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The '''Hodrick–Prescott filter''' is a mathematical tool used in [[macroeconomics]], especially in [[real business cycle theory]] to separate the cyclical component of a time series from raw data. It is used to obtain a smoothed-curve representation of a [[time series]], one that is more sensitive to long-term than to short-term fluctuations. The adjustment of the sensitivity of the trend to short-term fluctuations is achieved by modifying a multiplier <math>\lambda</math>. The filter was popularized in the field of economics in the 1990s by economists [[Robert J. Hodrick]] and [[Nobel Prize in Economics|Nobel Memorial Prize]] winner [[Edward C. Prescott]].<ref>Hodrick, Robert, and Edward C. Prescott (1997), [http://ideas.repec.org/a/mcb/jmoncb/v29y1997i1p1-16.html "Postwar U.S. Business Cycles: An Empirical Investigation,"] ''Journal of Money, Credit, and Banking'', 29 (1), 1&ndash;16.</ref> However, it was first proposed much earlier by [[E. T. Whittaker]] in 1923.<ref>Whittaker, E. T. (1923):  ''On a new method of graduation'', Proceedings of the Edinburgh Mathematical Association, 78, 81-89 - as quoted in [http://cowles.econ.yale.edu/P/cd/d17b/d1771.pdf Philips 2010]</ref>
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The reasoning for the methodology uses ideas related to the [[decomposition of time series]]. Let <math>y_t\,</math> for <math>t = 1, 2, ..., T\,</math> denote the logarithms of a time series variable. The series <math>y_t\,</math> is made up of a trend component, denoted by <math>\tau\,</math> and a cyclical component, denoted by <math>c\,</math> such that <math>y_t\ = \tau_t\ + c_t\,</math>.<ref>Kim, Hyeongwoo. "[http://business.auburn.edu/~hzk0001/hpfilter.pdf Hodrick–Prescott Filter]" March 12, 2004</ref> Given an adequately chosen, positive value of <math>\lambda</math>, there is a trend component that will solve
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:<math>\min_{\tau}\left(\sum_{t = 1}^T {(y_t - \tau _t )^2 }  + \lambda \sum_{t = 2}^{T - 1} {[(\tau _{t+1}  - \tau _t) - (\tau _t  - \tau _{t - 1} )]^2 }\right).\,</math>
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The first term of the equation is the sum of the squared deviations <math>d_t=y_t-\tau_t</math> which penalizes the cyclical component. The second term is a multiple <math>\lambda</math> of the sum of the squares of the trend component's second differences. This second term penalizes variations in the growth rate of the trend component. The larger the value of <math>\lambda</math>, the higher is the penalty. Hodrick and Prescott suggest 1600 as a value for <math>\lambda</math> for quarterly data. Ravn and Uhlig (2002) state that <math>\lambda</math> should vary by the fourth power of the frequency observation ratio; thus, <math>\lambda</math> should equal 6.25 for annual data and 129,600 for monthly data.<ref>{{cite journal
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  | last1= Ravn
  | first1=Morten
  | last2=Uhlig
  | first2=Harald
  | title=On adjusting the Hodrick–Prescott filter for the frequency of observations
  | journal=The Review of Economics and Statistics
  | year=2002
  | number=2
  | volume=84
  |  pages = 371–375
  | doi=
}}</ref>


==Drawbacks to the H–P filter==
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The Hodrick–Prescott filter will only be optimal{{clarify|date=February 2010|reason=hoe define optimal here}} when:<ref>French, Mark. "[http://www.federalreserve.gov/pubs/feds/2001/200144/200144pap.pdf Estimating changes in trend growth of total factor productivity: Kalman and H–P filters versus a Markov-switching framework]" September 6th, 2001</ref>
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*Data exists in a I(2) trend.
 
**If one-time permanent shocks or split growth rates occur, the filter will generate shifts in the trend that do not actually exist.
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*Noise in data is approximately normally distributed.
 
