Forecasting The Temperature Data:

This paper aims at describing the intraday temperature variations which is a challenging task in modern econometrics and environmetrics. Having a high-frequency data, we separate the dynamics within a day and over days. Three main models have been considered in our study. As the benchmark we employ a simple truncated Fourier series with autocorrelated residuals. The second model uses the functional data analysis, and is called the shape invariant model (SIM). The third one is the dynamic semiparametric factor model (DSFM). In this work we discuss rises and pitfalls of all the methods and compare their in- and out-of-sample performances.

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Localising Temperature Risk:

On the temperature derivative market, modelling temperature volatility is an important issue for pricing and hedging. In order to apply the pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern. The object of this research is to estimate this heteroscedastic function so that, after scale normalisation, a pure standardised Gaussian variable appears. Earlier works investigated temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the variance process well. Therefore, we consider a local adaptive modelling approach to find, at each time point, an optimal smoothing parameter to locally estimate the seasonality and volatility. Our approach provides a more flexible and accurate fitting procedure for localised temperature risk by achieving nearly normal risk factors. We also employ our model to forecast the temperature in different cities and compare it to a model developed in Campbell and Deibol (2005).