Efficient Tests of Nonstationary Hypotheses

Robinson, Peter

doi:10.2307/2291004

Cited by 434 publications

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“…12 jointly with the two alternative models (M1) and (M2) presented in Section 2. In all cases, we employ the methodology devised by Robinson (1994). This is a Lagrange multiplier (LM) method that uses a Whittle Robinson 1997Robinson , 2001Gil-Alana 2004).…”

Section: The Empirical Resultsmentioning

confidence: 99%

“…However, for the remaining series, this model is decisively rejected in favour of a long memory specification. 6 Note that though Robinson (1994) is a testing procedure, we may also use it as an estimation method by choosing the value of d (or d s ) that produces the lowest statistic in absolute value for a range of d-(d s ) values. Moreover, the estimation of the time trend coefficients is based on standard OLS/GLS methods since under the null hypothesis the model is supposed to be I(0) and thus well behaved.…”

Section: The Empirical Resultsmentioning

confidence: 99%

“…Moreover, the estimation of the time trend coefficients is based on standard OLS/GLS methods since under the null hypothesis the model is supposed to be I(0) and thus well behaved. (See Robinson 1994). On the other hand, the series are long enough to justify the use of I(d) techniques.…”

Section: The Empirical Resultsmentioning

confidence: 99%

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Long memory, seasonality and time trends in the average monthly temperatures in Alaska

Gil-Alana

2011

Theor Appl Climatol

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This paper deals with the analysis of monthly temperatures in 19 meteorological stations in Alaska during the last 50 years. For this purpose, we employ a procedure that permits us to examine in a single framework several features observed in climatological time series such as time trends, long-range persistence and seasonality. The results indicate that the highest degrees of persistence are observed in stations located in the southern regions and seasonality appears as a major issue in all cases. Removing the seasonal structure and focussing on the anomalies with respect to the monthly means, the time trend coefficients appear significantly positive in the majority of the cases, implying that temperatures have increased during the last 50 years.

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Section: The Empirical Resultsmentioning

confidence: 99%

Section: The Empirical Resultsmentioning

confidence: 99%

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Long memory, seasonality and time trends in the average monthly temperatures in Alaska

Gil-Alana

2011

Theor Appl Climatol

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“…The family of Lagrange Multiplier (LM) tests for fractional integration was introduced by Robinson (1991Robinson ( , 1994. Although dealing, under the null hypothesis, with possibly nonstationary time series fractionally integrated of order d 0 , only standard asymptotic distributions such as χ 2 apply.…”

Section: Introductionmentioning

confidence: 99%

“…Let y t , the observed process, be fractional white noise of order d. In order to test the null d = d 0 by means of the LM principle, one builds differences under the null hypothesis, x t = (1 − L) d 0 y t . Then, working in the frequency domain, Robinson (1994) derived the test statistic…”

Section: Introductionmentioning

confidence: 99%

Bias correction for the regression-based LM fractional integration test

Demetrescu

Tarcolea

2008

AStA

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Testing unit roots, structural breaks and linearity in the inflation rates of the G7 countries with fractional dependence techniques

Gil-Alana

Yaya

Solademi

2016

Appl Stoch Models Bus & Ind

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In this paper, we have examined the inflation rates in the Group of Seven countries, investigating issues such as the existence of unit roots, structural breaks, fractional integration and potential non-linearities using a fractional dependence (FD) approach based on Chebyshev polynomials in time. This robust FD approach allows one to test for persistence as well as non-linearity of the series. We first tested for stationarity and structural breaks using classical approaches and observed inconclusive results with regard to the stationarity levels of the series. Using Bai-Perron tests, we actually confirmed significant structural breaks, even up to five, in each of the inflation series. However, noting that structural breaks are significantly related to fractional differentiation, this latter approach was also conducted. Here, we observed that the estimates of the differencing parameter were quite stable across time, and evidence of unit roots was found in the cases of the UK, Canada, France, Japan and the USA; for Germany, we found some evidence of mean reversion, while estimates of d above 1 were found in the case of Italy. On the other hand, non-linear deterministic trends were clearly rejected in all cases. ‡ Asymmetry is a property explaining unequal movements of asset prices (stocks, inflation, oil prices, exchange rates, etc.) between equilibrium state to 'up' market and 'down' market to equilibrium state. There are quite a number of papers on linear unit root testing inflation rates. Starting with Lai [3] who applied the modified Dickey-Fuller (DF) unit root test of Park and Fuller [4], testing nonstationarity in the inflation rates of the Group of Seven (G7) countries, he concluded that inflation rates were stationary. Cook [5] also found stationarity for the US inflation rates when he applied the DF [6, 7] test. Charemza et al. [8] considered inflation rates for a selected group of 93 countries, applying the augmented DF (ADF, [6,7]) tests, and found nonstationarity of the inflation series. Because of the different sample sizes considered in the aforementioned papers, the authors have obtained contradictory results.Structural breaks may affect the stationarity level of the time series [9]. § Zivot and Andrews [10] proposed a unit root test that selects the breakpoint endogenously from the data. This test has been extended to include the case of two break points in both the level and the trend series [11]. Multiple structural breaks tests have been proposed in Bai and Perron [12,13]. Caporale and Paxton [14] investigated stationarity of the inflation rates for five Latin American countries using the ADF unit root test and the unit root test with multiple structural breaks of Bai and Perron [12,13]. These authors found stationarity for three countries with the ADF tests, whereas the unit root test with structural breaks pointed to stationarity for all five inflation series.Some studies have thought of inflation as a dynamic non-linear process, and in this case, non-linear approaches have been conducte...

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Efficient Tests of Nonstationary Hypotheses

Cited by 434 publications

References 0 publications

Long memory, seasonality and time trends in the average monthly temperatures in Alaska

Long memory, seasonality and time trends in the average monthly temperatures in Alaska

Bias correction for the regression-based LM fractional integration test

Testing unit roots, structural breaks and linearity in the inflation rates of the G7 countries with fractional dependence techniques

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