Find and Remove Trends

Interactively identify and remove a linear trend in array data with the Find and Remove Trends task in the Live Editor.

Create a vector x containing some fluctuation. Create a plot to visualize the data.

t = 0:8;
trend = 2*t+5;
sig = [0 1 -2 1 0 1 -2 1 0];
data = sig + trend;
plot(t,data)

Add the Find and Remove Trends task to the live script. Because the data has a polynomial trend, choose the Polynomial trend type.

Remove the polynomial trend from the data. Select data as the input data and Detrended data as the output to return. Alternatively, you can use the Output field to return the trend. Select t as the x-axis values associated with the input data. Identify a linear trend by specifying the polynomial type as Linear.

Display the resulting trend and the detrended data in a stacked plot.

Interactively identify and remove a piecewise polynomial trend in array data using the Find and Remove Trends task in the Live Editor.

A polynomial trend is a trend that best describes fluctuating data. A polynomial trend is used when your data both increases and decreases in value, and the degree of the polynomial trend increases as the data fluctuates.

Consider an electrocardiogram (ECG) signal that shows a pattern not intrinsic to the data that must be removed. Load the signal ecgnl using the sample file ecgSignals.mat and plot the signal.

load("ecgSignals.mat","ecgnl")

plot(ecgnl)
title("ECG Signals with Trends")
xlabel("Sample")
ylabel("Voltage (mV)")

Then, eliminate the nonlinear trend. Add the Find and Remove Trends task to the live script. Because the data has a polynomial trend, choose the Polynomial trend type.

Operate on the signal by selecting ecgnl as the input data. Select Detrended data as the output. The default x-axis values are the sample numbers. Because the wander of the heart rhythm does not occur with consistent frequency, identify a piecewise trend by specifying a vector of breakpoints in the sample data. Alternatively, you can select the breakpoints from a plot.

bp = [160 660 1160 1660];

Then, choose a custom polynomial type and specify the polynomial degree as 5. The resulting visualization displays the input data, piecewise polynomial trend, and the data with the trend removed. The detrended data is returned in detrendedData and has the same size as ecgnl. Alternatively, to return the trend, use the Output field.

Interactively decompose array data into its long-term trend, two periodic trends, and remainder using the seasonal trend decomposition using loess (STL) algorithm with the Find and Remove Trends task in the Live Editor.

Create a variable data that contains a long-term trend, two seasonal trends with different periods, and a noise component. Create a plot to visualize the data.

t = (1:200)';
trend = 0.001*(t-100).^2;
period1 = 20;
period2 = 30;
seasonal1 = 2*sin(2*pi*t/period1);
seasonal2 = 0.75*sin(2*pi*t/period2);
noise = 2*(rand(200,1) - 0.5);
data = trend + seasonal1 + seasonal2 + noise;

plot(data)

Add the Find and Remove Trends task to the live script. Because the data has a recurring, periodic trend, choose the Periodic trend type.

Decompose the data into its trend components by selecting data as the input data and All trends as the output to return. Because the periods of the seasonal trends in the data are known, choose the STL algorithm and specify the known period lengths as 20 and 30 data points.

Display the input data and the resulting long-term trend, two periodic trends, and remainder in a stacked plot. The Live Editor task returns the identified trends in arrays longterm and periodic. Alternatively, to return the detrended data, use the Output field to specify which trend types to remove.

Interactively identify and return periodic trends using the singular spectrum analysis (SSA) algorithm with the Find and Remove Trends task in the Live Editor.

Consider a timetable of monthly international airline passenger totals from 1949 to 1960. Load the timetable using the sample file Data_Airline.mat and plot the passenger data.

load("Data_Airline.mat","DataTimeTable");

plot(DataTimeTable,"Time","PSSG")
title("Passenger Data")

Notice that the timetable is irregularly spaced. The Find and Remove Trends task requires that the input timetable is regularly spaced.

isregular(DataTimeTable.Time)

ans = logical
   0

Make the timetable regular by resampling using the Retime Timetable task in the Live Editor. Interpolate the data onto a regular time vector with a time step of 30 days and return the resampled data in a timetable named monthly.

monthly=147×1 timetable
       Time         PSSG 
    ___________    ______

    01-Jan-1949       112
    31-Jan-1949    117.81
    02-Mar-1949     131.9
    01-Apr-1949       129
    01-May-1949       121
    31-May-1949    134.55
    30-Jun-1949    147.57
    30-Jul-1949       148
    29-Aug-1949    137.16
    28-Sep-1949     120.7
    28-Oct-1949    105.94
    27-Nov-1949    116.13
    27-Dec-1949    115.48
    26-Jan-1950    123.87
    25-Feb-1950    138.86
    27-Mar-1950    135.97
      ⋮

isregular(monthly.Time)

ans = logical
   1

The airline passenger data shows an increase in the seasonal variance over time. Because the Find and Remove Trends task analyzes the series using additive decomposition models, apply a log transformation to the data.

monthly.PSSGLog = log(monthly.PSSG);

Then, identify periodic trends in the passenger data by adding the Find and Remove Trends task to the live script. Because the data has a recurring, periodic trend, choose the Periodic trend type.

Operate on the passenger totals by specifying the input data as the PSSGLog variable of monthly. Because the periods of the seasonal trends in the data are unknown, choose the SSA algorithm. Increase the number of periodic trends until the baseline of the remainder is flat.

Display the input data and the resulting long-term trend, four periodic trends, and remainder in a stacked plot. The Live Editor task returns the identified trends in the array trends. Alternatively, to return the detrended data, use the Output field to specify which trend types to remove.