www.gusucode.com > econ 案例源码程序 matlab代码 > econ/NonseasonalandSeasonalDifferencingExample.m
%% Nonseasonal and Seasonal Differencing % This example shows how to apply both nonseasonal and seasonal differencing % using lag operator polynomial objects. The time series is monthly international % airline passenger counts from 1949 to 1960. % Copyright 2015 The MathWorks, Inc. %% % Load the airline data set (|Data_Airline.mat|). load(fullfile(matlabroot,'examples','econ','Data_Airline.mat')) y = log(Data); T = length(y); figure plot(y) h1 = gca; h1.XLim = [0,T]; h1.XTick = [1:12:T]; h1.XTickLabel = datestr(dates(1:12:T),10); title 'Log Airline Passenger Counts'; %% % The data shows a linear trend and a seasonal component with periodicity 12. %% % Take the first difference to address the linear trend, and the 12th difference % to address the periodicity. If $y_t$ is the series to be transformed, % the transformation is % % $$\Delta\Delta_{12}y_t=(1-L)(1-L^{12})y_t,$$ % % where $\Delta$ denotes the difference operator, and $L$ denotes the lag operator. % % Create the lag operator polynomials $1 - L$ and $1 - L^{12}$. % Then, multiply them to get the desired lag operator polynomial. D1 = LagOp({1 -1},'Lags',[0,1]); D12 = LagOp({1 -1},'Lags',[0,12]); D = D1*D12 %% % The first polynomial, $1 - L$, has coefficient 1 at lag 0 and coefficient % -1 at lag 1. The seasonal differencing polynomial, $1 - L^{12}$, % has coefficient 1 at lag 0, and -1 at lag 12. The product of these polynomials % is % % $$(1-L)(1-L^{12})=1-L-L^{12}+L^{13},$$ % %% % which has coefficient 1 at lags 0 and 13, and coefficient -1 at lags 1 % and 12. %% % Filter the data with differencing polynomial |D| to get the nonseasonally % and seasonally differenced series. dY = filter(D,y); length(y) - length(dY) %% % The filtered series is 13 observations shorter than the original series. % This is due to applying a degree 13 polynomial filter. %% figure plot(14:T,dY) h2 = gca; h2.XLim = [0,T]; h2.XTick = [1:12:T]; h2.XTickLabel = datestr(dates(1:12:T),10); axis tight; title 'Differenced Log Airline Passenger Counts'; %% % The differenced series has neither the trend nor seasonal component exhibited % by the original series.