A Report to the Arizona Department of Transportation

Forecast and Capacity Planning for Nogales' Ports of Entry

8 Forecasts

Once the forecasting models were built and validated using the available data, the next step was to use these models to provide forecasts of border crossings for the next 5, 10 and 15 years. However, given the unstable economic conditions at the time the models were built and the data was collected, instead of giving a single estimate for each of these time periods into the future it was decided to prepare multiple forecasts based on different scenarios.

For instance, during the model building stage, it was found that the Mexican Peso to US Dollar Exchange rate and the US Index of Industrial Production (IIP) significantly influenced border crossing traffic, especially commercial vehicle crossings. Thus, we first analyzed the trend scenarios of these two indices. Based on these scenarios we developed forecasts for border crossings for the different modes of traffic. In the following sections we provide forecasts for four modes of traffic: commercial vehicles, Privately Owned Vehicle (POV) pedestrians and Bus. For each mode, we provide a 5-year, 10-year and 15-year traffic forecast.

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8.1 Forecasts for Commercial Vehicles

Overview of Exchange Rate and Index of Industrial Production(IIP)

The historical data for the exchange rate (If we don't indicate specifically, the exchange rate means the exchange rate between US Dollar and Mexican Peso, represented by the value of 1 US Dollar in Pesos ) and US IIP(Index of Industrial Production) are available from the Federal Reserve Board. Various companies provide forecasts of these two indices, but most of these forecasts are only for a horizon of 36 months. We obtained the 36-month forecasts from the organization forecasts.org, and we call these forecasts the external forecasts. Since our intention was to give 5-year, 10-year and 15-year forecasts, we used forecast models in combination with these external forecasts. In cases where there was no external forecast available, we used only our own forecast. Due to the complexity of the forecast, we did not have a perfect forecast of these indices. What our forecasts did was to capture the general trend of the indices. We used simple regression for the 5 and 10 year forecast and used piecewise linear regression for the 15-year forecast. In the development of our forecasts, we considered different scenarios by assuming different trends of the underlying forecasting regressors (USIIP and Exchange rate). To begin we first reviewed the historical trends of the exchange rate and US IIP data. Figure 8-1 and Figure 8-2 plot the historical data (beginning March 2003) and the 36 month forecast (beginning May 2009) of the Exchange Rate and US IIP respectively, both of which were obtained from the organization forecasts.org. Figure 8-3 and Figure 8-4 show the data for a longer time span, where all available historical data was included and the forecasted data was excluded.

Considering that there was a devaluation of the Mexican Peso in late 1994 (Joseph A. Whitt 1996), we used the data starting from January 1995 to estimate the long term trend for the Exchange Rate. Also, because another significant devaluation of the Mexican Peso occurred during late 2008/early 2009, the trend of the Exchange Rate beginning in 1995 provided insightful information for the trend of the Exchange Rate after 2008/2009. The US IIP data, with its history dating back to 1919, provided relatively better historical records for estimating the future trends, especially for those trends occurring after recessions.

Figure 8-1 Mexican Peso to US Dollar Exchange Rate Forecast: Past Trend & Future Projection (forecasts.org)

Figure 8-2 U.S. Industrial Production Index Forecast: Past Trend & Future Projection (forecasts.org)

Figure 8-3 Mexican Peso to US Dollar Exchange Rate Historical Trend (Federal Reserve)

Figure 8-4 Historical data of U.S. Industrial Production Index (Federal Reserve)

Five-Year forecast

In order to estimate the 5 year trend of the exchange rate, we divided the historical data into groups of five-year length segments, and fitted those segments separately. We plotted the segmented data as shown in Figure 8-5. From this figure, we can tell that there are different possible trends for a 5 year time span, as shown by line segments 1, 2 and 3 which have very different slopes. For instance, segment 3 is almost a horizontal line, suggesting a very stable exchange rate. A similar situation occurred with the IIP data, which is shown in Figure 8-6, i.e., different 5-year segments resulted in significantly different trends.

In order to develop different forecast scenarios we chose different combinations of the exchange rate and the IIP trends as input to the models to obtain different forecasts of traffic. We defined different trends for the two indices (or variables) as shown in Table 8-1. There were 9 different combinations in total. For notation simplicity, we assigned each possible trend combination a two digit code, where the first digit represented the trend of the exchange rate and the second one represented the trend of US IIP. For example, the code 31 meant forecasts using "Staying relatively stable" for exchange rate and "Growing fast" for the US IIP. Figure 8-7 shows all the 9 different combinations of the future Exchange Rate and US IIP graphically. Figure 8-8 shows the forecasts of all the different scenarios graphically. Here the X axis represents the time and the Y axis represents the number of trucks crossing the border. Figure 8-9 aggregates the results to yearly level. The solid blue lines in Figure 8-8 are the forecasted values while the red dash lines represent one-standard deviation intervals. Note that all the scenarios have the same result for the first three years because they all used the same 36 months forecasts of the two indices from forecasts.org.

