Time series models autoregressive

An autoregressive time series model (16) seems to be less suitable for cumulative distribution data. This technique is primarily designed for finding trends and/or cycles for data recorded in a time sequence, under the null-hypothesis that the sequence has no effect. 

Comparing this with equation (3) shows that this can be considered as the output of a first order transfer function in response to a random input sequence. More generally, most stochastic disturbances can be modelled by a general autoregressive-integrated moving-average (ARIMA) time series model of order (p,d,q), that is,... 

The effects of autocorrelation on monitoring charts have also been reported by other researchers for Shewhart [186] and CUSUM [343, 6] charts. Modification of the control limits of monitoring charts by assuming that the process can be represented by an autoregressive time series model (see Section 4.4 for terminology) of order 1 or 2, and use of recursive Kalman filter techniques for eliminating autocorrelation from process data have also been proposed... 

The d3Tiamic response of e k) can be expressed as an autoregressive moving average (ARMA) model or a moving average (MA) time series model ... 

V Haggan and T Ozaki. Modeling nonlinear random vibrations using an amplitude dependent autoregressive time series model. Biometri-ka, 68 186-196, 1981. 

The mapping of the upper-trunk posture considers the above-lesion EMG signal, dented as y(k), to satisfy a pure autoregressive (AR) time-series model [7,29] ... 

The most general, time series model called a seasonal, autoregressive, integrated, moving-average (SARIMA) model of order (p, d, q) x (P, D, 2) has the form... 

The autoregressive, moving-average process denoted as ARMA(p, q) is one of the most common times series models that can be used. It has the general form given as... 

In this section, we present an iterative algorithm in the spirit of the generalized least squares approach (Goodwin and Payne, 1977), for simultaneous estimation of an FSF process model and an autoregressive (AR) noise model. The unique features of our algorithm are the application of the PRESS statistic introduced in Chapter 3 for both process and noise model structure selection to ensure whiteness of the residuals, and the use of covariance matrix information to derive statistical confidence bounds for the final process step response estimates. An important assumption in this algorithm is that the noise term k) can be described by an AR time series model given by... 

Table 17.2 gives important time-series models that are commonly encountered in industrial process control, including statistical process control applications (see Chapter 21). Stationary disturbance models (a) and (b) have a fixed mean that is, the sums of deviations above and below the line are equal to zero, but case (a) rarely occurs in industrial processes. Nonstationary disturbance models (c) and (d) do not have a fixed mean but are drifting in nature. Case (c), so-called random walk behavior, is often used to describe stock market index patterns. Case (b) is called an autoregressive... 

When experimental data are collected over time or distance there is always a chance of having autocorrelated residuals. Box et al. (1994) provide an extensive treatment of correlated disturbances in discrete time models. The structure of the disturbance term is often moving average or autoregressive models. Detection of autocorrelation in the residuals can be established either from a time series plot of the residuals versus time (or experiment number) or from a lag plot. If we can see a pattern in the residuals over time, it probably means that there is correlation between the disturbances. 

Hurvich, C. and C. L. Tsai. A Corrected Akaike Information Criterion for Vector Autoregressive Model Selection. J Time Series Anal 14, 271-279 (1993). 

A model which has found application in many areas of time series processing, including audio restoration (see sections 4.3 and 4.7), is the autoregressive (AR) or allpole model (see Box and Jenkins [Box and Jenkins, 1970], Priestley [Priestley, 1981] and also Makhoul [Makhoul, 1975] for an introduction to linear predictive analysis) in which the current value of a signal is represented as a weighted sum of P previous signal values and a white noise term ... 

The specification of ARIMA models is very expensive for the operator who analyzes time series. The first phase is the estimation of the order of three inherent processes, autoregression, integration, and moving average. 

The measurement at time t plus the time lag r is predictable on the basis of the autocorrelation coefficient, r(r), and the y value at time t. Here, e represents the random error. Note that this is a very simple model. Good predictions can only be expected for time series that really obey this simple autoregressive model. 

This section describes the class of the most common ARMA models and some of their extensions. The term ARMA combines both basic types of time-dependencies, the autoregressive (AR) model and the moving average (MA) model. Suppose a time series y = collected over T periods with zero mean. Autoregressive dependency means that any observation yt depends on previous observations yt-i of this time series with i = 1,. ..,p such that... 

In this section, we summarize an inventory model for collaborative forecasting studied in Aviv (2002a). In Aviv s model, the demand follows an autoregressive statistical time-series of order 1, as follows ... 

Although this model is very simple, it has the beneficial property that the estimation of its parameters can be performed using least-squares analysis. In many respects, this model is very similar to the autoregressive model previously considered for time series analysis. 

C. G. Soares and C. Cimha, Bivariate autoregressive models for the time series of significant wave height and mean period. Coast. Eng. 40, 297-311 (2000). 

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