A study on diagnostic techniques applied to the residuals at identification of the time series models

In this thesis study, it is firstly presented the features and types of the time series data, the aims of the time series analysis and the techniques used in this analysis and is made the consructional classification of the time series data and its models. It is discussed the abstract properties of ARIMA and SARIMA from the nonstationary models, and AR, MA and ARMA from the stationary time series models. It is presented the problem of which one can be chosen among the proper time series models for a time series data and some basic tecniques used for this purpose in the selection of the model. To check the suitability of the chosen model, it is discussed the diagnostic check methods carried out the residuals and it is shown how to do the applications. As a model application, it has been used the price per barrel of oil for EURO region taken from European Central Bank data. In this applicalitons, it has been fitted a time series model which is suitable for oil series and in order to test to fit the model it has been given place checking of the residual autocorrelation, checking of the square of the residuals, Portmanto lack-of-fit test, Durbin-Watson test, Lagranges multiplier tests , and the results of these tests has been interpreted.Keywords: Time Series Models, Model Selection Criteria, Model Diagnostic Checking.