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Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modelled as a stochastic process.
A time series database is a software system that is optimized for storing and serving time series through associated pairs of time(s) and value(s). [1] In some fields, time series may be called profiles, curves, traces or trends. [ 2 ]
Time series models are a subset of machine learning that utilize time series in order to understand and forecast data using past values. A time series is the sequence of a variable's value over equally spaced periods, such as years or quarters in business applications. [11]
Overview of a data-modeling context: Data model is based on Data, Data relationship, Data semantic and Data constraint. A data model provides the details of information to be stored, and is of primary use when the final product is the generation of computer software code for an application or the preparation of a functional specification to aid a computer software make-or-buy decision.
In statistics and econometrics, a distributed lag model is a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable. [1] [2]
Forecasts from such a model will still reflect cycles and seasonality that are present in the data. However, any information about long-run adjustments that the data in levels may contain is omitted and longer term forecasts will be unreliable. This led Sargan (1964) to develop the ECM methodology, which retains the level information. [4] [5]
The CRAN task view on Time Series contains links to most of these. Mathematica has a complete library of time series functions including ARMA. [11] MATLAB includes functions such as arma, ar and arx to estimate autoregressive, exogenous autoregressive and ARMAX models. See System Identification Toolbox and Econometrics Toolbox for details.
An additive model would be used when the variations around the trend do not vary with the level of the time series whereas a multiplicative model would be appropriate if the trend is proportional to the level of the time series. [3] Sometimes the trend and cyclical components are grouped into one, called the trend-cycle component.