Background

The purpose of this analysis is to utilize the US Census Bureau X-13ARIMA-SEATS software in R using the seasonal package and conduct time series modeling with seasonal adjustment.

Data

Tourism statistics on visitor arrivals by air were collected from the State of Hawaii Department of Business, Economic Development & Tourism (a.k.a. “DBEDT”) website. The timeframe of the data spans from 1990 to 2015 and was updated quarterly for a total of 102 observations.

Visitor arrival by air

There was an increase of 1,460,141 (or 21.72 percent change) total visitor arrivals to Hawaii since 1990, which included both domestic and international sources.

Autocorrelation function & partial correlation function

The four figures below represent the visitor arrival data. The autocorrelation function and partial autocorrelation function show that correlation gradually falls as lagged values increase, suggesting that an autoregressive model may help to capture the structuce of this time series.

Structure

Multiplicative decomposition was deemed appropriate because both seasonal and irregular variations were evident. After separating seasonal effects, trend, and noise, two stark periods of decline were evident in the time series. A reasoning for these periods of decline may be due to US recession.

Seasonal adjusted time series

Easter holiday

Unlike fixed holidays such as Christmas which occurs on every December 24 on the Gregorian calendar, moving holidays like Easter can have a potential incluence as it occurs in different quarters. Using the genhol function can help to generate Easter holidays that can then be controlled in the time series analysis.

## 
## Call:
## seas(x = ts.tourism, xreg = ts.easter, regression.usertype = "holiday")
## 
## Coefficients:
##                    Estimate   Std. Error z value             Pr(>|z|)    
## ts.easter        23977.3048   11089.2939    2.16                0.031 *  
## AO1991.1       -229689.6350   37987.1923   -6.05         0.0000000015 ***
## AO2001.4       -217678.4690   36156.8033   -6.02         0.0000000017 ***
## MA-Seasonal-04       0.9086       0.0531   17.11 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## SEATS adj.  ARIMA: (0 1 0)(0 1 1)  Obs.: 102  Transform: none
## AICc: 2.4e+03, BIC: 2.41e+03  QS (no seasonality in final):   0  
## Box-Ljung (no autocorr.): 21.6   Shapiro (normality): 0.974 *

Seasonally adjusted

The figure below represents the seasonally adjusted time series while controlling for holiday effects and additive outliers at both in the first quarter of 1991 and fourth quarter of 2001.

Forecast

Forecast looks optimistic for the next few years (maybe too good) and reflects DBEDT’s projected visitor arrivals (as of 10/10/2015). I have attached a screen shot of DBEDT’s projected visitor arrivals below for historic purposes.