Parameter Estimation for Periodically Stationary Time Series
نویسندگان
چکیده
The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule-Walker estimates.
منابع مشابه
On the Spectral Density Estimation of Periodically Correlated (Cyclostationary) Time Series
We consider the estimation of the spectral density matrix of a periodically correlated (PC) time series (also known as cyclostationary time series). We use the well known relation between the spectral density matrix of a periodically correlated time series and a stationary vector time series (Gladyshev, 1961). The spectral matrix of the stationary vector time series is estimated using the eigen...
متن کاملTREND-CYCLE ESTIMATION USING FUZZY TRANSFORM OF HIGHER DEGREE
In this paper, we provide theoretical justification for the application of higher degree fuzzy transform in time series analysis. Under the assumption that a time series can be additively decomposed into a trend-cycle, a seasonal component and a random noise, we demonstrate that the higher degree fuzzy transform technique can be used for the estimation of the trend-cycle, which is one of the ba...
متن کاملSpectral Estimation of Stationary Time Series: Recent Developments
Spectral analysis considers the problem of determining (the art of recovering) the spectral content (i.e., the distribution of power over frequency) of a stationary time series from a finite set of measurements, by means of either nonparametric or parametric techniques. This paper introduces the spectral analysis problem, motivates the definition of power spectral density functions, and reviews...
متن کاملInnovations Algorithm for Periodically Stationary Time Series
Periodic ARMA, or PARMA, time series are used to model periodically stationary time series. In this paper we develop the innovations algorithm for periodically stationary processes. We then show how the algorithm can be used to obtain parameter estimates for the PARMA model. These estimates are proven to be weakly consistent for PARMA processes whose underlying noise sequence has either finite ...
متن کاملA new adaptive exponential smoothing method for non-stationary time series with level shifts
Simple exponential smoothing (SES) methods are the most commonly used methods in forecasting and time series analysis. However, they are generally insensitive to non-stationary structural events such as level shifts, ramp shifts, and spikes or impulses. Similar to that of outliers in stationary time series, these non-stationary events will lead to increased level of errors in the forecasting pr...
متن کامل