TS sproj 041705221319041125051405220819
[NEAS: This candidate uses monthly border crossings in Texas. The choice is excellent, for several reasons.
The time series shows strong seasonal, trend, and autoregressive effects. Analyzing the seasonality, trend, and correlograms provides a good student project, even if no ARIMA model gives white noise residuals.
Border crossing at highest each December and second highest each July, as the candidate expects. The candidate suggests holiday shopping for December and summer vacations for July. The high December crossing may also reflect family visits for Christmas, and the high July crossing may reflect summer work harvesting crops.
The low months each year are January and June. These low months probably reflect the same phenomena. Many people cross the border in December for shopping or to visit relatives for Christmas. People who might cross in January are likely to come in December instead.
Statistical results are persuasive when they are well justified. This write-up is well done.
~ If your time series is seasonal, identify the months in your graphs. The candidate shows the high border crossing in December and July with arrows in the graphs.
~ If you can justify the seasonality, include a sentence of a paragraph doing so. The cause of the seasonality may help you decide what type of seasonally adjusted is best.
~ Construct the correlogram. Annual seasonality causes a high negative sample autocorrelation at lag 6. A 12 month seasonal parameter eliminates the negative sample autocorrelation at lag 6.
Many border crossings are the same people coming back year after year.
Illustration: A person might come each December for holiday shopping or each July for a job harvesting crops. This is an ideal scenario for a 12 month seasonal autoregressive parameter.
Contrast this process with religious pilgrimages. A pilgrimage has different people each year. A person who visits Mecca one year may not make the trip again, or may return only ten years later. The process is more likely to be white noise or a random walk, after adjusting for seasonality and trend.
Many exogenous effects occur gradually over the years. Relations between countries take years to improve or deteriorate, and border crossings increase or decrease over long periods. Relations between countries are not easily modeled as by-products of other events, so they are often best modeled by ARIMA processes. Sometimes elections affect relations among countries, but most changes are long-term social phenomena.
Economic conditions greatly affect border crossing, and these evolve slowly over time.
Illustration: Migrant labor from Mexico encourages U.S. farmers to plant labor intensive crops, and labor intensive crops on U.S. farms encourages migrant labor from Mexico.
Illustration: Mexicans crossing the border for holiday shopping in December encourages U.S. retailers to build stores near the border with goods geared to Mexican shoppers. The new stores further encourage Mexican shoppers to cross the border.
These relations are best modeled by ARIMA processes.]