Research On Prewhitening Modeling Method For Temperature Time Series

In recent years,great interests in the implications of greenhouse gases or global warming on the environment have led to a large amount of studies of temperature time series and predicting the future temperatures.The temperature time series have a significant upward trend and seasonal characteristics.With the occurrence of heat wave phenomenon and extreme weather,the temperature time series showed significant heavy tail phenomenon.In the analysis of temperature time series,researchers aim to model strong periodicities,such as the annual and daily cycles.The process by which an important cyclic fluctuation is removed from a time series is known as prewhitening.Prewhitening is the most commonly used procedure to eliminate the effect of serial correlation in trend analysis.It also efficiently removes a significant trend.In this thesis,we model maximum temperature time series using prewhitening.There are some missing data because the time span is large.We use the interpolation method to replace the missing data.Then,the Mann-Kendall test is used to identify an underlying trend.Hence,we consider the maximum temperature as three steps namely trend,auto-regressive moving average(ARMA)part and heavy tailed residuals.In the first step,we remove a linear or non-linear trend based on the statistic significant.The second step,we model the dependence structure by the ARMA model of orders p and q to in which are determined by the Akaike information criteria and Bayesian information criterion,white noise is justified by the Ljung-Box test.Then,we analyze the heavy tailed characteristic of the white noise residuals obtained by the prewhitening method.Compared with the original temperature observation series and the traditional autoregressive moving average model,it can be found that the prewhitening modeling method has obvious advantages in removing the significant trend of time series and dependence structure.Modeling of heavy tail requires another statistical tools.In Chapter 3,we generate the seasonal time series and the heavy tailed time series separately.The heavy tailed time series include heavy tailed time series on one side and heavy tailed time series on both sides.We use the prewhitening modeling method and ARMA method to model the seasonal time series and the heavy tail time series separately.Then,we analyze the trend and heavy tailed characteristic.We can find that the prewhitening method has a significant advantage in removing the trend and dependence structure.At last,we consider the trend,ARMA model and residuals together to forecast future temperatures using the ordinary least square method,Newton-Raphson method and resampling.The resampling method includes common sampling and moving-block sampling.There are three forecast methods including FC method,FCP method and FCP method.The FCPMB method is more stable.But the FCP method has a better performance in the real data.The analysis of CET data provides an evidence for these conclusions.