Editing Forecasting (section)

===Relational methods===

Some forecasting methods try to identify the underlying factors that might influence the variable that is being forecast. For example, including information about climate patterns might improve the ability of a model to predict umbrella sales. Forecasting models often take account of regular seasonal variations. In addition to climate, such variations can also be due to holidays and customs: for example, one might predict that sales of college football apparel will be higher during the football season than during the off season.<ref name="NahmiasOlsen2015">{{cite book|author1=Steven Nahmias|author2=Tava Lennon Olsen|title=Production and Operations Analysis: Seventh Edition|url=https://books.google.com/books?id=SIsoBgAAQBAJ&q=forecasting|date=15 January 2015|publisher=Waveland Press|isbn=978-1-4786-2824-8}}</ref>

Several informal methods used in causal forecasting do not rely solely on the output of mathematical [[algorithm]]s, but instead use the judgment of the forecaster. Some forecasts take account of past relationships between variables: if one variable has, for example, been approximately linearly related to another for a long period of time, it may be appropriate to extrapolate such a relationship into the future, without necessarily understanding the reasons for the relationship.

Causal methods include:

*[[Regression analysis]] includes a large group of methods for predicting future values of a variable using information about other variables. These methods include both [[parametric statistics|parametric]] (linear or non-linear) and [[Nonparametric regression|non-parametric]] techniques.
*[[ARMAX|Autoregressive moving average with exogenous inputs (ARMAX)]]<ref>{{cite book|last=Ellis|first=Kimberly|title=Production Planning and Inventory Control Virginia Tech|year=2008|publisher=McGraw Hill|isbn=978-0-390-87106-0}}</ref>

Quantitative forecasting models are often judged against each other by comparing their in-sample or out-of-sample [[mean square error]], although some researchers have advised against this.<ref>{{cite journal | url = http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/armstrong-errormeasures-empirical.pdf | title = Error Measures For Generalizing About Forecasting Methods: Empirical Comparisons | author = [[J. Scott Armstrong]] and Fred Collopy | journal = [[International Journal of Forecasting]] | volume = 8 | pages = 69–80 | year = 1992 | doi = 10.1016/0169-2070(92)90008-w | url-status = dead | archive-url = https://web.archive.org/web/20120206182744/http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/armstrong-errormeasures-empirical.pdf | archive-date = 2012-02-06 | citeseerx = 10.1.1.423.508 }}</ref> Different forecasting approaches have different levels of accuracy. For example, it was found in one context that [[GMDH]] has higher forecasting accuracy than traditional ARIMA.<ref>16. Li, Rita Yi Man, Fong, S., Chong, W.S. (2017) [http://www.tandfonline.com/eprint/pgjIcAMrJBP4WcHIZH7F/full Forecasting the REITs and stock indices: Group Method of Data Handling Neural Network approach], Pacific Rim Property Research Journal, 23(2), 1-38</ref>