LAX Average Domestic Airfares Report 1995 - 2012
PURPOSE STATEMENT
Airlines are an increasingly competitive industry – with budget airlines emerging around the world
competing for the leisure and business traveller. It is clear that airfares are affected by increasing
competition and keeping prices low. As well, the last twenty years has seen the world economy falter in
various places around the world effecting travelling numbers. The American Economy in the last ten years
has been particularly volatile. As well air fuel prices have also been volatile with a steep rise for much of
the first decade of the 21st century.
The purpose of my investigation will be to track the average domestic airfares at LAX airport for 1995 to
2012. I will see if there are any seasonal trends and identify the long term trend. As well I will use HoltWinters to make further predictions and make a judgement on whether these predictions would be
accurate and reliable.
I would also like to extend my investigation and see if average airfares can be related to the general
economy by looking at GDP figures over the time period considered. As well, I will compare these values to
inflation generally. Finally I will look at the impact of oil prices on the airfares and see whether this could
be a factor.
TRENDS
Time series plot for LAX
420
400
380
360
340
320
300
280
1995
2000
2005
2010
The above graph shows the average domestic airfares at LAX (Los Angeles Airport) from 1995 to 2012. The
redline is the trend line and the black line is the raw data.
The long term trend of average airfares are increasing over the period. However there are fluctuations with this
trend. There is a period of growth between 1997 to 2001. Then average domestic airfares form LAX decrease in
2002 and the downward trend continues until 2005. After 2005 where there is a period of increasing growth until
2009. In 2009 there is a sharp fall in average airfare prices. In 2010 to 2012 there is another period of growth. Over
the time period shown there are many changes in trend. However, the average price at LAX has increased from
about $305 to about $400. This has an average increase per year of about $6 per year which is a small rise for the
time period give.
SEASONAL TRENDS IN AVERAGE DOMESTIC AIRFARES
Estimated seasonal effects
400
2011
4
420
Seasonal plot for LAX
2
380
2008
2007
2011
2012
2005
2004
280
300
1998
1995
1996
0
2001
2004
1997
1995
-4
2005
2002
2003
1999
1998
-2
2006
2000
2009
2001
2002
2010
2000
2007
2003
2006
1999
2009
1996
-6
320
340
360
2010
2008
1997
Jan - Mar
Apr - Jun
Jul - Sep
Quarter
Oct - Dec
Jan - Mar
Apr - Jun
Jul - Sep
Oct - Dec
Quarter
The average seasonal effect has the highest fares in the April to Jun period followed by the Oct-Dec period and the
July-Sept period. The lowest fares tend to be in the Jan-March Quarter. These trends are not always consistent as
shown by the seasonal plot and are very inconsistent. However, when averaged there are differences between the
quarters. The inconsistent and random seasonal plot indicates that the seasonality in the data is not a major factor.
However the differences between seasons are quite small compared to the overall average airfares and the overall
variation. As shown in the table below it only accounts for about 7% of the overall variation.
Data Title
Min
Max
Range
Raw Data
Trend
Seasonal
Residual
280
270
-5
-18
420
380
5
20
140
110
10
38
Approx %
Contribution
79%
7%
As shown in the seasonal aspect of airfares accounts for only approximately 7% of the total variation in
airfares. This means that most of the variation in the average airfares is accounted for by the trend in the
data presented (approximately 79%). This does mean that there is a significant amount of variation that
cannot be explained by the trend or the seasons. This is shown by the residuals. This kind of variation is not
predictable or systematic.
RESIDUALS
As well unexplained variation as shown by the residuals is a significant factor in some cases. The residual
can be as high as 20 which are about 14% of the total variation. This means some of the residuals are
significant being more than 10%. This means we may not have full confidence in our model and the
predictions we make from it. As well, the trend is not linear and does not seem to follow a regular
mathematical curve and making predictions for future years may not be appropriate. This is further
evidenced by the huge range in our interval of predicted values.
Decomposition of data: LAX
Trend
Raw data
400
350
300
Seasonal
30
20
10
0
-10
-20
15
5
-5
Residuals
1995
2000
2005
2010
To summarise the average airfares have a reasonably small seasonal component and most of the variation
is explained by the trend. The residuals are significant in some cases and this would indicate that it may be
hard to predict future average airfares at LAX with the Holt-Winters model.
There does not seem to be a pattern of residuals . Throughout the period shown there does not seem to be
a period of increased uncertainty. However, many of the residuals are significant indicating that the model
and the predictions that stem from them.
PREDICTIONS
The following is the predictions of number values for Q3 2012 –Q4 2014 in table and graph form.
fitted lower 95% bound upper 95% bound
2012 Q3 416.1906
385.4838
446.8974
2012 Q4 416.5274
378.1195
454.9353
2013 Q1 398.0637
352.6647
443.4628
2013 Q2 425.3483
373.3558
477.3407
2013 Q3 424.7154
363.0502
486.3806
2013 Q4 425.0521
357.4880
492.6163
2014 Q1 406.5885
333.1638
480.0133
2014 Q2 433.8730
354.6014
513.1447
Holt-Winters prediction for LAX
Raw data
Fitted
Prediction
500
450
400
350
300
1995
2000
2005
2010
Time
The predictions show that the model suggests that there will be growth in 2013 and 2014 with airfares
increasing to around $425. However, the interval given around these predicted values is large which is
evidence that the confidence in the predictions may be low.
The fitted data shown in green in the above graph does not always fit well with the raw data again giving
further evidence that our model may not be able to accurately predict future domestic average airfares at
LAX. Our forecasts are therefore not that reliable and we do not have full confidence in them.
RELATING TO OTHER VARIABLES
The GDP graph above shows similar trends to our time series graph. There is a period of decreasing
growth rates in 2001 and 2002 where growth becomes close to zero. There is a sharp decline in 2008 and
2009 where the US economy has negative growth . These are also reflected in our time series graph of
average airfares. The periods where there is a decrease in average airfares is in 2001 – 2003 and a very
sharp fall in 2009 and 2010.
The inflation rate for the US economy also has periods of less inflation around the 2001 and 2002 mark and
a fall in prices in 2009. This is again mirrored by the average airfare prices at LAX.
All of this does show that the average airfare prices are affected by the greater American Economy.
Oil Prices.
Oil prices are often reported as a reason that airfares increase or otherwise – below is a graph showing oil prices.
Again the oil prices reflect the us economy and the airfares at LAX with the periods where there is decreasing
average airfares. The two notable periods being 2001 – 2002 and the sharp decline in 2009. The increase in oil prices
does also correspond with increasing domestic airfares.
SUMMARY
Average domestic airfares at LAX have generally increased in the period 1990 to 2012. However, like the
factors that contribute to airfare prices: oil costs, inflation, us economy there is volatility in the price of
domestic airfares. The rise in airfares is reasonably small about 2% per year and it would be an interesting
exercise to see if the increase in airfares is less than other consumer goods or travel products.
Seasonality in average domestic airfares at LAX seems to be a minor factor as the seasons only change the
airfares by on average a few dollars. Most of the variation in our time series was from the long term trend.
However, the residuals can be significant in our data – meaning the variation cannot be fully explained.
The Holt-Winters model and the predictions we have made may not be reliable as our long term trend is
very volatile and does not have a clear pattern.
The other graphs in this report of GDP, inflation and Oil prices do have similar trends at similar times
reflecting their interdependence between these factors.
Overall, the Average Domestic Airfares at LAX are difficult to model and predict from. Continued
uncertainty seems assured.