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In time series analysis, a fan chart is a chart that joins a simple line chart for observed past data, by showing ranges for possible values of future data together with a line showing a central estimate or most likely value for the future outcomes. As predictions become increasingly uncertain the further into the future one goes, these ...
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]
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor.
Forecasting is the process of making predictions based on past and present data. Later these can be compared with what actually happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results creating a variance actual analysis.
A working paper by Robert J. Hodrick titled "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data" [10] examines whether the proposed alternative approach of James D. Hamilton is actually better than the HP filter at extracting the cyclical component of several simulated time series calibrated to approximate U.S. real GDP ...
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and wavelet analysis; the latter include auto-correlation and cross-correlation analysis.
Probabilistic forecasting summarizes what is known about, or opinions about, future events. In contrast to single-valued forecasts (such as forecasting that the maximum temperature at a given site on a given day will be 23 degrees Celsius, or that the result in a given football match will be a no-score draw), probabilistic forecasts assign a probability to each of a number of different ...