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  • 1
    Electronic Resource
    Electronic Resource
    A Continuous Time Approximation to the Stationary First-Order Autoregressive Model (1991)
    New York : Cambridge University Press
    Econometric theory 7 (1991), S. 236-252 
    Details
    ISSN: 0266-4666
    Source: Cambridge Journals Digital Archives
    Topics: Economics
    Notes: We consider the least-squares estimator in a strictly stationary first-order autoregression without an estimated intercept. We study its continuous time asymptotic distribution based on an asymptotic framework where the sampling interval converges to zero as the sample size increases. We derive a momentgenerating function which permits the calculation of percentage points and moments of this asymptotic distribution and assess the adequacy of the approximation to the finite sample distribution. In general, the approximation is excellent for values of the autoregressive parameter near one. We also consider the behavior of the power function of tests based on the normalized leastsquares estimator. Interesting nonmonotonic properties are uncovered. This analysis extends the study of Perron [15] and helps to provide explanations for the finite sample results established by Nankervis and Savin [13].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1017/S0266466600004436
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Test Consistency with Varying Sampling Frequency (1991)
    New York : Cambridge University Press
    Econometric theory 7 (1991), S. 341-368 
    Details
    ISSN: 0266-4666
    Source: Cambridge Journals Digital Archives
    Topics: Economics
    Notes: This paper considers the consistency property of some test statistics based on a time series of data. While the usual consistency criterion is based on keeping the sampling interval fixed, we let the sampling interval take any equispaced path as the sample size increases to infinity. We consider tests of the null hypotheses of the random walk and randomness against positive autocorrelation (stationary or explosive). We show that tests of the unit root hypothesis based on the first-order correlation coefficient of the original data are consistent as long as the span of the data is increasing. Tests of the same hypothesis based on the first-order correlation coefficient of the first-differenced data are consistent against stationary alternatives only if the span is increasing at a rate greater than T½, where T is the sample size. On the other hand, tests of the randomness hypothesis based on the first-order correlation coefficient applied to the original data are consistent as long as the span is not increasing too fast. We provide Monte Carlo evidence on the power, in finite samples, of the tests Studied allowing various combinations of span and sampling frequencies. It is found that the consistency properties summarize well the behavior of the power in finite samples. The power of tests for a unit root is more influenced by the span than the number of observations while tests of randomness are more powerful when a small sampling frequency is available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1017/S0266466600004503
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  • 3
    Electronic Resource
    Electronic Resource
    The HUMP-shaped behavior of macroeconomic fluctuations (1993)
    Springer
    Empirical economics 18 (1993), S. 707-727 
    Details
    ISSN: 1435-8921
    Keywords: Measures of persistence ; unit root ; trend-stationarity ; ARMA models ; non-stationarity ; structural change ; C22 ; E32
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract We analyze the nature of persistence in macroeconomic fluctuations. The current view is that shocks to macroeconomic variables (in particular realGNP) have effects that endure over an indefinite horizon. This conclusion is drawn from the presence of a unit root in the univariate time series representation. Following Perron (1989), we challenge this assessment arguing that most macroeconomic variables are better construed as stationary fluctuations around a breaking trend function. The trend function is linear in time except for a sudden change in its intercept in 1929 (The Great Crash) and a change in slope after 1973 (following the oil price shock). Using a measure of persistence suggested by Cochrane (1988) we find that shocks have small permanent effects, if any. To analyze the effects of shocks at finite horizon, we select a member of theARMA(p, q) class applied to the appropriately detrended series. For the majority of the variables analyzed the implied weights of the moving-average representation have the once familiar humped shape.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205417
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  • 4
    Electronic Resource
    Electronic Resource
    A note on Johansen's cointegration procedure when trends are present (1993)
    Springer
    Empirical economics 18 (1993), S. 777-789 
    Details
    ISSN: 1435-8921
    Keywords: Cointegration ; Vector Autoregressive Models ; Hypothesis Testing ; Unit Roots ; Nonstationary Time Series ; C32
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract This note discusses some issues that arise when Johansen's (1991) framework is used to analyze cointegrating relationships among variables with deterministic linear time trends. We cistinguish “stochastic” and “deterministic” cointegration, arguing that stochastic cointegration is sufficient for the existence of an error correction representation and that it is often the hypothesis of interest in empirical applications. We show that Johansen's (1991) method, which includes only a constant term in the estimated regession system, does not allow for stochastic cointegration. We propose to modify Johansen's method by including a vector of deterministic linear trends in the estimated model. We present tabulated critical values of the maximal eigenvalue and trace statistics appropriate for this case. We discuss the circumstances under which our modification may be useful.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205421
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  • 5
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    Temporal Aggregation and Long Memory for Asset Price Volatility (2020)
    Molecular Diversity Preservation International
    Details
    Publication Date: 2020-08-15
    Description: The effects of temporal aggregation and choice of sampling frequency are of great interest in modeling the dynamics of asset price volatility. We show how the squared low-frequency returns can be expressed in terms of the temporal aggregation of a high-frequency series. Based on the theory of temporal aggregation, we provide the link between the spectral density function of the squared low-frequency returns and that of the squared high-frequency returns. Furthermore, we analyze the properties of the spectral density function of realized volatility series, constructed from squared returns with different frequencies under temporal aggregation. Our theoretical results allow us to explain some findings reported recently and uncover new features of volatility in financial market indices. The theoretical findings are illustrated via the analysis of both low-frequency daily Standard and Poor’s 500 (S&P 500) returns from 1928 to 2011 and high-frequency 1-min S&P 500 returns from 1986 to 2007.
