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    %% Test Time Series Data for a Unit Root
% This example shows how to test a univariate time series for a unit root.
% It uses wages data (1900-1970) in the manufacturing sector. The series is
% in the Nelson-Plosser data set.
%%
% Load the Nelson-Plosser data. Extract the nominal wages data.

% Copyright 2015 The MathWorks, Inc.

load Data_NelsonPlosser
wages = DataTable.WN;
%%
% Trim the |NaN| values from the series and the corresponding dates (this step
% is optional, since the test ignores |NaN| values).
wDates = dates(isfinite(wages));
wages = wages(isfinite(wages));
%%
% Plot the data to look for trends.
plot(wDates,wages)
title('Wages')
%%
% The plot suggests exponential growth.
%%
% Transform the data using the log function to linearize the series.
logWages = log(wages);
plot(wDates,logWages)
title('Log Wages')
%%
% The data appear to have a linear trend.
%%
% Test the hypothesis that the series is a unit root process with a trend
% (difference stationary), against the alternative that there is no unit
% root (trend stationary).  Set |'lags',[7:2:11]|, as suggested in
% Kwiatkowski et al., 1992.
[h,pValue] = kpsstest(logWages,'lags',[7:2:11])
%%
% |kpsstest| fails to reject the hypothesis that the wages series is
% trend stationary. If the result would have been [1 1 1], the two
% inferences would provide consistent evidence of a unit root. It remains
% unclear whether the data has a unit root. This is a typical result of
% tests on many macroeconomic series.
%%
% The warnings that the test statistic "...is below tabulated critical
% values" does not indicate a problem. |kpsstest| has a limited set of
% calculated critical values. When it calculates a test statistic that is
% outside this range, the test reports the p-value at the appropriate
% endpoint. So, in this case, |pValue| reflects the closest tabulated
% value. When a test statistic lies inside the span of tabulated values,
% |kpsstest| linearly interpolates the p-value.