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Dr. Harry M. Karamujic. Univariate Analysis of Seasonal Variations in Building Approvals for New Houses: Evidence from Australia. Objectives.
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Dr. Harry M. Karamujic Univariate Analysis of Seasonal Variations in Building Approvals for New Houses: Evidence from Australia
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, ascertainingweather it isdeterministic or stochastic; (iii) determining out of sample forecasting capabilities of the considered modelling specifications; and (iv) speculating on possible interpretation of results.
BANHs • BANHs denote a number of new housesbuilding 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.
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, Harvey’s (1989) structural time series model involves an explicit modelling of seasonality as an unobserved component.
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 + γt + εt (1)where rt represents the actual value of the series at time t, µt is the trend component of the series, γt is the seasonal component and εt is the irregular component (assumed to be ‘white noise’).
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 sampleperiod). - 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 .
Results and Discussion • The structural time series model represented by (1) is applied to seasonally unadjusted monthly BANHs data for Victoria, between 2000:06 and 2009:05. • 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)
Results and Discussion Table 1:Estimated Coefficients of Final State Vector
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 ε. 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.
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
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
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.)
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.
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.
