336 research outputs found
Nonlinear cross-spectrum analysis via the local Gaussian correlation
Spectrum analysis can detect frequency related structures in a time series
, but may in general be an inadequate tool if
asymmetries or other nonlinear phenomena are present. This limitation is a
consequence of the way the spectrum is based on the second order moments (auto
and cross-covariances), and alternative approaches to spectrum analysis have
thus been investigated based on other measures of dependence. One such approach
was developed for univariate time series in Jordanger and Tj{\o}stheim (2017),
where it was seen that a local Gaussian auto-spectrum , based on
the local Gaussian autocorrelations from Tj{\o}stheim and
Hufthammer (2013), could detect local structures in time series that looked
like white noise when investigated by the ordinary auto-spectrum .
The local Gaussian approach in this paper is extended to a local Gaussian
cross-spectrum for multivariate time series. The local
cross-spectrum has the desirable property that it coincides
with the ordinary cross-spectrum for Gaussian time series,
which implies that can be used to detect non-Gaussian traits
in the time series under investigation. In particular: If the ordinary spectrum
is flat, then peaks and troughs of the local Gaussian spectrum can indicate
nonlinear traits, which potentially might discover local periodic phenomena
that goes undetected in an ordinary spectral analysis.Comment: 41 pages, 12 figure
Nonlinear spectral analysis: A local Gaussian approach
The spectral distribution of a stationary time series
can be used to investigate whether or not periodic
structures are present in , but has some
limitations due to its dependence on the autocovariances . For
example, can not distinguish white i.i.d. noise from GARCH-type
models (whose terms are dependent, but uncorrelated), which implies that
can be an inadequate tool when contains
asymmetries and nonlinear dependencies.
Asymmetries between the upper and lower tails of a time series can be
investigated by means of the local Gaussian autocorrelations introduced in
Tj{\o}stheim and Hufthammer (2013), and these local measures of dependence can
be used to construct the local Gaussian spectral density presented in this
paper. A key feature of the new local spectral density is that it coincides
with for Gaussian time series, which implies that it can be used to
detect non-Gaussian traits in the time series under investigation. In
particular, if is flat, then peaks and troughs of the new local
spectral density can indicate nonlinear traits, which potentially might
discover local periodic phenomena that remain undetected in an ordinary
spectral analysis.Comment: Version 4: Major revision from version 3, with new theory/figures.
135 pages (main part 32 + appendices 103), 11 + 16 figure
Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series
This paper establishes a suite of uniform consistency results for nonparametric kernel density and regression estimators when the time series regressors concerned are nonstationary null-recurrent Markov chains. Under suitable conditions, certain rates of convergence are also obtained for the proposed estimators. Our results can be viewed as an extension of some well-known uniform consistency results for the stationary time series case to the nonstationary time series case.β-null recurrent Markov chain, nonparametric estimation, rate of convergence, uniform consistency
Investment under price uncertainty : an empirical study of the Norwegian petroleum industry
Investments are based on expectations of future profits. The common perception of the investment and uncertainty relationship is that increased uncertainty reduces willingness to invest. Uncertainty is here defined as deviation from the expected outcome. In uncertain conditions, it may be difficult to establish a clear profit expectation. However, from the early development of investment theory the sign has been debated. Uncertainty can also be exploited for profit seeking and the sign may therefore be positive. Petroleum extraction is a complicated, slow and expensive process. Historically petroleum prices have been quite volatile, and it is a major uncertainty factor for petroleum producers. The forward looking nature of investment behavior creates several issues for investment theories and empirical modeling. Expectations of return and uncertainty are unobserved and challenging to quantify. When controlling for dynamic panel bias I find a negative relationship between investment and price uncertainty. If price uncertainty increases, investors on the Norwegian continental shelf are more likely to postpone or drop new investments
Estimation in threshold autoregressive models with a stationary and a unit root regime
This paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models have basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result. This paper proposes a parameter estimation method for such nonlinear threshold autoregressive models using the theory of null recurrent Markov chains. Under certain assumptions, we show that the ordinary least squares (OLS) estimators of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is asymptotically proportional to n-1/4, whereas it is n-1 in the nonstationary regime. The proposed theory and estimation method are illustrated by both simulated data and a real data example.Autoregressive process; null-recurrent process; semiparametric model; threshold time series; unit root structure.
Poisson Autoregression
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of the asymptotic covariance, which is used in the simulations and the analysis of some transaction data. Our approach to verifying geometric ergodicity proceeds via Markov theory and irreducibility. Finding transparent conditions for proving ergodicity turns out to be a delicate problem in the original model formulation. This problem is circumvented by allowing a perturbation of the model. We show that as the perturbations can be chosen to be arbitrarily small, the differences between the perturbed and non-perturbed versions vanish as far as the asymptotic distribution of the parameter estimates is concerned.generalized linear models; non-canonical link function; count data; Poisson regression; likelihood; geometric ergodicity; integer GARCH; observation driven models; asymptotic theory
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