prediction errors) Autoregressive integrated moving average (ARIMA) (ARMA on the period-to-period change in the forecast variable) e.g. Box–Jenkins Seasonal ARIMA or SARIMA or ARIMARCH, Extrapolation Linear prediction Trend estimation (predicting the variable as a linear or polynomial function of time) Growth curve (statistics) Recurrent neural network 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. Several informal methods used in causal forecasting do not rely solely on the output of mathematical algorithms, 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 (linear or non-linear) and non-parametric techniques. Autoregressive moving average with exogenous inputs (ARMAX) 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. 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. Judgmental methods Judgmental forecasting methods incorporate intuitive judgement, opinions and subjective probability estimates. Judgmental forecasting is used in cases where there is a lack of historical data or during completely new and unique market conditions. Judgmental methods include: Composite forecasts Cooke's method Delphi method Forecast by analogy Scenario building Statistical surveys Technology forecasting Artificial intelligence methods Artificial neural networks Group method of data handling Support vector machines Often these are done today by specialized programs loosely labeled Data mining Machine learning Pattern recognition Geometric extrapolation with error prediction Can be created with 3 points of a sequence and the "moment" or "index". This type of extrapolation has