Business Forecasting Free Essay Example, 2250 words

The existence of outliers in the series or incorrect specification in a more complicated model are signified if the forecasts generated under complicated models are less accurate than those under an ARIMA model. No matter what methodology is eventually adopted, effective auto ARIMA modelling capability displays an important role in forecasting (Sowell, 1992). The AR operators are normally placed on the left hand side of the model in almost all time series books using ARIMA models. When a constant term is present in the model, the model expression makes it hard to supply an interpretable meaning. Therefore, it is more advantageous to place the AR operators on the right hand side of the model to make it easy to obtain an interpretable meaning (Brooks, 2008). Aspects of the Model Stationarity of the AR process In the case where previous values of the error term would contain a non-decreasing effect on the current value of the dependent variable, this will suggest that the AR model is not motionless. It would also mean that since the lag length is increasing, the coefficients on the MA process would not turn to a zero. We will write a custom essay sample on Business Forecasting or any topic specifically for you Only $17.96 $11.86/pageorder now The coefficients on the corresponding MA process decrease with lag length resulting in zero, an AR model would be stationary (Barndorff†Nielsen, 2002). AR Process The roots of the distinguishing equation lies outside the unit circle which is greater than 1 is a test for stationarity in an AR model (with p lags), the equation would be (Brooks, 2008): Unit Root One needs to describe as testing for a â€Å"unit root† as it is needed for testing for stationarity for any variable since this is based on this same idea. AR (1) model is the most basic AR model such as the Dickey-Fuller test, on which almost all the tests for stationarity are subjected to. The characteristic equation for unit root test is as follows (Gujarati, 2012) The characteristic equation of (1-z) = 0 along the AR (1) model suggests that the root of z is equal to 1. Rather than outside it, it lies on the unit circle hence one can conclude that this is non-stationary. The potential number of roots increases with the increase in the lags of the AR model. Therefore in case of two lags, the quadratic equation producing 2 roots will be available, and they both need to lie outside the unit circle for the model to be stationary (Brooks, 2008). For an AR(1) process with a constant (ÃŽ ¼) of the unconditional mean, is denoted by (Brooks, 2008): Excluding the constant, variance for an unconditional AR process of order 1 will be (Brooks, 2008): Box-Jenkins Methodology Based on the PACF and ACF as a means of determining the lag lengths of the ARIMA model and the stationarity of the variable in question, this is a method for estimating ARIMA models.