Nearly Nonstationary Arma Processes: Second Order Properties
نویسنده
چکیده
Second order properties of nearly nonstationary ARMA processes are investigated in the cases when the autoregressive polynomial equation has (i) a real root close to 1; (ii) a real root close to -1; (iii) a pair of complex roots close to the unit circle. The effect of the closeness to the unit circle of the ARMA poles on its covariance and spectral density functions is considered. The obtained results demonstrate three specific ways of degeneracy of these functions, as the roots tend to I in modulus. As a consequence three different estimates of the ARMA parameters located in the neighbourhood of the border of the stationarity region for ARMA process are derived and their asymptotic distributions are examined.
منابع مشابه
Some problems in the overspeci cation of ARMA and ARIMA processes using ARFIMA models
Nonstationary ARIMA processes and nearly nonstationary ARMA processes, such as autoregressive processes having a root of the AR polynomial close to the unit circle, have sample autocovariance and spectral properties that are, in practice, almost indistinguishable from those of a stationary longmemory process, such as a Fractionally Integrated ARMA (ARFIMA) process. Because of this, model misspe...
متن کاملUnderdifferencing versus Overdifferencing Tests
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...
متن کاملTracking of Nonstationary Eeg with the Roots of Arma Models
The tracking of nonstationary EEG with time-varying ARMA models is discussed. A method for detecting spindles in rat EEG is presented. The method is based on tracking of a single system pole of the ARMA model.
متن کاملCharacterization of the Partial Autocorrelation Function of Nonstationary
The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function is that it is subject to very simple constraints in comparison with the autocovariance function which...
متن کاملOn some probabilistic properties of periodic GARCH processes
This paper examines some probabilistic properties of the class of periodicGARCH processes (PGARCH) which feature periodicity in conditional heteroskedasticity. In these models, the parameters are allowed to switch between different regimes, so that their structure shares many properties with periodic ARMA process (PARMA). We examine the strict and second order periodic stationarities, the exist...
متن کامل