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Estimation of Olympic gold medals for Italy

Alex Teymouri

Posted 8 months ago

Dear All, According to the data list, Italy has won 10 and 2 Olympic gold medals in 2020 and 2022. I tried to estimate the number of gold medals for these two years using a simple time series model. Is the method correct? I appreciate your time. data = {{1952., 8.}, {1956., 8.}, {1960., 13.}, {1964., 10.}, {1968., 3.}, {1972., 5.}, {1976., 2.}, {1980., 8.}, {1984., 14.}, {1988., 6.}, {1992., 6.}, {1994., 7.}, {1996., 13.}, {1998., 2.}, {2000., 13.}, {2002., 4.}, {2004., 10.}, {2006., 5.}, {2008., 8.}, {2010., 1.}, {2012., 8.}, {2014., 0.}, {2016., 8.}, {2018., 3.}, {2020., 10.}, {2022., 2.}}; year = Map[#[[1]] &, data]; gold = Map[#[[2]] &, data]; Length[gold]; train = Take[gold, 24]; Length[train]; tsm = TimeSeriesModelFit[train]; tsm["BestFit"]; for = TimeSeriesForecast[tsm, {2}];

Dear All,

According to the data list, Italy has won 10 and 2 Olympic gold medals in 2020 and 2022. I tried to estimate the number of gold medals for these two years using a simple time series model. Is the method correct? I appreciate your time.

data = {{1952., 8.}, {1956., 8.}, {1960., 13.}, {1964., 10.}, {1968., 
    3.}, {1972., 5.}, {1976., 2.}, {1980., 8.}, {1984., 14.}, {1988., 
    6.}, {1992., 6.}, {1994., 7.}, {1996., 13.}, {1998., 2.}, {2000., 
    13.}, {2002., 4.}, {2004., 10.}, {2006., 5.}, {2008., 8.}, {2010.,
     1.}, {2012., 8.}, {2014., 0.}, {2016., 8.}, {2018., 3.}, {2020., 
    10.}, {2022., 2.}};

year = Map[#[[1]] &, data];

gold = Map[#[[2]] &, data];

Length[gold];

train = Take[gold, 24];

Length[train];

tsm = TimeSeriesModelFit[train];

tsm["BestFit"];

for = TimeSeriesForecast[tsm, {2}];

POSTED BY: Alex Teymouri

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Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 8 months ago

Hi Alex, I guess you do not need `TimeSeriesForecast[]` as `TimeSeriesModel` does already give a forecast. If I really had to, I would do it like so - but under normal circumstances I would not even try! I do not believe that those simple values of the past contain information about the future. data = {{1952., 8.}, {1956., 8.}, {1960., 13.}, {1964., 10.}, {1968., 3.}, {1972., 5.}, {1976., 2.}, {1980., 8.}, {1984., 14.}, {1988., 6.}, {1992., 6.}, {1994., 7.}, {1996., 13.}, {1998., 2.}, {2000., 13.}, {2002., 4.}, {2004., 10.}, {2006., 5.}, {2008., 8.}, {2010., 1.}, {2012., 8.}, {2014., 0.}, {2016., 8.}, {2018., 3.}, {2020., 10.}, {2022., 2.}}; dateGold = TimeSeries[{DateObject[{Round@#1}, "Year"], #2} & @@@ data]; train = TimeSeriesWindow[dateGold, {DateObject[{1952}, "Year"], DateObject[{2018}, "Year"]}]; tsm = Quiet@TimeSeriesModelFit[train]; DateListPlot[{tsm["TemporalData"], {#, Around[tsm[#], tsm["PredictionLimits"][#] - tsm[#]]} & /@ {DateObject[{2020}, "Year"], DateObject[{2022}, "Year"]}}, ImageSize -> Large, GridLines -> Automatic] As you see the "forecast" is basically the mean value - with huge error bars, as there is no trend in the data. If you do give your data some trend, then one can see that this approach is trying the best it can do: data = MapIndexed[{#1[[1]], #1[[2]] + First[#2]} &, data] Does that help? Regards -- Henrik

Hi Alex,

I guess you do not need TimeSeriesForecast[] as TimeSeriesModel does already give a forecast. If I really had to, I would do it like so - but under normal circumstances I would not even try! I do not believe that those simple values of the past contain information about the future.

data = {{1952., 8.}, {1956., 8.}, {1960., 13.}, {1964., 10.}, {1968., 
    3.}, {1972., 5.}, {1976., 2.}, {1980., 8.}, {1984., 14.}, {1988., 
    6.}, {1992., 6.}, {1994., 7.}, {1996., 13.}, {1998., 2.}, {2000., 
    13.}, {2002., 4.}, {2004., 10.}, {2006., 5.}, {2008., 8.}, {2010.,
     1.}, {2012., 8.}, {2014., 0.}, {2016., 8.}, {2018., 3.}, {2020., 
    10.}, {2022., 2.}};

dateGold = TimeSeries[{DateObject[{Round@#1}, "Year"], #2} & @@@ data];
train = TimeSeriesWindow[dateGold, {DateObject[{1952}, "Year"], DateObject[{2018}, "Year"]}];
tsm = Quiet@TimeSeriesModelFit[train];
DateListPlot[{tsm["TemporalData"], {#, Around[tsm[#], tsm["PredictionLimits"][#] - tsm[#]]} & /@ {DateObject[{2020}, "Year"], DateObject[{2022}, "Year"]}}, ImageSize -> Large, GridLines -> Automatic]

enter image description here

As you see the "forecast" is basically the mean value - with huge error bars, as there is no trend in the data. If you do give your data some trend, then one can see that this approach is trying the best it can do:

data = MapIndexed[{#1[[1]], #1[[2]] + First[#2]} &, data]

enter image description here

Does that help? Regards -- Henrik

POSTED BY: Henrik Schachner

M.A. Ghorbani

M.A. Ghorbani, University of Tabriz

Posted 8 months ago

Hi Henrik, I tried to use Markov process with SequencePredict[] for 2020 as follows: In[13]:= SequencePredict[{train}, {{}}] Out[13]= {8.} What do you think about this approach? Is acceptable? Thank you for your help.

POSTED BY: M.A. Ghorbani

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 8 months ago

Hello Prof. Ghorbani, I guess for `SequencePredict[]` you rather need a bunch of sequences ... Regards -- Henrik

POSTED BY: Henrik Schachner

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