This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE, and some M-type estimators. As an application, we verify the a...

Abstract Evapotranspiration (ET) is an important process in the hydrological cycle and needs to be accurately quantified for proper irrigation scheduling and optimal water resources systems operation. The time variant characteristics of ET necessitate the need for forecasting ET. In this paper, two techniques, namely a seasonal ARIMA model and Winter's exponential smoothing model, have been inv...

With the increasing competition in the telecommunications industry, the operators try their best to increase telecom income via various measures, one of which is to set an amount of income as a goal to make the encouragement. Since accurate forecast of income plays an important role in income target setting, this paper builds a time series Autoregressive Integrated Moving Average Model (ARIMA) ...

and Applied Analysis 3 is the order of regular differences and φ(B) and θ(B) are, respectively, defined as follows φ (B) = 1 − φ 1 B − φ 2 B 2 − ⋅ ⋅ ⋅ − φ p B p θ (B) = 1 − θ 1 B − θ 2 B 2 − ⋅ ⋅ ⋅ − θ q B q . (5) Random errors, ε t , are assumed to be independently and identically distributed with a mean of zero and a constant variance of σ, and the roots of φ(x) = 0 and θ(x) = 0 all lie outsid...

We investigate changes in the time series characteristics of postwar U.S. inflation. In a model-based analysis the conditional mean of inflation is specified by a long memory autoregressive fractionally integrated moving average process and the conditional variance is modelled by a stochastic volatility process. We develop a Monte Carlo maximum likelihood method to obtain efficient estimates of...

in recent years, various time series models have been proposed for financial markets forecasting. in each case, the accuracy of time series forecasting models are fundamental to make decision and hence the research for improving the effectiveness of forecasting models have been curried on. many researchers have compared different time series models together in order to determine more efficient ...

2 1 1 =0 | | d t t t p p q q d d k k t () () ()(1) () = () (0) () () (1) (1) = () ())(+ 1) () () 0 5 1. Fractionally integrated timeseries and ARFIMA modelling 1 This presentation of ARFIMA modelling draws heavily from Baum and Wiggins (2000). The model of an autoregressive fractionally integrated moving average process of a timeseries of order , denoted by ARFIMA , with mean , may be written u...