Remove Linear Trends from Timetable Data

This example shows how to remove a linear trend from daily closing stock prices in a timetable to emphasize the price fluctuations about the overall increase. If the data does have a trend, detrending it forces its mean to zero and reduces overall variation. The example simulates stock price fluctuations using a distribution taken from the gallery function.

Create a simulated timetable containing the daily price of a stock.

t = 0:300;
D = days(t);
dailyFluct = randn(size(t));
price = cumsum(dailyFluct) + 20 + t/100;
tt = timetable(D',price',VariableNames="StockPrice");

Find the average daily price of a stock.

mean(tt.StockPrice)

ans = 28.2260

Plot and label the data. Notice the systematic increase in the stock prices.

plot(tt,"Time","StockPrice");
legend("Original Data","Location","northwest");
xlabel("Time (days)");
ylabel("Stock Price (dollars)");

Apply detrend, which performs a linear fit to the stock prices, removes the trend, and appends the detrended data to the input timetable.

tt = detrend(tt,ReplaceValues=false);

Compute the trend line by subtracting the detrended data from the input data.

trend = tt.StockPrice - tt.StockPrice_detrended;
tt = addvars(tt,trend,NewVariableNames="Trend")

tt=301×3 timetable
     Time      StockPrice    StockPrice_detrended    Trend 
    _______    __________    ____________________    ______

    0 days       20.538            -14.588           35.126
    1 day        22.382            -12.698            35.08
    2 days       20.133            -14.901           35.034
    3 days       21.005            -13.983           34.988
    4 days       21.334            -13.608           34.942
    5 days       20.036             -14.86           34.896
    6 days       19.612            -15.238            34.85
    7 days       19.965            -14.839           34.804
    8 days       23.553            -11.204           34.758
    9 days       26.333            -8.3791           34.712
    10 days      24.993            -9.6729           34.666
    11 days      28.038             -6.582            34.62
    12 days      28.773            -5.8006           34.574
    13 days       28.72            -5.8077           34.528
    14 days      29.445            -5.0369           34.482
    15 days       29.25            -5.1859           34.436
      ⋮

Find the average of the detrended data.

mean(tt.Trend)

ans = 28.2260

As expected, the detrended data has a mean very close to 0.

Display the results by adding the trend line, the detrended data, and its mean to the graph.

plot(tt,"StockPrice")
hold on
plot(tt,"Trend")
plot(tt,"StockPrice_detrended")
plot(tt.Time,zeros(size(t)))
legend("Original Data","Trend","Detrended Data",...
       "Mean of Detrended Data","Location","northwest")
xlabel("Time (days)"); 
ylabel("Stock Price (dollars)");