Time Series Models Test And Bootstrap Forecast

Time series analysis is widely used in varies fields such as financial, economic,weather, military and so on. In this paper, ARMA and GARCH, which are most commonlyused in time series are introduced, and give some analysis and research as for the followfinancial data. Random simulation of smooth test for uniformity on the unit internal is alsopresented. The main work is as follows:(1) For the given British-American(B/A) exchange rates, I present model identification,fixed-order, parameter estimation, error checking and prediction of the whole process ofARMA-GARCH hybrid model. As well as the parameter estimation and testing results withNormal distribution, T-distribution and Generalized error distribution errors forARMA(1,1)-GARCH(1,1) model;(2) In this paper we introduce power simulation of the smooth tests, which shows the effectorder of smooth tests against various alternatives does not exist. While for a data set, theeffect order can be determined by applying a sequence of the smooth tests to a particularalternative. The smooth test used in error testing of time series due to the uncertainty of errordistribution, so we need test these k one by one. We refuse the null hypothesis once a k doesnot accept the hypothesis.(3) Give the point forecast of B/A exchange of-sample, and give Bootstrap of-sample internalprediction of the mean and conditional variance of returns data of B/A exchange consideringthe absolutely uncertainty of the real error distribution as well.