Time Series Analysis - Essay Example

This presentation can be used to model many time series procedures and as an identifying tool of a model in the auto- covariance function. ARIMA (1, 1, 1) vs. ARIMA (0, 1, 2) The ARIMA models as observed help in fitting provided data with the condition that the data is not stationary. There are many models of the ARIMA but in our case we will discuss ARIMA (1, 1, 1) and ARIMA (0, 1, 2) looking at the trees presented with relevant discussion about them. ARIMA (1, 1, 1) is also referred to as the mixed model, this is due to the fact that as depicted from the graphs by the 9 trees, we see he features of both the autoregressive and moving average models brought together to form a single model.

ARIMA (1, 1, 1) which is non-linear in nature can be used to define the data set that shows unpredictable bursts, outliers and extremely flat stretches at quite irregular time intervals (Cromwell, 1994). The data may have been collected from the economic unit variables like those for the pricing of items like onion\ns and their variations in the market. The research may have also been conducted in conjunction of other extreme models like the Gaussian Mixture Transition (GMTD), Mixed Autoregressive (MAR) as well as MAR-Autoregressive Conditional Heteroscedastic (MAR-ARCH), the differences are determined and graphs depicting differences depicted as in the Trees 1-9 ARIMA (1, 1, 1).

The graphs represented by the numbers and the progress show an eliminating trend with quite seasonal fluctuations as shown from the fittings in the Box-Jenkins hence residual series (Vandaele, 1983). The figures and graphs from the trees 1-9 are employed in testing for non-seasonality or seasonality in the respective stochastic trends with the appropriate filters being used through the Box-Jenkins model examining the same. Trees 1-9 show us that the Lagrange multiplier (LM) is used to define ARCH while the value parameters are quantified using Expectation maximization (EM) (Cromwell, 1994).

The figures, graphs and diagrams show a case where out of sample forecasting the first and the second steps and there after a naive approach devised in forming a conclusion. With ARIMA (0, 1, 2) on the other hand, we ask ourselves how the data would look like, and the pattern that would exist. As shown by the trees 1-9, the data is non-stationery as show by the linear filters and transfer functions indicating smoothing potentials. From the tools, that is the plots of data and both the PACF and ACF, the evidence for the claims above are vividly observable by the graphical trends and the trends by ACF of residuals, standardized residuals and p values for Ljung box (Cromwell, 1994).

The models of ARIMA (0, 1, 2) as opposed to that of the ARIMA (1, 1, 1) has its parameters estimated using a statistical software with the outputs indicated on the representation showing outputs for parameter estimates, test statistics, goodness of fits, diagnostics and residuals. All the above parameters are highly non-stationery as well (Vandaele, 1983). In both the models, it is to be determined whether they fit data by correctly extracting all information and ensuring that residuals as shown are a white noise.

The key measures in both the models are the ACF, standardized