Air Passenger Forecasts Methodology

Method

Air4casts employs a sophisticated range of forecasting techniques. Monthly data for each airport is analyzed within custom software and is rechecked in two serious and commercially available forecasting packages.

Demand Side Based

The online forecasts are entirely demand side dependent.

There is no doubt that the system would benefit from supply side inclusion which, at the most basic level, would comprise airports capital formation plans and the expected effects of those on passenger capacity.

The difficulty lies in the availability and quality of airport expansion plans which are in the public domain:

◊ many airports, but not the majority, have published well cast and quantified investment project information but because

◊ the majority have not, it would not be sensible or appropriate to modify forecasts on an eclectic basis; supply side forecasting input can only work if it is capable of uniform application either to limit demand growth or to support it.

Summary for the Non-Technical

This section will not necessarily be of use to all, indeed it is not designed to be; but there are three central issues which are relevant to all:
◊ the forecasting is systematic
◊ there is no intervention, no adjusting of "awkward" results
◊ providing the capability for rational error estimation.

Further, this form of analysis lends itself exceptionally well to analysis of airport passenger trends after 9/11. It plays a vital role in interpreting data which is seen to be the result of external factors which are interruptive.

It does not postulate a workable relationship between national gross domestic product and air passenger numbers; the case against is explored separately.

Analysis Base

Most time series can be described in terms of three components:
◊ trend
◊ seasonal pattern and
◊ random fluctuation

Because of this the basis of the analysis is ARIMA [see Box & Jenkins] which allows the use of auto correlation, partial correlation and moving average techniques.

There are two ARIMA models in use:

Autoregressive Moving Average Model
combining:
◊ a linear combination of prior observations and
◊ a random error component

This can be summarized in the equation:

In descriptive terms the series relates:
◊ random shocks, the unexplained element within any time series and
◊ a linear combination of prior random shocks.

Moving Average Model

This can be summarized in a second equation:

By contrast the description for this series is:
◊ random shocks plus
◊ a linear combination of past random shocks.

ARIMA

Combines the two processes, indeed, the original and seminal work for this approach used as its base post war international air passenger statistics.

ARIMA explores the enigmatic duality of the two expressions through inverting the two equations into a single expression but with different conditions. It uses the three parameters of:
◊ autoregressive parameters [P]
◊ number of passes [D]
◊ moving average parameters [Q].

There are two stages within the modeling.

Identification

The input series, a given variable from a given airport, needs to be stable over time for the analysis to function: its mean, variance and autocorrelation co-efficient must be stationary over the time series and to accomplish this the data will have to be differenced; log transformation and the number of passes [D].

The number of parameters [P] and[Q] is set.

Estimation

Parameters are estimated using function minimization procedures. This means that within the time series the squared variances in the random or residual components are minimized.

These best fit parameters are used in forecasting and in determining future confidence limits around those forecasts.

Future Trends

The trend spread moves through a range which is defined from:
◊ exponential to
◊ linear and then to
◊ damped.

In short term forecasting an exponential outcome is not extraordinary. It occurred, for example, when air passenger numbers were “recovering” from the external shock of 9/11. It occurred in the case of Indian airports for a while.

In the medium to long term an exponential series is less likely to exist; in real terms it would be difficult for it to be maintained.

Interruptions

There is, especially now, a need to know not just how external events have affected passenger numbers but how that effect will carry forward through time. There are three types of interruption:
◊ permanent abrupt
◊ permanent gradual
◊ abrupt temporary.

In order better to interpret events two types of analysis are employed:
◊ Seasonal Decomposition (Census 1)
◊ Spectrum Analysis (Fast Fourier)

Seasonal Decomposition allows data to be broken into four components:
◊ trend [T]
◊ seasonal component [S]
◊ cyclical component [C]
◊ random component [R].

There are two seasonal possibilities:
◊ stable over time

Xt = TC1 + St + Rt

◊ growing over time

Xt = Tt * Ct * St * Rt

Both possibilities isolate the random element and allow the cyclical elements to be related to interruption recovery. They allow an important input into ARIMA and smoothing generally.

Spectrum Analysis looks simultaneously at the correlation between two series at different times.

Specifically GDP and passenger numbers are examined over different time spans to identify cycles but there is a difficulty in determining periodicity in GDP in the last quarter of the twentieth century. The question is whether the two are “in sync” but lagged by the cycle. GDP is not a useful input for the forecasting of air travel demand.

To fulfil the three stages in the work which are identification, estimation of parameters and forecasting, the analysis program is rerun with a forecast horizon of 350 months. The software makes 35 passes at each airport's data line to determine the best fit - die. the forecast which implies the lowest error spread.

Relative error is more informative than absolute error. There is also the application of interruption analysis whereby it is possible to quantify the effect of a given specific event; a major decline in air passenger numbers, for example.

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