Forecasting Basics: The basic idea behind self-projecting time series forecasting models is to find a mathematical formula that will approximately generate the historical patterns in a time series.
Time Series: A time series is a set of numbers that measures the status of some activity over time. It is the historical record of some activity, with measurements taken at equally spaced intervals (exception: monthly) with a consistency in the activity and the method of measurement.
Approaches to time Series Forecasting: There are two basic approaches to forecasting time series: the self-projecting time series ...view middle of the document...
There are both statistical tests for verifying model validity and statistical measures of forecast uncertainty. In contrast, traditional forecasting models offer a limited number of models relative to the complex behavior of many time series with little in the way of guidelines and statistical tests for verifying the validity of the selected model.
Data: The misuse, misunderstanding, and inaccuracy of forecasts is often the result of not appreciating the nature of the data in hand. The consistency of the data must be insured and it must be clear what the data represents and how it was gathered or calculated. As a rule of thumb, Box-Jenkins requires at least 40 or 50 equally-spaced periods of data. The data must also be edited to deal with extreme or missing values or other distortions through the sue of functions as log or inverse to achieve stabilization.
Preliminary Model Identification Procedure: A preliminary Box-Jenkins analysis with a plot of the initial data should be run as the starting point in determining an appropriate model. The input data must be adjusted to form a stationary series, one whose values vary more or less uniformly about a fixed level over time. Apparent trends can be adjusted by having the model apply a technique of "regular differencing," a process of computing the difference between every two successive values, computing a differenced series which has overall trend behavior removed. If a single differencing does not achieve stationarity, it may be repeated, although rarely if ever, are more than two regular differencings required. Where irregularities in the differenced series continue to be displayed, log or inverse functions can be specified to stabilize the series such that the remaining residual plot displays values approaching zero and without any pattern. This is the error term, equivalent to pure, white noise.
Pure Random Series: On the other hand, if the initial data series displays neither trend nor seasonality and the residual plot shows essentially zero values within a 95% confidence level and these residual values display no pattern, then there is no real-world statistical problem to solve and we go on to other things.
Model Identification Background
Basic Model: With a stationary series in place, a basic model can now be identified. Three basic models exist, AR (autoregressive), MA (moving average) and a combined ARMA in addition to the previously specified RD (regular differencing) combine to provide the available tools. When regular differencing is applied together with AR and MA, they are referred to as ARIMA, with the I indicating "integrated" and referencing the differencing procedure.
Seasonality: In addition to trend, which has now been provided for, stationary series quite commonly display seasonal behavior where a certain basic pattern tends to be repeated at regular seasonal intervals. The seasonal pattern may additionally...