Moving average model

Autoregressive Integrated Moving Average Model (ARIMA) ... 

A general approach was developed by G.E.P. Box and G.M. Jenkins (S) which combines these various methods into an analysis which permits choice of the most appropriate model, checks the forecast precision, and allows for interpretation. The Box-Jenkins analysis is an autoregressive integrated moving average model (ARIMA). This approach, as implemented in the MINITAB computer program is one used for the analyses reported here. 

NARMA Modelling. The NARMA (Non-Linear AutoRegressive Moving Average) model was introduced by Leontaritis and Billings [Leontaritis and Billings, 1985] and defined by ... 

Durbin, 1959] Durbin, J. (1959). Efficient estimation of parameters in moving-average models. Biometrika, 46 306-316. 

A special model from this type (autoregression with an explanatory variable), an autoregression model combined with a moving average model was applied by VAN STRA-TEN and KOUWENHOVEN [1991] to the time dependence of dissolved oxygen in lakes. 

ARIMA connects both autoregressive and moving average models and includes integrating effects, e.g. trends or seasonal effects. 

First an ARMA (autoregressive moving average) model will be explained without taking into account trends and seasonal effects in order to get a better understanding of the method. 

AutoRegressive Moving Average model with eXogenous inputs (ARMAX). If the same denominator is used for G and H... 

Liu W.S. 2005. The study of Shanghai stock price index based on Grey Theory and Autiregressive integrated moving average models. Master dissertation. HoHai University, Nan Jing. 

Moving-Average Model in this model, all polynomials except the Bq(z )-polynomial are assumed to have zero order. This gives a model of the form... 

It is called a moving-average model, since it computes the (weighted) average of the past random values. Eq. (5.30) can be written as... 

For the analysis of time series models, two concepts need to be introduced causality and invertibility. A process is said to be causal, if and only if, the current value of the process can be determined solely using past or current values of the process. This means that no unavailable, future values of the process are required. A process is said to be causal if and only if all roots of the denominator (i.e. the A-polynomials) lie inside the unit circle in the complex domain, that is, z < 1. Under such circumstances, a causal process is also stationary. Furthermore, for a causal process, the infinite-order moving-average model will converge to a finite value. 

Autoregressive, moving-average model, ARMA(p, q) S(z-i) A combination of the MA and AR graphs from which an estimate of the orders can be obtained. ... 

The moving averaging model, as shown in the example in Table 4.3, uses the average of the past period data in a time series to forecast future activities. In another simple example, assume the sales of the last 4 months of a mobile handset is 10,000, 12,000, 11,500 and 13,000. Then using a 4-month moving average, the forecast for the fifth month would be the average of the past 4 months, that is (10,000 +12,000 +11,500 +13,000)74 or 11,625. 

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