使用matlab的一个实例（时间序列）.rar_time series_时间序列_时间序列matlab

Air Passenger Data

First we create an array of monthly counts of airline passengers, measured in thousands, for the

period January 1949 through Decemter 1960.

% 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960

y = [112 115 145 171 196 204 242 284 315 340 360 417 % Jan

118 126 150 180 196 188 233 277 301 318 342 391 % Feb

132 141 178 193 236 235 267 317 356 362 406 419 % Mar

129 135 163 181 235 227 269 313 348 348 396 461 % Apr

121 125 172 183 229 234 270 318 355 363 420 472 % May

118 140 166 194 201 229 278 306 336 337 405 432 ]; % Dec

% Source:

% Hyndman, R.J., Time Series Data Library,

% http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/.

% Copied in October, 2005.

Create Time Series Object

When we create a time series object, we can keep the time information along with the data values.

We have monthly data, so we create an array of dates and use it along with the Y data to create the

time series object.

yr = repmat((1949:1960),12,1);

Examine Trend and Seasonality

This series seems to have a strong seasonal component, with a trend that may be linear or

quadratic. Furthermore, the magnitude of the seasonal variation increases as the general level

increases. Perhaps a log transformation would make the seasonal variation be more constant. First

we'll change the axis scale.

set(gca,'YScale','log');

It appears that it would be easier to model the seasonal component on the log scale. We'll create

a new time series with a log transformation.

tscol = addts(tscol, log(ts.data), 'logAirlinePassengers');

logts = tscol.logAirlinePassengers;

Now let's plot the yearly averages, with monthly deviations superimposed. We want to see if the

data as a matrix in a month-by-year format, it's more convenient to operate on the original data

x = yr + (mo-1)/12;

plot(x,ymean,'b-',x,ymean+ydiff,'r-')

title('Monthly variation within year')

xlabel('Year')

Now let's reverse the years and months, and try to see if the year-to-year trend is constant for

each month.

set(gca,'Position',[0.13 0.58 0.78 0.34]);

subplot(2,1,2);

t = reshape(datenum(time),12,12);

mmean = repmat(mean(logy,2),1,12);