence for 16 OECD countries. International Review of Economics and Finance 8: 267–280
Lindbeck A, Snower DJ (1989) The insider-outsider theory of employment and unemployment. MIT Press, Cambridge
Lucas RE (1972) Expectations and neutrality of money. Journal of Economic Theory 4: 103–124
Lucas RE (1974) Some international evidence on output inflation tradeoffs. American Economic Review 63: 326–334
Lumsdaine R, Papell D (1997) Multiple trend breaks and the unit-root hypothesis. Review of Economics and Statistics 79: 212–218
Maddala GS, Kim I-M (2000) Unit roots, cointegration and structural change. Cambridge University Press, Cambridge
Mankiw NG, Romer D, Weil DN (1992) A contribution to the empirics of economic growth. Quarterly Journal of Economics 107: 407–438
Mikhail O, Eberwein CJ, Handa J (2003) The measurement of persistence and hysteresis in aggregate unemployment. Working Paper, Department of Economics, University of Central Florida
Montañés A (1997) Level shifts, unit roots and misspecification of the breaking date. Economics Letters 54: 7–13
Montañés A, Reyes M (1998) Effect of a shift in the trend function on Dickey-Fuller unit root tests. Econometric Theory 14: 355–363
Nelson CR, Kang H (1981) Spurious periodicity in inappropriately detrended time series. Econometrica 49: 741–751
Nelson CR, Kang H (1984) Pitfalls in the use of time as an explonatory variable in regression. Journal of Business and Economic Statistics 2: 73–82
Nelson CR, Plosser CI (1982) Trends and random walks in macroeconomic time series. Journal of Monetary Economics 10: 139–162
Newey W, West K (1987) A simple positive semi-definite heteroskedasticity and autocorrelation-consistent covariance matrix. Econometrica 55: 703–708
Newey W, West K (1994) Automatic lag selection and covariance matrix estimation. Review of Economic Studies 61: 631–653
Ng S, Perron P (1995) Unit root tests in ARMA models with data dependent methods for the selection of the truncation lag. Journal of the American Statistical Association 90: 268–281
Ng S, Perron P (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69: 1519–1554
Nunes L, Newbold P, Kuan C (1996) Spurious number of breaks. Economics Letters 50: 175–178
Nunes L, Newbold P, Kuan C (1997) Testing for unit roots with breaks: Evidence on the great crash and the unit root hypothesis reconsidered. Oxford Bulletin of Economics and Statistics 59: 435–448
Officer LH (1982) Purchasing power parity and exchange rate: Theory, evidence and relevance. JAI Press, Greenwich
Pantula SG, Hall A (1991) Testing for unit roots in autoregressive moving average models. Journal of Econometrics 48: 325–353
Papell DH, Murray CJ, Ghiblawi H (2000) The structure of unemployment. The Review of Economics and Statistics 82: 309–315
Park HJ, Fuller WA (1995) Alternatives estimators and unit root tests for the autoregressive process. Journal of Time Series Analysis 16: 415–429
Perron P (1988) Trends and random walks in macroeconomic time series: Further evidence from a new approach. Journal of Economic Dynamics and Control 12: 297–332
Perron P (1989) The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57: 1361–1401
Perron P. (1990), “Testing for a unit root in a time series with a changing mean”, Journal of Business and Economic Statistics, 8, 153–162.
Perron P (1993) The great crash, the oil price shock, and the unit root hypothesis: Erratum. Econometrica 61: 248–249
Perron P (1997) Further evidence on breaking trend functions in macroeconomic variables. Journal of Econometrics 80: 355–385
Perron P, Ng S (1996) Useful modifications to unit root tests with dependent errors and their local asymptotic properties. Review of Economic Studies 63: 435–465
Perron P, Rodriguez G (2003) GLS detrending, efficient unit root tests and structural change. Journal of Econometrics 115: 1–27
Perron P, Rodriguez G (2003) Searching for additive outliers in nonstationary time series. Journal of Time Series Analysis 24: 193–220
Perron P, Vogelsang TJ (1992) Nonstationarity and level shifts with an application to purchasing power parity. Journal of Business and Economic Statistics 10: 301–320
Perron P, Vogelsang TJ (1992) Testing for a unit root in a time series with a changing mean: corrections and extensions. Journal of Business and Economic Statistics 10: 467–470
Perron P, Vogelsang TJ (1993) A note on the asymptotic distributions of unit root tests in the additive outlier model with breaks. Revista de Econometria 13: 181–201
Phelps E (1967) Phillips curves, expectations of inflation and optimal unemployment over time. Economica 34: 254–281
Phelps E (1968) Money wage dynamics and labor market equilibrium. Journal of Political Economy 76: 678–711
Phelps E (1994) Structural slumps: The modern equilibrium theory of unemployment, interest, and assets. Harvard University Press, Cambridge.
