Univariate Analysis of Seasonal Variations in Building Approvals for New Houses: Evidence from Australia

1
Dr. Harry M. Karamujic
Univariate Analysis of Seasonal Variations in
Building Approvals for New Houses Evidence from
Australia
2
Objectives

• The paper examines the impact of seasonal
  influences on Australian housing approvals,
  represented by the State of Victoria (Australia)
  building approvals for new houses (BANHs).
• The paper focuses on BANHs as they are seen as a
  leading indicator of investment and as such the
  general level of economic activity and employment
  .
• In particular, the paper seeks to cast some
  additional light on modelling the seasonal
  behaviour of BANHs by (i) establishing the
  presence, or otherwise, of seasonality in
  Victorian BANHs (ii) if present, ascertaining
  weather it is deterministic or stochastic (iii)
  determining out of sample forecasting
  capabilities of the considered modelling
  specifications and (iv) speculating on possible
  interpretation of results.

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BANHs

• BANHs denote a number of new houses building work
  approved. According to the ABS, statistics of
  building work approved are compiled from
• - permits issued by local government authorities
  and other principal certifying authorities, and
• - contracts let or day labour work authorised by
  commonwealth, state, semi-government and local
  government authorities.
• In Australia, a new house (a building which
  previously did not exist) is defined as the
  construction of a detached building that is
  primarily used for long term residential
  purposes. From July 1990, the statistics includes
  all approved new residential building valued at
  10,000 or more.

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Seasonality

• The focus of this study is not on modelling the
  behaviour of time series in terms of explanatory
  variables (the conventional modelling approach).
  Instead, this study uses a univariate structural
  time series modelling approach (allows modelling
  both stochastic and deterministic trend and
  seasonality) and as such shows that conventional
  assumptions of deterministic trend and
  seasonality are not always applicable.
• The conventional modelling approach assumes that
  the behaviour of the trend and seasonality can be
  effectively captured by a conventional
  regression equation that assumes deterministic
  trend and seasonality.
• The paper utilises a basic structural time series
  model of Harwey (1989). Compared to the
  conventional procedure, Harveys (1989)
  structural time series model involves an explicit
  modelling of seasonality as an unobserved
  component.

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Methodology
- Within a structural time series approach, the
term structural implies that a time series (in
this paper, BANHs) is observed as a set of
components not observable directly. The approach
allows the selected time series, including
intervention variables, to be modelled
simultaneously with the unobserved components.
The intention is to decompose the selected time
series in terms of its respective components and
to understand how these components relate to the
underlying forces that shape its evolution.-
The empirical analysis uses the model as
presented in Harvey (1985, 1990), whereby time
series are modelled in terms of their components.
The model can be written as rt µt ?t
et (1)where rt represents the actual value of
the series at time t, µt is the trend component
of the series, ?t is the seasonal component and
et is the irregular component (assumed to be
white noise).
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Methodology
- The major reason for selecting the structural
time series modeling approach is that it allows
for both stochastic and deterministic seasonality
. - Conventional dynamic modeling with a
deterministic seasonality approach totally
ignores the likely possibility of stochastic
seasonality (manifested as changing seasonal
factors over the sample period). - Evidently, a
problem with the conventional procedure is that
deterministic seasonality is imposed as a
constraint, when in fact it should be a testable
hypothesis .
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Results and Discussion

• The structural time series model represented by
  (1) is applied to seasonally unadjusted monthly
  BANHs data for Victoria, between 200006 and
  200905.
• The data have been sourced from the Australian
  Bureau of Statistics. For consistency, the sample
  for each variable is standardised to start with
  the first available July observation and end with
  the latest available June observation.
• As shown in Table 1, The paper considers the
  following three modelling specifications
• - Model 1 (Stochastic Trend and Stochastic
  Seasonality)
• - Model 2 (Stochastic Trend and Deterministic
  Seasonality)
• - Model 3 (Deterministic Trend and Deterministic
  Seasonality)

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Results and Discussion Table 1Estimated
Coefficients of Final State Vector
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Results and Discussion

