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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.
Cointegration is a crucial concept in time series analysis, particularly when dealing with variables that exhibit trends, such as macroeconomic data. In an influential paper, [1] Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends.
For example, time series are usually decomposed into: , the trend component at time t, which reflects the long-term progression of the series (secular variation). A trend exists when there is a persistent increasing or decreasing direction in the data. The trend component does not have to be linear. [1]
In order to still use the Box–Jenkins approach, one could difference the series and then estimate models such as ARIMA, given that many commonly used time series (e.g. in economics) appear to be stationary in first differences. Forecasts from such a model will still reflect cycles and seasonality that are present in the data.
Time series datasets can also have fewer relationships between data entries in different tables and don't require indefinite storage of entries. [6] The unique properties of time series datasets mean that time series databases can provide significant improvements in storage space and performance over general purpose databases. [6]
The most important structured finite distributed lag model is the Almon lag model. [3] This model allows the data to determine the shape of the lag structure, but the researcher must specify the maximum lag length; an incorrectly specified maximum lag length can distort the shape of the estimated lag structure as well as the cumulative effect ...
In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. [ 1 ] [ 2 ] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.
For example, in economics a regression to explain and predict money demand (how much people choose to hold in the form of the most liquid assets) could be conducted with either cross-sectional or time series data. A cross-sectional regression would have as each data point an observation on a particular individual's money holdings, income, and ...