Xycoon logo
Time Series Analysis
Home    Site Map    Site Search    Xycoon College    Free Online Software    
horizontal divider
vertical whitespace

Time Series Analysis - ARIMA models - Model Checking

[Home] [Up] [Identification] [ARIMA Estimation] [ARIMA Forecasting] [ARIMA Extensions] [ARIMA Checking]

V.I.3 Univariate Stochastic ARIMA Model Checking

The techniques used in model checking are not different from those used in model identification. In fact, the estimated residual series (from an estimated ARIMA model) is analyzed: it is investigated whether an ARMA pattern can be recognized in the residual ACF and PACF. In case the residuals contain an ARMA structure, the model should be modified accordingly: otherwise the assumption that

Time Series Analysis - ARIMA models - Model Checking

is violated.

In order to check whether the ACF and PACF spikes are significantly different from zero, several Chi-square-based tests exist. In the recent literature many likewise, and alternate test procedures have been proposed:


the reversed residuals approach (LAWRANCE and LEWIS 1990);


the score or Lagrange Multiplier tests (LJUNG 1988);


the approximation of simultaneous confidence intervals for the ACF (HOSKING and RAVISHANKER 1990); etc...

Another approach, is to use the standardized cumulative periodogram of the residuals, due to Bartlett.

An unbiased estimate of the cumulative periodogram is given by


Other diagnostic checks could be considered, such as the SMP for residual heteroskedasticity checking, histograms (or suspended root displays; see MILLS 1990) for normality checks, R-square for interpolation performance, the Durbin-Watson statistic for first order autocorrelation, the residual mean and its standard error for testing whether E(e) = 0, runs-tests for autocorrelation, and many others.

vertical whitespace

ARIMA Estimation
ARIMA Forecasting
ARIMA Extensions
ARIMA Checking
horizontal divider
No news at the moment...
horizontal divider

© 2000-2012 All rights reserved. All Photographs (jpg files) are the property of Corel Corporation, Microsoft and their licensors. We acquired a non-transferable license to use these pictures in this website.
The free use of the scientific content in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission.

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically updates the information without notice. However, we make no warranties or representations as to the accuracy or completeness of such information, and it assumes no liability or responsibility for errors or omissions in the content of this web site. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Contributions and Scientific Research: Prof. Dr. E. Borghers, Prof. Dr. P. Wessa
Please, cite this website when used in publications: Xycoon (or Authors), Statistics - Econometrics - Forecasting (Title), Office for Research Development and Education (Publisher), http://www.xycoon.com/ (URL), (access or printout date).

Comments, Feedback, Bugs, Errors | Privacy Policy Web Awards