• With respect to the goodness of fit, all models
  are relativelly well defined.
• Overall, the diagnostic tests are also
  predominately passed. The only exception is the
  test for serial correlation (Q), for the Model
  two (which is slightly above the statistically
  acceptable level) and Model three (significantly
  above the statistically acceptable level). The Q
  statistics for Model three indicate that the
  model suffers from serial correlation, implying a
  misspecified model. In all cases the slope is
  insignificant and the level is significant.
• As shown in Table 1, out of three modelling
  specifications, Model two has the highest R2s and
  lowest e. On the other hand, Model three
  (deterministic trend and deterministic
  seasonality) with negative R2s implies that the
  model is badly determined i.e. the model is worst
  then a seasonal random walk model.
• Overall, all of goodness of fit measures imply
  that Model three is significantly inferior to
  Models one and two, and that Model two is
  somewhat better then Model one.

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Results and Discussion
Figure 1 Model 1 - Seasonal Component
Figure 2 Model 2 - Seasonal Component
Figure 3 Model 3 - Seasonal Component
Figure 4 Individual Seasonals
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Results and Discussion

• Figures 1, 2 and 3 provide a visual
  interpretation of the seasonal elements for each
  considered modeling specification. The seasonal
  components evidenced in each of the figures show
  a constant repetitive pattern over the sample
  period, providing an additional evidence of the
  deterministic nature of the seasonal component
  (fixed seasonal components) in the number of new
  dwellings approved in Victoria.
• Figure 4 shows this even more clearly with
  individual monthly seasonals represented by
  horizontal lines, implying an unchanging seasonal
  effect across the whole sample period.
• In summary, the analysis points out that the
  behaviour of BANHs exhibits stochastic trend and
  deterministic seasonality. As a result, any
  regression model based on assumptions of
  deterministic trend and seasonality is bound to
  be misspecified

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Results and Discussion

• Consequently, the interpretation of the modeling
  results focuses on the Model two. Out of the
  eleven seasonal factors relating to the Model
  two, presented in Table 1, factors corresponding
  to June, April, December and November are found
  to be significant at 5 level.
• A possible explanation for the observed
  statistically significant reduction in BANHs
  during December and November is the reduction of
  the level of activity caused by the summer
  holidays season. (The summer holidays season
  typically covers the period from the second half
  of November to the end of January. It is the
  period of summer school holiday, several
  public/religious holidays and the time when most
  people take annual leaves.
• On the other hand season-related increases
  during June and April may be explained by a spike
  in the level of activity during the end of
  financial year season and preparation for a
  surge in contraction activity during the spring
  season (The end of financial year season
  typically starts by the end of April or the
  beginning of May, and finishes at the end of the
  first week in July.)

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Conclusion

• The modeling focus has been to (i) establishing
  the presence, or otherwise, of seasonality in
  Victorian BANHs, (ii) if present, ascertaining is
  it deterministic or stochastic, (iii) determining
  out of sample forecasting capabilities of the
  considered models and (iv) speculating on
  possible interpretation of results.
• This is done by estimating three modelling
  specifications comprised of stochastic and
  deterministic trend and seasonal components. The
  goodness of fit measures and the diagnostic test
  statistics indicate that Model two, which is
  comprised out of stochastic trend and
  deterministic seasonality, is superior to the
  other two specifications. Furthermore, the
  analysis of the three presented modelling
  specifications evidently indicates that the
  conventional modelling approach, characterised by
  assumptions of deterministic trend and
  deterministic seasonality, would not identify
  seasonal behaviour of time series characterised
  by stochastic trend and/or seasonality.

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Conclusion

• The examination of the out-of-sample forecasting
  power of the three models clearly shows that the
  seasonality apparent in the actual data is well
  picked up by specifications entailing
  deterministic seasonal factor, corroborating the
  earlier finding that the seasonal pattern in the
  number of dwelling units approved in Victoria is
  deterministic and not stochastic.
• Finally, the analysis of Model two points out
  that the behaviour of BANHs exhibits
  statistically significant seasonal components. A
  possible explanation for the observed
  statistically significant reduction in BANHs
  during December and November is the reduction
  of the level of activity caused by approaching to
  the summer holidays season, while the
  season-related increases during June and April
  may be explained by a spike in the level of
  activity during the end of financial year
  season and preparation for a surge in contraction
  activity during the spring season.

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Questions