    Print ISSN: 1911-8066
    Electronic ISSN: 1911-8074
    Topics: Economics
    Published by Molecular Diversity Preservation International
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  • 6
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    Testing for a unit root in time series regression (1988)
    Oxford University Press
    Details
    Publication Date: 1988-01-01
    Print ISSN: 0006-3444
    Electronic ISSN: 1464-3510
    Topics: Biology , Mathematics , Medicine
    Published by Oxford University Press
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  • 7
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    Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model (2019)
    Molecular Diversity Preservation International
    Details
    Publication Date: 2019-05-21
    Description: In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients, possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the variance (or in the coefficients). In this note, we provide evidence that such procedures have poor finite sample properties when the changes in the first step are not correctly accounted for. In doing so, we show that testing for changes in the coefficients (or in the variance) ignoring changes in the variance (or in the coefficients) induces size distortions and loss of power. Our results illustrate a need for a joint approach to test for structural changes in both the coefficients and the variance of the errors. We provide some evidence that the procedures suggested by Perron et al. (2019) provide tests with good size and power.
    Electronic ISSN: 2225-1146
    Topics: Economics
    Published by Molecular Diversity Preservation International
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  • 8
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    Unit Roots and Structural Breaks (2017)
    Molecular Diversity Preservation International
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    Publication Date: 2017-05-30
    Electronic ISSN: 2225-1146
    Topics: Economics
    Published by Molecular Diversity Preservation International
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  • 9
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    Fractional Unit Root Tests Allowing for a Structural Change in Trend under Both the Null and Alternative Hypotheses (2017)
    Molecular Diversity Preservation International
    Details
    Publication Date: 2017-01-08
    Electronic ISSN: 2225-1146
    Topics: Economics
    Published by Molecular Diversity Preservation International
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  • 10
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    Statistically derived contributions of diverse human influences to twentieth-century temperature changes (2013)
    Springer Nature
    Details
    Publication Date: 2013-11-10
    Description: The warming of the climate system is unequivocal as evidenced by an increase in global temperatures by 0.8C over the past century. However, the attribution of the observed warming to human activities remains less clear, particularly because of the apparent slow-down in warming since the late 1990s. Here we analyse radiative forcing and temperature time series with state-of-the-art statistical methods to address this question without climate model simulations. We show that long-term trends in total radiative forcing and temperatures have largely been determined by atmospheric greenhouse gas concentrations, and modulated by other radiative factors. We identify a pronounced increase in the growth rates of both temperatures and radiative forcing around 1960, which marks the onset of sustained global warming. Our analyses also reveal a contribution of human interventions to two periods when global warming slowed down. Our statistical analysis suggests that the reduction in the emissions of ozone-depleting substances under the Montreal Protocol, as well as a reduction in methane emissions, contributed to the lower rate of warming since the 1990s. Furthermore, we identify a contribution from the two world wars and the Great Depression to the documented cooling in the mid-twentieth century, through lower carbon dioxide emissions. We conclude that reductions in greenhouse gas emissions are effective in slowing the rate of warming in the short term. © 2013 Macmillan Publishers Limited.
    Print ISSN: 1752-0894
    Electronic ISSN: 1752-0908
    Topics: Geosciences
    Published by Springer Nature
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