Phillips P.C.B. (1987), “Time series regression with a unit root”, Econometrica, 55, 277–301.
Phillips PCB, Perron P (1988) Testing for unit root in time series regression. Biometrika 75: 347–353
Phillips PCB, Xiao Z (1998) A primer on unit root testing. Journal of Economic Surveys 12: 1–51
Rappoport P, Reichlin L (1989) Segmented trends and non-stationary time series. Economic Journal 99: 168–177
Rebelo S (1991) Long-run policy analysis and long-run growth. Journal of Political Economy 99: 500–521
Røed K (1997) Hysteresis in unemployment. Journal of Economic Surveys 11: 389–418
Rogoff K (1996) The purchasing power parity puzzle. Journal of Economic Literature 34: 647–668
Romer PM (1986) Increasing returns and long-run growth. Journal of Political Economy 94: 1002–1037
Said SE, Dickey DA (1984) Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71: 599–607
Said SE, Dickey DA (1985) Hypothesis testing in ARIMA(p,1,q) models. Journal of the American Statistical Association 80: 369–374
Saikkonen P, Luukkonen R (1993) Testing for a moving average unit root in autoregressive integrated moving average models. Journal of the American Statistical Association 88: 596–601
Schmidt P, Phillips PCB (1992) LM tests for a unit root in the presence of deterministic trends. Oxford Bulletin of Economics and Statistics 54: 257–289
Schwert GW (1987) Effects of model specification on tests for unit roots in macroeconomic data. Journal of Monetary Economics 20: 73–103
Schwert GW (1989) Tests for unit roots: A Monte Carlo investigation. Journal of Business and Economic Statistics 7: 147–160
Sen A (2003) On unit-root tests when the alternative is a trend-break stationary process. Journal of Business and Economic Statistics 21: 174–184
Shin DW, Fuller WA (1998) Unit root tests based on unconditional maximum likelihood estimation for the autoregressive moving average. Journal of Time Series Analysis 19: 591–599
Shin DW, Sarkar S, Lee JH (1996) Unit root tests for time series with outliers. Statistics and Probability Letters 30: 189–197
Shin DW, So BS (2001) Recursive mean adjustment and tests for unit roots. Journal of Time Series Analysis 22: 595–612
Shin DW, So BS (2002) Recursive mean adjustment and tests for nonstationarities. Economics Letters 75: 203–208
Solow RM (1956) A contribution of the theory of economic growth. The Quarterly Journal of Economics 70: 65–94
Stock JH (1990) A class of tests for integration and cointegration. Manuscript, Harvard University
Stock JH (1994) Unit roots, structural breaks and trends. In Engle, McFadden (eds) Handbook of econometrics, Vol. 4, North-Holland
Tanaka K (1990) Testing for a moving average unit root. Econometric Theory 6: 433–444
Taylor AMR (2002) Regression-based unit root tests with recursive mean adjustment for seasonal and nonseasonal time series. Journal of Business and Economic Statistics 20: 269–281
Tsay RS (1988) Outliers, level shifts, and variance changes in time series. Journal of Forecasting 7: 1–20
Vogelsang TJ (1999) Two simple procedures for testing for a unit root when there are additive outliers. Journal of Time Series Analysis 20: 237–252
Vogelsang TJ, Perron P (1998) Additional tests for a unit root allowing the possibility of breaks in the trend function. International Economic Review 39: 1073–1100
Xiao Z (2001) Testing the null hypothesis of stationarity against an autoregressive unit root alternative. Journal of Time Series Analysis 22: 87–105
Xiao Z, Phillips PCB (1998) An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy. The Econometrics Journal 1: 27–43
Yap SF, Reinsel GC (1995) Results on estimation and testing for unit roots in the nonstationary autoregressive moving-average model. Journal of Time Series Analysis 16: 339–353
Yin Y, Maddala GS (1997) The effects of different types of outliers on unit root tests. In Fomby, Hill (eds), Advances in econometrics, Vol. 13, JAI Press, Greenwich, Conn
Zivot E, Andrews DWK (1992) Further evidence on the great crash, the oil price shock and the unit root hypothesis. Journal of Business and Economic Statistics 10: 251–270
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Darné, O., Diebolt, C. (2005). Non-stationarity Tests in Macroeconomic Time Series. In: Diebolt, C., Kyrtsou, C. (eds) New Trends in Macroeconomics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28556-3_9
Download citation
DOI: https://doi.org/10.1007/3-540-28556-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21448-9
Online ISBN: 978-3-540-28556-4
eBook Packages: Business and EconomicsEconomics and Finance (R0)