Table 6.
SARIMAX/(E)GARCH models of monthly visitor arrivals by air transport to New Zealand (January 1993‒;December 2013).
| Explanatory variables | Australia |
Canada |
China |
Germany |
Japan |
South Korea |
United Kingdom |
United States |
|---|---|---|---|---|---|---|---|---|
| SARIMAX/EGARCH |
SARIMAX/EGARCH |
SARIMAX/EGARCH |
SARIMAX/EGARCH |
SARIMAX/EGARCH |
SARIMAX/EGARCH |
SARIMAX/EGARCH |
SARIMAX/GARCH |
|
| Mean Equation | ||||||||
| Trend† | −0.152 (−1.03) | 0.017*** (3.86) | −0.124 (−1.24) | −0.067** (−2.53) | 0.017 (1.23) | −0.021 (−0.27) | −0.117** (−2.15) | −0.009 (−0.17) |
| Δln(GDP per capita) | – | 0.101 (0.24) | – | −0.723 (−1.43) | – | – | – | – |
| Δln(GDP per capita(-1)) | 0.264 (0.45) | – | −0.176 (−0.67) | – | 0.005 (0.03) | 1.473*** (4.36) | −0.03 (−0.08) | −0.154 (−0.21) |
| Δln(bilateral trade volumes(-1)) | 0.081* (1.81) | 0.079*** (2.66) | −0.069 (−0.56) | 0.130** (2.04) | 0.177* (1.82) | −0.018 (−0.34) | 0.194*** (2.64) | 0.004 (0.11) |
| ΔExchange rate | −0.054 (−0.36) | 0.027 (0.18) | 0.028 (1.08) | 0.148 (1.02) | 0.002 (1.29) | −0.001 (−1.47) | 0.210 (0.78) | −0.231 (−1.64) |
| ΔFuel prices† | −0.035*** (−2.56) | 0.019 (1.41) | −0.091* (−1.90) | 0.008 (0.38) | −0.031 (−0.78) | −0.005 (−0.11) | 0.015 (0.63) | −0.006 (−0.31) |
| SARS outbreak 2003 | 0.011** (2.03) | 0.0005 (0.14) | −0.007 (−0.51) | 0.004 (0.67) | 0.011 (1.22) | 0.007 (0.17) | 0.007 (1.38) | 0.008 (1.54) |
| Global financial crisis 2008 | −0.003 (−0.54) | −0.005 (−0.86) | −0.042*** (−4.11) | −0.006 (−1.31) | −0.024** (−2.49) | 0.027 (1.22) | −0.017*** (−3.52) | −0.019*** (−3.23) |
|
Christchurch earthquakes 2011/12 |
−0.002 (−0.31) |
−0.019*** (−4.95) |
0.016 (1.19) |
−0.015*** (−3.71) |
−0.003 (−0.29) |
0.034 (1.18) |
−0.015 (−1.49) |
−0.007 (−1.41) |
| AR(1) | – | −0.642*** (−4.19) | −0.093 (−0.94) | 0.333 (0.46) | −0.312** (−2.43) | −0.024 (−0.18) | 0.415 (0.93) | −0.400*** (−2.96) |
| AR(2) | – | −0.663*** (−6.98) | – | −0.031 (−0.16) | 0.311*** (3.40) | 0.143 (1.16) | −0.024 (−0.22) | 0.329*** (3.95) |
| AR(3) | – | – | – | 0.052 (0.81) | – | 0.550*** (5.70) | −0.111 (−1.51) | – |
| AR(10) | −0.300*** (−5.02) | – | – | – | – | – | – | – |
| SAR(12) | 0.998*** (662.57) | 1.002*** (216.38) | 1.005*** (233.12) | 0.988*** (210.75) | 0.968*** (59.91) | 0.969*** (99.87) | 0.994*** (352.37) | 0.991*** (81.65) |
| MA(1) | −0.759*** (−17.07) | −0.220 (−1.51) | −0.671*** (−10.85) | −1.054 (−1.43) | −0.173 (−1.52) | −0.233 (−1.44) | −1.140** (−2.57) | −0.174 (−1.36) |
| MA(2) | – | – | – | 0.062 (0.09) | −0.810*** (−7.19) | −0.298* (−1.73) | 0.198 (0.47) | −0.795*** (−6.10) |
| MA(3) | – | −0.775*** (−7.94) | −0.197*** (−4.01) | – | – | −0.447*** (−3.03) | – | – |
| SMA(12) |
−0.914*** (−54.20) |
−0.724*** (−15.15) |
−0.821*** (−35.68) |
−0.518*** (−8.77) |
−0.587*** (−9.26) |
−0.816*** (−24.17) |
−0.839*** (−32.10) |
−0.465*** (−8.72) |
|
Variance Equation |
||||||||
| −0.052 (−0.91) | 0.195 (1.06) | 0.838*** (3.57) | 0.229 (1.58) | 0.493*** (3.65) | 0.309** (2.08) | 0.308*** (2.89) | 0.195** (2.56) | |
| −0.012 (−0.46) | −0.067 (−0.71) | −0.178 (−1.31) | −0.244** (−2.25) | −0.225** (−2.50) | −0.276*** (−2.80) | −0.239* (−1.84) | – | |
| −0.988*** (−37.06) | −0.668*** (−2.92) | 0.293** (2.24) | 0.484** (2.24) | −0.219 (−1.22) | 0.736*** (5.40) | 0.922*** (18.67) | 0.492*** (2.60) | |
| Adj-R2 | 0.95 | 0.93 | 0.38 | 0.95 | 0.75 | 0.69 | 0.87 | 0.91 |
| AIC | −2.85 | −1.95 | −0.32 | −1.76 | −0.94 | −0.68 | −1.45 | −2.10 |
| SIC | −2.60 | −1.67 | −0.06 | −1.47 | −0.66 | −0.37 | −1.15 | −1.84 |
| RMSE | 0.06 | 0.11 | 0.33 | 0.21 | 0.21 | 0.39 | 0.20 | 0.19 |
| MAE | 0.05 | 0.08 | 0.26 | 0.15 | 0.16 | 0.30 | 0.14 | 0.16 |
| MAPE (%) | 0.46 | 1.03 | 3.03 | 1.91 | 1.73 | 3.61 | 1.49 | 1.68 |
Remarks: The dependent variable is ln(visitor arrivals by air transport). The explanatory variables transformed into logarithmic form should be interpreted as growth in the variable. *, ** and *** indicate that the explanatory variable is significant at the 0.10, 0.05 and 0.01 significance level, respectively. t-statistics are printed in parentheses. The AR and MA terms included in the SARIMAX model aim to capture the autoregressive and moving average relationships in the tourism time series data. † indicates that the coefficients of the trend and fuel variables were multiplied by 100 for ease of presentation. Constant was included in regression analysis but has not been reported for space limitations.