Inference of nonlinear panel time series modelling with application to climate financial analysis

Abstract

This thesis aims at developing proper threshold panel time series modelling approaches applicable to analysis of climate financial problems. More specifically, we are concerned with the problems of estimation and determining the number of threshold parameters efficiently for nonlinear threshold panel time series models with cross-sectional dependence so that we can study the impact of extreme climate or weather, such as heavy downpours and heatwaves, on a stock market.

With the increasing concerns about climate change, there have been a number of studies, in the literature, of the weather effects on the financial markets in the financial journals. However, these studies are based on linear model time series or panel data analysis, and hence the nonlinear effects of a climate or weather variable are unable to be identified and modelled well. With this situation taken into account, we therefore propose to explore the nonlinear relationship between a climate variable such as precipitation and stock returns. By nonparametric analysis of panel stocks in the FTSE100, we first demonstrate why using threshold panel time series model that may characterise the rainfall having a significant impact on the stock market. The analysis results suggest different amounts of rainfall have diverse effects on the stocks in the London Stock Exchange market, which provide a novel insight into the relationship between financial market and weather.

The idea of threshold effect has been popular in nonlinear time series analysis. Although this idea has been extended to panel data analysis, it basically assumes cross-sectional independence, which cannot facilitate the climate financial analysis of the shocking effect of extreme climate or weather on the stock prices or returns that are actually cross-sectionally dependent in a stock market. We, therefore, propose considering panel threshold time series regression where the processes including both regressors and error terms are allowed to be cross-sectionally dependent. In theory, we have established the asymptotic distribution of the proposed least squares based estimators under the time series length T and cross-section size n tending to infinity. The estimated coefficients are shown to be asymptotically normal with convergence rate of root-nT and asymptotic variance characterised by cross-sectional dependence, which is different from those obtained under cross-sectional independence assumptions in the literature. The asymptotic distribution for the estimators of the threshold parameters is highly non-standard. Moreover, differently from the relevant studies in the literature, we also allow the threshold effects diminishing at different rates of T and n in temporal and cross-sectional directions. Monte Carlo simulations are conducted to demonstrate the finite sample performance of the proposed estimators. Especially, the simulations further suggest that the estimated asymptotic variance ignoring cross-sectional dependence may lead to inaccurate inference, with spurious significance incurred for the estimated parameters. An empirical application to climate financial analysis is also investigated and it concludes that the heavy rainfall has a strongly negative impact on the stock market.

Another important problem arising from panel threshold time series regression analysis is how to determine the number of threshold parameters, especially considering cross-sectional dependence. The existing method suggests using the test statistics by bootstrap but it may only work well under cross-sectional independent conditions owing to potential issues with bootstrap for cross-sectional and time series dependence. In this thesis we consider the estimation and inference of threshold panel time series model via adaptive group fused Lasso letting selection of the thresholds and estimation of the models be done in a simultaneous data-driven manner. Under the assumption of both regressors and error terms allowed to be cross-sectionally dependent, we show that with probability tending to one, the suggested Lasso estimation can correctly determine the number of the thresholds and estimate the panel threshold regression parameters consistently. Monte Carlo simulations demonstrate the Lasso estimation working well in the finite samples. In particular, we further compare it with the bootstrap test statistics and it concludes that the proposed Lasso estimation works better to select threshold parameters under the cross- sectional dependent conditions. We then apply our proposed method to the cli- mate financial problems and find multiple threshold parameters in our model.

This thesis is mainly concerned with the statistical inference for nonlinear panel time series model analysis in theory. On the empirical side, the proposed non-linear panel time series methods can be applied widely to real data analysis, especially, to deal with the strong dependence in most climate, economic and financial data. In view of the popularity of spatio-temporal panel data analysis, it also has the great potential of extending the overall ideas of this thesis to spatio-temporal panel modelling and empirical applications following the research of this thesis.

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Identifiers

ORCID for Zudi Lu: orcid.org/0000-0003-0893-832X

ORCID for Maria Kyriakou: orcid.org/0000-0001-7996-2015

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