Nonlinear cross-spectrum analysis via the local Gaussian correlation

Spectrum analysis can detect frequency related structures in a time series $\{Y_t\}_{t\in\mathbb{Z}}$, 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 $f_{v}(\omega)$, based on the local Gaussian autocorrelations $\rho_v(\omega)$ 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 $f(\omega)$. The local Gaussian approach in this paper is extended to a local Gaussian cross-spectrum $f_{kl:v}(\omega)$ for multivariate time series. The local cross-spectrum $f_{kl:v}(\omega)$ has the desirable property that it coincides with the ordinary cross-spectrum $f_{kl}(\omega)$ for Gaussian time series, which implies that $f_{kl:v}(\omega)$ 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

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.

Contours of Cognition

This thesis concerns the nature of cognition. It posits that cognitive processes primarily are means to maintain allostasis in organisms whose ecological niches require movement to approach food-resources and avoid predation. Hence triggering, or motivation, of behaviours are a consequence of prediction errors from the body resulting from biological variables moving away from homeostasis. Depending on circumstance and the nature of the particulars of the ecological niche, an organism may require the ability to find the way to a goal-site containing food or water, perceive its surroundings in order to trigger allostatic behaviour, make choices and priorities, and predict outcomes. Hence, cognition is situated in a larger context of staying alive, but efforts are also made to zoom in on exactly how some important cognitive processes may plausibly work, on the level of neural units and networks. These processes include visual perception, spatial cognition, predictive simulation processes (intelligence), and familiarity based trust, as well as reflection, decision-making, and memory

Estimation in nonlinear time series models

A general framework for analyzing estimates in nonlinear time series is developed. General conditions for strong consistency and asymptotic normality are derived both for conditional least squares and maximum likelihood types estimates. Ergodie strictly stationary processes are studied in the first part and certain nonstationary processes in the last part of the paper. Examples are taken from most of the usual classes of nonlinear time series models

Parameter estimation in a spatial unit root autoregressive model

Spatial unilateral autoregressive model $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\gamma X_{k-1,\ell-1}+\epsilon_{k,\ell}$ is investigated in the unit root case, that is when the parameters are on the boundary of the domain of stability that forms a tetrahedron with vertices $(1,1,-1), \ (1,-1,1),\ (-1,1,1)$and$(-1,-1,-1)$. It is shown that the limiting distribution of the least squares estimator of the parameters is normal and the rate of convergence is$n$when the parameters are in the faces or on the edges of the tetrahedron, while on the vertices the rate is$n^{3/2}$.Comment: 47 pages, 1 figur