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...

Monte Carlo simulations are used to compare the power properties of three simple tests for the seasonal differencing filter when the data contain seasonal mean shifts. Overall, the results favour the HEGY–GLN test.  2001 Elsevier Science B.V. All rights reserved.

Maximum likelihood (ML) estimation maximizes the likelihood function and is a celebrated principle in linear regression analysis. Asymptotically, the Cramér-Rao lower bound for the covariance matrix of unbiased estimated parameters is reached by the maximum likelihood estimator. With asymptotic arguments, it has been proved that this principle can also be applied to autoregression and to the mo...

In the ARIMA modeling of business, ̄nancial, and macroeconomic time series, a very important question consists on the determination of the degree of integration of the data under analysis. There are essentially three di®erent approaches to this problem. In the ̄rst approach, the analyst tests for underdi®erencing, i.e., for the existence of one or more autoregressive unit roots, in order to deci...

Accurate estimates of final tracer concentrations guide adjustment of individual species levels so that forward integration of stiff families can proceed at time steps an order of magnitude larger than inherent loss constants. Maintenance of a unified concentration vector in the solver ensures mass conservation. The sequence was perfected by raising the step size upward from 100s in a standard ...

We consider the problem of modeling a long-memory time series using piecewise fractional autoregressive integrated moving average processes. The number as well as the locations of structural break points and the parameters of each regime are assumed to be unknown. A four-step procedure is proposed to find out the break points and to estimate the parameters of each regime. Its effectiveness is s...

Implicit–explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave–slow-wave problems in which the fast wave has relatively low amplitude and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on Adams methods or on backward differenci...

Recent work on nonparametric identification of average partial effects (APEs) from panel data require restrictions on individual or time heterogeneity. Identifying assumptions under the “generalized first-differencing” category, such as time homogeneity (Chernozhukov, Fernandez-Val, Hahn, and Newey, 2013), have testable equality restrictions on the distribution of the outcome variable. This pap...

A coupled system of two singularly perturbed linear reaction–diffusion two-point boundary value problems is examined. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solutions to the system have boundary layers that overlap and interact. The structure of these layers is analysed, and this leads to the constru...

Economic and financial processes are complex and highly nonlinear. However, somewhat surprisingly, linear models like ARMAXGARCH often describe these processes reasonably well. In this paper, we provide a possible explanation for the empirical success of these models. 1 Formulation of the Problem Economic and financial processes are very complex. It is well know that economic and financial proc...