Nonparametric Estimation Of Periodic Time Series With Variable Coefficient Covariates

Time series,which are periodic and susceptible to external factors,are widely found in finance,economy,social science,astronomy and other fields.The influence of external factors on the sequence is not invariable,which requires us to choose a reasonable method to estimate the influence of external factors in real time.At the same time,the period of some time series is unknown,which requires us to first provide a relatively accurate periodic estimation,and then further estimate the influence of periodic series and exogenous factors,so as to predict and test the time series.However,the existing model does not have a good solution to the above problems,so this paper discusses and studies this situation.Since the existence of periodicity in time series may affect the estimation of exogenous component,and the existence of exogenous factors and the changes of their influence also affect the estimation of periodicity,we need an estimation method that can accurately separate periodic and exogenous factors to obtain more accurate estimates.For this problem,time series separation involves two important issues,the first is the selection of decomposition model,and the second is how to estimate the real-time impact of external factors.In the first problem,the classical time series decomposition is to decompose the time series into periodic terms,trend terms,error terms,etc.,which does not involve exogenous components and does not take into account the influence of other factors when estimating the period.While machine learning method takes exogenous variables into account,it is not effective in estimating periodic components.Therefore,for the sequences susceptible to external factors,this paper does not apply the previous model,but decompositions the time series into periodic terms,exogenous variables and error terms,and makes in-depth mining of the decomposed components to obtain more extensive information.The periodicity and the term affected by external factors are modeled and estimated respectively,and then the sum is obtained through the common addition model in time series.In the second problem,based on previous literatures at home and abroad digging out the research on the time series has obvious effects of exogenous factors,previous studies directly by using the methods of regression,and machine learning to such exogenous factors directly into the model,and argues that these exogenous factors influence degree coefficient in the investigation to time average.Through analysis,the influence of these exogenous factors on time series data is not invariable,but varies with time.Therefore,this paper constructs a variable coefficient function for such exogenous factors,and uses a non-parametric method to analyze the influence changes of these exogenous factors,so as to grasp the latest estimation results.Based on the above analysis,this paper aims to construct a periodic sequence model with variable coefficient parameters.The classical time series model is written as a partial linear model.Firstly,B-splines are used to approximate the variable coefficient function of exogenous variables.Combining with the result of approximation,we obtain the estimated result of unknown period by the least square regression with penalty term.At the same time,the estimation results of the periodic term and the influence term of exogenous variables in the decomposition model can be obtained.In chapter 3,the theoretical properties of estimators are also given,including the consistency of periodic estimation,the asymptotic properties of periodic sequence estimation and variable coefficient function estimation.Through the simulation in chapter 4,we demonstrate the superiority of the method in this paper,and obtain the comparison between the results of decomposition estimation in this paper and the results of previous studies.Through the comparison,it is concluded that the method in this paper is more conducive to the estimation of the period of time series,and the model in this paper also captures the basic trend of the variable coefficient function well.Especially under the circumstance of the influence of external factors,the method in this paper still performs well.The fifth chapter,the empirical part of the first to apply this model to January 1998 to September 2018 in Australia travel,decompose the travel periodic sequence estimation,and get the exogenous variables affect the number of tourist variable coefficient estimation results,and found that exogenous factors affect to Macao tourism number change the interpretation of the practical work.It also forecasts the number of tourists to Australia from October 2018 to September 2019.By defining the evaluation index,the prediction effect of this method is evaluated.Then,by decomposing the number of tourists in Hong Kong,this paper compares and evaluates the similarities and differences between the periodic term and the variable coefficient estimation term of inbound tourists in Hong Kong and Macao,showing the practicability of this method.Finally,for the oil price series with unknown cycle,the cycle of crude oil obtained by the method in this paper is about 9 years,and the method in this paper is used to separate the periodic terms.The consistency of the method in this paper is proved to be very good by the residual diagnosis.