The
Limits of the| by Andrew Rowson, supervised by Prof. A.R.Champneys | ||
| Home A Dismal Science Economic TheoryClassical Neoclassical Keynesian Cycles and Crises Measuring cycles Economic Time Series Data Processing Spectral Analysis Cycle Modelling Kaldor's Trade Cycle A Kaldorian model Conclusion Full Report |
Data Processing
Parametric methods A trend is loosely defined as a long term change in the mean. It evolves slowly and has to be removed to reveal the faster cyclical elements. Seasonal effects are faster still and would also need to be removed, if the data wasn't already adjusted, so that only the intermediate cycles remained. A simple method for removing a trend is to fit a low order polynomial curve to the data using the method of least squares. The difference between the two gives a third series referred to as 'residuals' that give the local fluctuations. 
UK GDP with 4th order polynomial fitted Nonarametric methods For more control over the filtering procedure, a linear filter such as a moving average may be preferred. By increasing the the span of the sampling 'window' the degree of smoothing can be controlled. A narrow window follows the data closely and tends to emphasise shorter cycles while a large window does not remove the trend. In practice a window of around 25 terms was found to be a reasonable compromise for a dataset with an overall length of 192. 
UK GDP with moving average filter applied A rectangular window is not particularly sensitive to changes but the problem is reduced by using more sophisticated filters such as the Hodrick-Prescott filter which is more sensitive to long term than short term fluctuations and has become a favourite among economic researchers. Although in the following instance the results are fairly similar, this is not true in general. 
UK GDP with Hodrick-Prescott filter applied |
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