THE SEASONALITY OF TRANSACTIONS AND REAL ESTATE CYCLE The case of the city of Bordeaux Benoit FAYE and Eric LE FUR INSEEC Business Schools June

Litterature : a topic little explored In France : Annual bulletin of INSEE presents the seasonal variations of prices according to the type of goods (apartment / house) and the type of region (Paris/ Province) ( BEAUVOIS (2004, 2006)) In the USA : The sub-annual variations are presented either with the internal migrations ( ROSEN ( 1979 ), WHEATON ( 1990 ), GOODMAN (1993), TUCKER, LONG and MARX (1995) ) either with financial markets ( KRAINER (2000), ORTALO-MAGNE and RADY (2005), ROSENTHAL (2006) ) In the research in real estate economy or in urban economy Studies of long cycles analyze trends by neglecting generaly seasonality of the series ( FRIGGIT (2001a, 2003b), GRANELLE (1998), LAFERRÈRE and DUBUJET (2003) ) Studies of sub-annual cycles analyze seasonality by elimining trends in series ( FRIGGIT (2006), NGAI and TENREYRO (2008 )) By consequence, it isn’t exist studies showing the link between the seasonality and the movements of market on the long term

Interests and risks of the negligence of the seasonality Seasonal movements are often considered as negligible Series of medians of price per square meter

Quarterly growth rate of prices in Bordeaux on 85 quarters between and Quarterly growth rate of prices in the province (INSEE, 2004) Using a nonlinear regression (polynomial) is common MED PM² = 321,045+30,076 t - 0,842 t² +8,409E-03 t3 (R²=0,986). However, the heteroscedasticity resulting from a real seasonality makes doubtful the use of such a modeling approach.

We use a modeling of SARIMA by the method of BOX and JENKINS. This using permits us to identify an underlying model ARIMA (0, 2, 1) with a seasonal component (0, 2, 1). However, tests of normality of residue are doubtful and suggest the possibility of heteroscedasticity. In other words, the model could admit structural modifications, so under periods with differential fluctuations. StatisticDDLValuep-value Jarque-Bera23,1910,203 Box-Pierce36,6330,085 Ljung-Box36,9450,074 Box-Pierce414,6370,006 Ljung-Box415,5510,004 Stability tests on the residuals of the model

Research question and working assumptions This paper tries to identify the existence of links between the seasonality of transaction prices and the cycle of the residential market Two assumptions are successively posed H1: the residential market knows seasonality with characteristics which are disturbed by the cyclical movements H2: disturbance of the seasonality doesn’t result of a modification of the transactions structure during the time.

Our database We use the database registered by the notarial network since This database notifies sales of residential goods (except social housing and new construction) This database presents two principal characteristics: representativeness : the number of registered transactions is very high representing a very strong cover rate. limited information: the number of considered variables by the database is weak in regard other databases available in France.

Characteristics of Bordeaux cycle

Our methodology Identification of phases of cycle (Test of CHOW) Choice of a reference period (most little number of quarters presenting a stable seasonality) Calculation (from ti to ti+20) of the FAC for each sequence of 20 quarters (show of correlation coefficients for gaps of 1, 2, 3 and 4 quarters) N = 20

Results A1 A2 Breaking 1Breaking 2 Phase 1Phase 2Phase 3 D4 medium amplitude D4 weak amplitude D4 high amplitude

Each type of surface presents a different seasonality Gap ,2520,1940,2190,2460,3400,2710,2800, ,0270,2570,2290,2390,2820,2420,2240,126 During the 20 last years, the structure of the transactions by type of surface had changed with a strong growth of change of goods from 60 to 120 m². It’s evident that the previous observations originate in part of a structure effect. This situation imposes the verification of the previous behaviors of the series by type of surface.

Series of medians of price per square meter by striates of surface [0-30[ [ 30-60[[60-90[[90-120[ [ [ [ [[ [ [ 400-max[

Observation of the link between rupture of trend and arrhythmia of seasonality By withdrawing the surface 400 m², the relationship between rupture of trend and arrhythmia length is linear.

Evaluation of the link between the arrhythmia and trend rupture

Conclusions Finally, several interesting observations emerge from our study: On the one hand, for the whole of transactions, two observations: Firstly, the amplitude of the seasonality declines with the growth rate of prices. Secondly, we have showed that the seasonality of the residential market of Bordeaux city was a real phenomenon but disturbed. On the other hand, for the whole of transactions and more precisely for the surfaces situated between 60 and 120 m², two observations are important. Firstly, the amplitude of the seasonality is linked to the growth rate of the market. Secondly, each rupture of price trend implies an arrhythmia period with a length which is proportional to the importance of the rupture.

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