Non-period Of Economic Time Series Analysis And Applications

The analysis of time-series is important for economic statistics and for- casting. At present, most datum are concerned with periodic economic time- series, but few discussed unperiodic economic time-series. However, unperi odic economic time-series exists popularly.For example,in 1997,a company records the number of the workers at the end of each month; And there are average number time-series and relative number time-series. For example, the average salary of each year is average time-series and salary exponent is relative time- series. In this paper ,the author discussed the stationary time-piont economic AR(p) model which is observed every equal time. Their number characters, initial identification of AR(p) model, estimation for Autoregressive model and forcasting are discussed. In order to express simply, time-point econom- ic time-series which is observed every equal time is defined as time-point economic time-series. Because it is no point in adding up the number of time-point economic time- series, it is not suitable to use the old formula, which are redifined in this paper. The first section mainly discussed the basic definition and number char- acter and the property of the sample character of the time-point economic time-series. 1)The meaning of the sample is defined as (0.1). and autocovariance function as (0.2). The autocovariance function of the sample and the partial autocorrelation function have been correspondingly changed. 2)The properties of the sample character a) is the unbiased and consistented estimation of jt. b)Autocovariance function of the sample (k and autocorrelation function of the sample 13k are asymptotic unbiased estimation of tk and Pk. and sat- isfied formula (0.3) and (0.4). c)Let{xt} be AR(p) model.{a} be the white noise series. Eat 0, Ea and satistied formula and when k its partial autocorrelation function is asymptotic normality The second section is the initial identification of AR model, that is, ini- tially identify the type of the sample model, according to the principle that the partial autocorrelation function of AR model is truncated. Then we detect the order of the model. The third section is the estimation of parameter. Three ways, Yule- Walker estimation, Least Squared estimation and Maximum Likelyhood es- timation are used. a)The Yule-Walker estimation of AR(P) model M F, in which, P, is the autocorrelation function matrix of the sample, R ( )The Least Squared estimation of AR(p) model LS [FL(p)DRL(p) in which, PL(P) satisfied formula (0.7).satisfied formula (0.8). c)The Maximum Likelyhood estimation of AR(p) model in which D and d satisfied formula (0.9). satisfied formula (0.10). Compared with, when n is a large number, three estimations are almost the same. But Y-W estimation is easy to be calculated, so we always use Y-W estimation generally. The forth section is the specification of AR(p) model. In this section AIIC criterion is mainly used to specificate. The fifth section is the forcasting of AR(p) series. a)Let (Xt, tzvxt be a random vector of Ex ?0.Yar(xt) 00,x1(T) be the optmium forcasting of(xt,...,xt.N) ,so b)The forcasting fomula of AR(p) series which is gotten step by step. This formula is (0.11). c) The direct forcasting formula of AR(p) series for AR(p) series, the optimum linear forecasting of r step isin which /3 j 1,2,...