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 ...

1 Short-term Traffic Flow Forecasting (STFF), the process of predicting future traffic conditions 2 based on historical and real-time observations is an essential aspect of Intelligent Transportation 3 Systems (ITS). The existing well-known algorithms used for STFF include time-series analysis 4 based techniques, among which the seasonal Autoregressive Moving Average (ARMA) model 5 is one of th...

The objective of this paper is to develop a novel wind speed forecasting technique, which produces more accurate prediction. The Wavelet Transform (WT) along with the Auto Regressive Moving Average (ARMA) is chosen to form a hybrid whose combination is expected to give minimum Mean Absolute Prediction Error (MAPE). A simulation study has been conducted by comparing the forecasting results using...

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between 'input' and 'output' time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modelin...

This paper addresses model-based analysis of string instrument sounds. In particular, it reviews the application of autoregressive (AR) modeling to sound analysis/synthesis purposes. Moreover, a frequency-zooming autoregressive moving average (FZ-ARMA) modeling scheme is described. The performance of the FZ-ARMA method on modeling the modal behavior of isolated groups of resonance frequencies i...

A powerful parametric spectral estimation technique, 2D-ARMA (Auto Regressive Moving Average) modeling, has been applied to contrast transfer function (CTF) detection in electron microscopy. Parametric techniques such as AR (auto regressive) and ARMA models allow a more exact determination of the CTF than traditional methods based only on the Fourier Transform (FT). Previous works revealed that...

In this paper we derive (weak) consistency and the asymptotic distribution of pseudo maximum likelihood estimates for multiple frequency I(1) processes. By multiple frequency I(1) processes we denote processes with unit roots at arbitrary points on the unit circle with the integration orders corresponding to these unit roots all equal to 1. The parameters corresponding to the cointegrating spac...

This paper presents an improvement of hybrid of nonlinear autoregressive with exogenous input (NARX) and autoregressive moving average (ARMA) for long-term machine state forecasting based on vibration data. In this study, vibration data is considered as a combination of two components which are deterministic data and error. The deterministic component may describe the degradation index of machi...

Abstract Spectral analysis of the Greenland Ice Sheet Project 2 (GISP2) δ 18 O record has been interpreted to show a 1/(1470 yr) spectral peak that is highly statistically significant ( p < 0.01). The presence such peak, if accurate, provides an important clue about mechanisms controlling glacial climate. As standard, however, statistical significance was judged relative null model, H 0 , co...

Time-series Autoregressive Moving Average (ARMA) models were employed to model tree crown profiles for two California hardwood species (blue oak and interior live oak). There are three major components of these models: a polynomial trend, an ARMA model, and unaccounted for variation. The polynomial trend was used to achieve a stationary series. For these crown profiles, the use of a quadratic t...