*Analysis is purely historical and static (closed domain). The filter causes misleading predictions when used dynamically since the algorithm changes (during iteration for minimization) the past state (unlike a [[moving average]]) of the time series to adjust for the current state regardless of the size of <math>\lambda</math> used.
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The standard two-sided HP-filter is non-causal as it is not purely backward looking. Hence, it should not be used when estimating DSGE models based on recursive state-space representations (e.g., likelihood-based methods that make use of the Kalman-Filter). The reason is that the HP-filter uses observations at  <math>t+i, i>0 </math> to construct the current time point  <math>t</math>, while the recursive setting assumes that only current and past states influence the current observation. One way around this is to use the [[one sided HP-filter]].<ref>{{cite journal
  <li>[http://www.dlxjkj.com/bbs/forum.php?mod=viewthread&tid=1652220 http://www.dlxjkj.com/bbs/forum.php?mod=viewthread&tid=1652220]</li>
   | last1= Stock
 
  | last2=Watson
</ul>
  | title=Forecasting Inflation
  | journal=Journal of Monetary Economics
  | year=1999
  | volume=44
  | pages = 293-335
  | doi=
}}</ref>
 
==See also==
 
* [[Kalman filter]]
* [[Band-pass filter]]
 
==References==
 
<references/>
 
==External links==
*[http://www.web-reg.de/hp_addin.html ''a freeware Hodrick Prescott Excel Add-In'']
*[http://dge.repec.org/codes/prescott/hpfilter.for ''Prescott's Fortran code'']
*[http://www.mathworks.com/matlabcentral/fileexchange/3972-hodrick-prescott-filter ''Hodrick–Prescott filter in matlab'']
*[http://cran.r-project.org/web/packages/mFilter/mFilter.pdf ''HP filter in R with package 'mFilter''']
*[http://jaac.wz.cz/hponlineapp.php ''HP filter online app'']
 
{{DEFAULTSORT:Hodrick-Prescott Filter}}
[[Category:Macroeconomics]]
[[Category:Time series analysis]]

Latest revision as of 21:41, 14 December 2014

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It's time again to close the publication on another successful Dollars from Heaven campaign.

Nonetheless while the 19th annual strategy, which helps feed the fewer fortunate by fundraising for the Christmas Cheer Board with Winnipeg and Winnipeg Harvest, is closing, volunteers at the Cheer Board are hard at work counting the gold and silver coins that are the backbone in our fundraiser.

This year, it was some sort of bittersweet campaign because in the middle of the idea, our fundraiser's founder, former Absolutely free Press editor Mike Ward, died. With gratitude plus honour, I saw lots of people Mike's friends, but also people affected by the fundraiser he started give in his memory.

Thanks check out many people who helped with a campaign, and if I ignore to mention some, it's not since i don't value their contribution.

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Because of students in the Louis Riel School Split and their parents, teachers and also division administrators, led by way of superintendent Duane Brothers. The coins people collected are still being counted, however it looks like they raised nearly $10,000 for their own Nickels for LRSD campaign, which flows into our fundraiser.

On account of the volunteers at the Cheer Board and also Harvest for helping get your bins out to their regions and for going out regularly so that you can retrieve the coins.

Thanks to all the Walmarts and their employees, together with Portage Place, Jensen Nursery and Desjardins Memorial service Chapel, for Nike Free Run Sale Uk serving as go Cheap Oakley Sunglasses Uk away locations this year.

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And the biggest thanks is always to you, the people who contribute money, donate dollar bills or perhaps write cheques to our campaign. Most people couldn't do it without people.

I must confess we have been thus busy raising money we've not had a chance to take a close look at the suggestions for a new marketing campaign name. This was sparked from the federal government's move to stop minting pennies Adidas Jeremy Scott Wings last year. We'll inform you about the result as soon as we can.

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Jackson seemed to be part of the Neil Munro Intern Directors Project for the Shaw Festival last season along with assisted on such stage productions as Misalliance, His Girl Feb 5th and Hedda Gabler.

The former actress started off her career appearing within Manitoba Theatre Centre 1986 production of Brighton Shore Memoirs. Next season she is engaged to direct Carolyn Gray modern Cheap Nike Shoes funny inspired by Moliere The Miser inside co production with Cinema Projects Manitoba, as well as helm RMTC centrepiece output of The Seagull for next The month of january ChekhovFest.

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