Figure 8-5 Historical Exchange Rate data with external forecast (5 year segments)

Figure 8-6 Historical data of US IIP with forecast from forecasts.org (5-year segments)

Figure 8-7 Different scenarios of Exchange Rate and US IIP

Figure 8-8 Forecasts under different scenarios; solid blue line: the forecast, dashed red lines: one time standard deviation interval

Figure 8-9 Yearly aggregation of the 5-year truck crossings forecast

Table 8-2 shows the percentage of increase of commercial vehicle crossings compared to the number of crossings in 2008. We can see the increment will be between 7.7% and 17.6%, based on the different trends of the exchange rate and the change of US IIP. The biggest increase will happen if the Exchange rate stays relatively stable and the US IIP grows fast. Comparing Table 8-2 by columns, we can tell that for the same trend of Exchange Rate, a "growing fast" trend of US IIP renders the largest increase of truck crossings. We can also conclude that for the same US IIP trend, a stable trend of Exchange Rate results in the biggest increase of truck crossings. Ten-Year forecast

For the ten-year forecast, we applied a similar procedure. When examining the trend of the Exchange Rate over a ten-year time span, we found that it was unlikely to be stable, as can be seen in Figure 8-10. Therefore, we only prepared two scenarios for the Exchange Rate, "growing fast" and "growing mildly". Figure 8-11 shows all the 10-year segments of the historical US IIP data. For the US IIP, historical data leads us to believe that all three possible trends could still occur during a 10-year time span, so we kept the same three US IIP scenarios as we did for the 5-year forecast. We used a similar coding method to that used in the five-year forecast to indicate the different scenario combinations. Table 8-3 lists all the scenarios we considered for the Exchange Rate and US IIP. Due to the long term uncertainty, we only give yearly forecasts as opposed to the monthly forecasts that were given in the 5-year forecast.

Figure 8-13 below shows the forecast of yearly commercial vehicle crossings under different scenarios and Table 8-4 shows the increase in number of crossings forecasted in 2019 when compared to those in 2008. From this table we can see that the ten year increase will be in the range of 18.8% and 32.9%. When comparing across columns, we can see that a "Growing mildly" trend of Exchange Rate renders a larger increase in the crossing of commercial vehicles. When comparing across rows, we can see that a "Growing fast" trend of US IIP renders a faster increase of the commercial vehicle crossings. Figure 8-13 depicts these differences graphically; here we can see the difference of increase is more significant among the scenarios with different US IIP trends. For the maximum growth of truck traffic, the US IIP should increase fast and the exchange rate kept relatively stable. For the minimum growth of truck traffic, the US IIP should stay relatively stable and the exchange rate grows fast.

Figure 8-10 Historical Exchange Rate data with external forecast (10-year segments)

Figure 8-11 Historical data of US IIP with forecast from forecasts.org (10-year segments)

Figure 8-12 Different scenarios of exchange rate and US IIP (10-year segments)

Figure 8-13 Yearly aggregation of the 10-year truck crossings forecast

Fifteen-Year forecast

For the fifteen year forecast we had to use a different approach to handle each of the scenarios for exchange rate changes because we only had 14 years of historical data available. Instead of separating the data into different segments and determining the speed of growth (stable, mild or fast), we used different forms of piecewise linear regression methods to build the scenarios. We used a package named "segmented" (Muggeo 2008) in the R system (R Development Core Team 2009) to locate the breakpoints. The two scenarios for Exchange rate are shown in Figure 8-14, where the blue lines indicates scenario 1 and the green lines indicates scenario 2. For the US IIP, we used a similar approach as the one used in 5-year and 10-year forecasts. Figure 8-15 shows the 15-year segments of the historical US IIP data. We categorized the trends into three different types as listed in Table 8-5.

Figure 8-16 shows all the possible combined scenarios of exchange rate and US IIP. Figure 8-17 shows the forecasted yearly truck crossings within a 15-year time span. The two vertical dash lines in Figure 8-17 mark the years 2014 and 2019. For this forecast, we focused on the data points after 2019. Table 8-6 shows the increase the yearly truck crossings for the year of 2024 compared to that of 2008. From this table we can see the increase will be between 29.1% and 47.2% in accordance with our various scenarios. When examining Figure 8-17, one can see that for forecasts with the same US IIP trend, the predicted forecasts over the 15-year time span will be very close. In long term, the US IIP may play a more important role than the exchange rate in influencing border crossing traffic. A fast growing US IIP trend Is the scenario associated with the fastest growth in truck traffic.

Figure 8-14 Different segment methods for Exchange Rate

Figure 8-15 Historical data of US IIP with forecast from forecasts.org (15-year segments)

Figure 8-16 Different scenarios of exchange rate and US IIP

Figure 8-17 Yearly crossing forecasts of different scenarios

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8.2 Forecast for the POV

As we stated previously, we used the time series model to produce the five-year forecast and used the regression model to produce the extended forecasts.

Figure 8-18 depicts the five-year forecast of POV crossing, which mainly is an extension of the decreasing trend of segment 3 in Figure 7-5. Considering the recession started in late 2007, this forecast seemed reasonable. However, we were not sure what the trend would be after the economy recovers from the recession. Segment 1 in Figure 7-5 shows the trend of POV crossings after the 1994 Mexican Peso crisis, which was increasing until "9/11" happened.

Figure 8-19 depicts the forecast for 10 years and 15 years, where we assumed the POV traffic would start to recover after the current recession is over. Extra attention should be paid to the turning point marked by the red dashed circle around 2014. Although it was drawn around 2014, it was meant to suggest that the turning point will occur when the economy recovers from the recession, which will happen at an unknown point of time into the future. The two scenarios in Figure 8-19 were based on the trends of segment 1 and segment 2 in Figure 7-5 respectively. They showed a significant difference in long run. Table 8-7 shows the forecasted POV crossing under these two scenarios. When comparing the highest previous crossing level, which was 2000, scenario 1 was equal to the previous high, while scenario 2 slightly exceeded it.

Figure 8-18 Five Year forecast of the POV crossing

Figure 8-19 10 & 15-Year forecast of the POV crossing

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8.3 Forecast for pedestrian crossings

As we did for the POV data, we produced the 5-year forecast of the pedestrian traffic by ARIMA model and the extended forecast by the regression method. We used "Arizona Employment" as an external variable in the ARIMA model, thus we first produced a forecast of "Arizona Employment". We used a 2^nd order polynomial function to fit the "Arizona Employment", which is shown in Figure 8-20. Again, the forecast for "Arizona Employment" was not meant as an accurate forecast, but as an attempt to capture the main trend.

Figure 8-21 depicts our 5-year forecast of the pedestrian traffic, which was a monthly forecast. The overall trend was going down, which continued the trend of segment 4 in Figure 7-8. As we mentioned in previous section, we were unsure when the current recession would be over, thus we were not sure when the descending trend of the pedestrian crossings would end, since pedestrian crossings are very sensitive to economic climate changes.

Figure 8-20 Historical data and a 2-order polynomial fit

Figure 8-21 5-Year forecast of the pedestrian crossings

Figure 8-22 10 & 15-year forecast of pedestrian crossings

Figure 8-22 shows the 10 & 15-year forecasts of pedestrian crossings. Scenarios 1 to 3 correspond to the trend of segments 1 to 3 in Figure 7-8. The dashed red circle in Figure 8-22 indicated the end of the economic recession, which would occur at an undetermined point in time in the future. Table 8-8 shows the predicted yearly crossings of pedestrians in 10 & 15 years and how these compared to the number in 2008. In scenario 1, the 2019 crossing of pedestrian will be around 70% of 2008, while the other two scenarios will be about 135%. For 15 years, scenario 1 will be about 73% of 2008, scenario 2 will be 209% of 2008 and scenario 3 will be 191% of 2008. Scenarios 2 and 3 are very similar in long run, while both of them had a significant difference when compared to scenario 1. Both scenarios 2 and three predicted the increasing rate to be much faster than that of scenario 1.

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8.4 Forecast for Bus Passengers

We used the time series model we built in the model section to produce the five-year forecast, and used simple regression models to produce the extended forecast. The number of passengers between 2002 and 2007 increased much faster than other years, so we used the data from 2000 to 2007 to build one regression model, and used all the data to build another one. Thus, we have two scenarios for forecasts.

1. Scenario 1: Used all the data and the regression model had a slope of 88.54.
2. Scenario 2: Used data between 2002 and 2007, and the regression model had a slope of 155.6.

Note that when building the models, we numbered the time periods consecutively. For example, for the data between 2002 and 2007, we marked January 2002 as 1, February 2002 as 2, and so on.

All the forecasts were given at a yearly level. As we observed from the data there is a great deal of variability in the data so we think a monthly forecast is not likely to be useful.

Figure 8-23 shows the five year forecast of the bus passengers. According to the ARIMA model, bus traffic will stay relatively stable over the next few years if the current condition does not change. Figure 8-24 shows the yearly forecasts of the bus passengers. Similarly, the turning point circled by the dashed red circle was an imaginary point, which indicated the ending of the current recession. Table 8-9 shows the forecasted bus passengers of 2014, 2019 and 2024 respectively. Also, we compared the predicted number of crossings to the crossings of 2008. In both of the scenarios, the number of crossings will increase. However, the scenarios differ in terms of the increasing rate. For the 2019 and 2024 forecasts, we had two scenarios, which were based on the different regression models we described previously. The future increases will be higher if the factors influencing bus passenger traffic are similar to those between 2002 and 2007. However, the factors driving bus passenger traffic still should be subject to further study.

Figure 8-23 5-Year Forecast for the Bus passengers

Figure 8-24 10 & 15 Year forecasts for Bus passengers